Integer specifying the index of the current iteration of the bootstrap.

Number of time points to simulate.

Data table containing the observed data.

Vector of integers specifying the seeds. One seed is used to initialize each bootstrap iteration.

Character string specifying the "type" of the outcome. The possible "types" are: "survival", "continuous_eof", and "binary_eof".

List, whose elements are vectors of character strings. The kth vector in intvars specifies the name(s) of the variable(s) to be intervened on in each round of the simulation under the kth intervention in interventions.

List, whose elements are lists of vectors. Each list in interventions specifies a unique intervention on the relevant variable(s) in intvars. Each vector contains a function implementing a particular intervention on a single variable, optionally followed by one or more "intervention values" (i.e., integers used to specify the treatment regime).

List, whose elements are lists of vectors. The kth list in int_times corresponds to the kth intervention in interventions. Each vector specifies the time points in which the relevant intervention is applied on the corresponding variable in intvars. When an intervention is not applied, the simulated natural course value is used. By default, this argument is set so that all interventions are applied in all time points.

Integer denoting the intervention to be used as the reference for calculating the risk ratio and risk difference. 0 denotes the natural course, while subsequent integers denote user-specified interventions in the order that they are named in interventions.

List of vectors, where each vector contains information for one parameter used in the modeling of the time-varying covariates (e.g., model statement, family, link function, etc.). Each vector must be the same length as covnames and in the same order. If a parameter is not required for a certain covariate, it should be set to NA at that index.

Vector of character strings specifying the names of the time-varying covariates in obs_data.

Vector of character strings specifying the "type" of each time-varying covariate included in covnames. The possible "types" are: "binary", "normal", "categorical", "bounded normal", "zero-inflated normal", "truncated normal", "absorbing", "categorical time", and "custom".

Vector containing custom fit functions for time-varying covariates that do not fall within the pre-defined covariate types. It should be in the same order covnames. If a custom fit function is not required for a particular covariate (e.g., if the first covariate is of type "binary" but the second is of type "custom"), then that index should be set to NA.

Vector containing custom prediction functions for time-varying covariates that do not fall within the pre-defined covariate types. It should be in the same order as covnames. If a custom prediction function is not required for a particular covariate, then that index should be set to NA.

Vector of character strings specifying the names of baseline covariates in obs_data.

List of vectors. The kth vector specifies the names of the variables for which the kth history function in histories is to be applied.

List of length two. The first element is a numeric vector specifying the lags used in the model statements (e.g., if lag1_varname and lag2_varname were included in the model statements, this vector would be c(1,2)). The second element is a numeric vector specifying the lag averages used in the model statements.

Vector of history functions to apply to the variables specified in histvars.

Model statement for the outcome variable.

Function specifying a custom outcome model. See the vignette "Using Custom Outcome Models in gfoRmula" for details.

Function obtaining predictions from the custom outcome model specified in ymodel_fit_custom. See the vignette "Using Custom Outcome Models in gfoRmula" for details.

List of vectors. Each vector containins as its first entry a condition and its second entry an integer. When the condition is TRUE, the outcome variable is simulated according to the fitted model; when the condition is FALSE, the outcome variable takes on the value in the second entry.

List of vectors. Each vector containins as its first entry a condition and its second entry an integer. When the condition is TRUE, the competing event variable is simulated according to the fitted model; when the condition is FALSE, the competing event variable takes on the value in the second entry.

List of vectors. Each vector contains as its first entry a covariate for which a priori knowledge of its distribution is available; its second entry a condition under which no knowledge of its distribution is available and that must be TRUE for the distribution of that covariate given that condition to be estimated via a parametric model or other fitting procedure; its third entry a function for estimating the distribution of that covariate given the condition in the second entry is false such that a priori knowledge of the covariate distribution is available; and its fourth entry a value used by the function in the third entry. The default is NA.

Logical scalar indicating the presence of a competing event.

Model statement for the competing event variable.

Character string specifying the name of the time variable in obs_data.

Character string specifying the name of the outcome variable in obs_data.

Character string specifying the name of the competing event variable in obs_data.

List of vectors. Each vector contains the minimum and maximum values of one of the covariates in covnames.

Logical scalar indicating whether to parallelize simulations of different interventions to multiple cores.

Integer specifying the number of cores to use in parallel simulation.

A vector of one or more values denoting the maximum number of times a binary covariate representing a visit process may be missed before the individual is censored from the data (in the observed data) or a visit is forced (in the simulated data). Multiple values exist in the vector when the modeling of more than covariate is attached to a visit process. A value of NA should be provided when there is no visit process.

Logical scalar indicating whether the hazard ratio should be computed between two interventions.

List of two numbers indicating a pair of interventions to be compared by a hazard ratio. The default is NA, resulting in no hazard ratio calculation.

Logical scalar indicating whether to return the coefficients, standard errors, and variance-covariance matrices of the parameters of the fitted models in the bootstrap samples. The default is FALSE.

Number of subjects for whom to simulate data. By default, this argument is set equal to the number of subjects in obs_data.

Logical scalar for specifying the convention used for lagi and lag_cumavgi terms in the model statements when pre-baseline times are not included in obs_data and when the current time index, t, is such that t < i. If this argument is set to FALSE, the value of all lagi and lag_cumavgi terms in this context are set to 0 (for non-categorical covariates) or the reference level (for categorical covariates). If this argument is set to TRUE, the value of lagi and lag_cumavgi terms are set to their values at time 0. The default is FALSE.

Logical scalar indicating whether the observed data set contains rows for time t < 0.

Numeric scalar specifying lowest value of time t in the observed data set.

Logical scalar indicating whether to print a progress bar for the number of bootstrap samples completed in the R console. This argument is only applicable when parallel is set to FALSE and bootstrap samples are used (i.e., nsamples is set to a value greater than 0). The default is TRUE.

Progress bar R6 object. See progress_bar for further details.

Vector of logicals. The kth element is a logical specifying whether to carry forward the intervened value (rather than the natural value) of the treatment variables(s) when performing a carry forward restriction type for the kth intervention in interventions. When the kth element is set to FALSE, the natural value of the treatment variable(s) in the kth intervention in interventions will be carried forward. By default, this argument is set so that the intervened value of the treatment variable(s) is carried forward for all interventions.

Logical scalar indicating whether to truncate simulated covariates to their range in the observed data set. This argument is only applicable for covariates of type "normal", "bounded normal", "truncated normal", and "zero-inflated normal".

Other arguments

Matrix containing risks over time under the natural course and under each user-specific intervention.

Matrix containing risk ratios over time under the natural course and under each user-specific intervention.

Matrix containing risk differences over time under the natural course and under each user-specific intervention.

List of the coefficients of the fitted models. If the argument boot_diag is set to FALSE, a value of NA is given.

List of the standard errors of the coefficients of the fitted models. If the argument boot_diag is set to FALSE, a value of NA is given.

Data table containing the simulated data at time t.

Data table containing the simulated data at times before t.

List of vectors. Each vector contains as its first entry the covariate affected by the restriction; its second entry the condition that must be TRUE for the covariate to be modeled; its third entry a function that executes other specific actions based on the condition (in this case, this function); and its fourth entry some value used by the function (in this case, this entry is not used).

Character string specifying the name of the time variable in pool and newdf.

Integer specifying the current time index.

Logical scalar specifying whether to carry forward the intervened value (rather than the natural value) of the treatment variables(s) when performing a carry forward restriction type

A vector specifying the name(s) of the variable(s) to be intervened on.

Object of class "gformula".

Other arguments.

Character string specifying the name of the ID variable in obs_data.

Number of subjects for whom to simulate data.

List, whose elements are vectors of character strings. The kth vector in intvars specifies the name(s) of the variable(s) to be intervened on in each round of the simulation under the kth intervention in interventions.

List, whose elements are lists of vectors. Each list in interventions specifies a unique intervention on the relevant variable(s) in intvars. Each vector contains a function implementing a particular intervention on a single variable, optionally followed by one or more "intervention values" (i.e., integers used to specify the treatment regime).

List, whose elements are lists of vectors. The kth list in int_times corresponds to the kth intervention in interventions. Each vector specifies the time points in which the relevant intervention is applied on the corresponding variable in intvars. When an intervention is not applied, the simulated natural course value is used. By default, this argument is set so that all interventions are applied in all time points.

Vector of character strings, each describing an intervention.

Vector of character strings specifying the names of the time-varying covariates in obs_data.

Vector of character strings specifying the "type" of each time-varying covariate included in covnames. The possible "types" are: "binary", "normal", "categorical", "bounded normal", "zero-inflated normal", "truncated normal", "absorbing", "categorical time", and "custom".

Vector of character strings specifying the names of baseline covariates in obs_data.

List of vectors. The kth vector specifies the names of the variables for which the kth history function in histories is to be applied.

Vector of history functions to apply to the variables specified in histvars.

Model statement for the competing event variable.

Logical scalar indicating whether the hazard ratio should be calculated between two interventions.

List of two numbers indicating a pair of interventions to be compared by a hazard ratio. The default is NA, resulting in no hazard ratio calculation.

Number of time points to simulate.

Character string specifying the "type" of the outcome. The possible "types" are: "survival", "continuous_eof", and "binary_eof".

Character string specifying the name of the time variable in obs_data.

Data table containing the observed data.

Logical scalar indicating whether to parallelize simulations of different interventions to multiple cores.

Integer specifying the number of cores to use in parallel simulation.

Integer specifying the number of bootstrap samples to generate.

Logical scalar indicating whether to return the simulated data set. If bootstrap samples are used (i.e., nsamples is set to a value greater than 0), this argument must be set to FALSE.

Character string specifying the name of the outcome variable in obs_data.

Character string specifying the name of the competing event variable in obs_data.

Logical scalar indicating the presence of a competing event.

Logical scalar indicating the presence of a censoring variable in obs_data.

Character string specifying the name of the censoring variable in obs_data.

Vector of model statements for the time-varying covariates.

List of length 3. First element contains a vector of integers specifying the number of lags back for the lagged function. Second element contains a vector of integers indicating the number of lags back for the lagavg function. The last element is an indicator whether a cumavg term appears in any of the model statements.

Percentile by which to truncate inverse probability weights.

Cutoff value by which to truncate inverse probability weights.

Logical scalar indicating whether the "old" intervention convention was used (i.e., by specifying interventions, intvars, and int_times).

List of vectors, where each vector contains information for one parameter used in the modeling of the time-varying covariates (e.g., model statement, family, link function, etc.).

Vector of link functions.

Name of the covariate at index j.

Data on which the model is fit.

Integer specifying the index of the covariate.

Logical scalar indicating whether to return the fitted models. The default is FALSE.

List of vectors, where each vector contains information for one parameter used in the modeling of the time-varying covariates (e.g., model statement, family, link function, etc.).

Vector of link functions.

Vector of character strings specifying the names of the family functions to be used for fitting the GLM.

Data on which the model is fit.

Integer specifying the index of the covariate.

Logical scalar indicating whether to return the fitted models. The default is FALSE.

List of vectors, where each vector contains information for one parameter used in the modeling of the time-varying covariates (e.g., model statement, family, link function, etc.).

Data on which the model is fit.

Integer specifying the index of the covariate.

Logical scalar indicating whether to return the fitted models. The default is FALSE.

List of vectors, where each vector contains information for one parameter used in the modeling of the time-varying covariates (e.g., model statement, family, link function, etc.).

Data on which the model is fit.

Integer specifying the index of the covariate.

Logical scalar indicating whether to return the fitted models. The default is FALSE.

List of vectors, where each vector contains information for one parameter used in the modeling of the time-varying covariates (e.g., model statement, family, link function, etc.).

Vector of link functions.

Name of the covariate at index j.

Data on which the model is fit.

Integer specifying the index of the covariate.

Logical scalar indicating whether to return the fitted models. The default is FALSE.

Object of class "gformula_survival", "gformula_continuous_eof", or "gformula_binary_eof".

Vector of character strings specifying the names of the time-varying covariates to be plotted. The ordering of covariates given here is used in the plot grid.

Vector of character strings specifying the "type" of each time-varying covariate included in covnames. The possible "types" are: "binary", "normal", "categorical", "bounded normal", "zero-inflated normal", "truncated normal", "absorbing", "categorical time", and "custom".

Character string for the x axes of all plots.

Vector of character strings for the y axes of the plots for the covariates. This argument must be the same length as covnames. The i-th element of this argument corresponds to the plot for the i-th element of covnames.

Object of class "gformula_survival".

Logical scalar indicating whether to include a plot for the risk.

Logical scalar indicating whether to include a plot for the survival.

Character string for the x axes of all plots.

Character string for the y axis of the plot for the risk (if applicable).

Character string for the y axis of the plot for the survival (if applicable).

Logical scalar specifying whether to include error bars for the 95% confidence intervals of the estimated risk under the natural course. This argument is only effective if the argument nsamples was set to a positive value in gformula_survival.

Character string specifying the name of the outcome variable in obs_data.

Character string specifying the name of the competing event variable in obs_data.

Character string specifying the name of the competing event variable in obs_data if competing events are treated as censoring events.

Character string specifying the name of the censoring variable in obs_data.

Character string specifying the name of the time variable in obs_data.

Character string specifying the name of the ID variable in obs_data.

Number of time points to simulate.

Vector of character strings specifying the names of the time-varying covariates in obs_data.

Vector of character strings specifying the "type" of each time-varying covariate included in covnames. The possible "types" are: "binary", "normal", "categorical", "bounded normal", "zero-inflated normal", "truncated normal", "absorbing", "categorical time", and "custom".

Pooled-over-time data table containing simulated data under the natural course.

Vector containing the mean outcome over all subjects at each time for natural course.

Logical scalar indicating the presence of a competing event.

Logical scalar indicating whether competing events are treated as censoring events.

Logical scalar indicating the presence of a censoring variable in obs_data.

Model fit for the competing event variable if competing events are treated as censoring events.

Model fit for the censoring variable.

Character string specifying the "type" of the outcome. The possible "types" are: "survival", "continuous_eof", and "binary_eof".

Data table containing observed data.

Percentile by which to truncate inverse probability weights.

Cutoff value by which to truncate inverse probability weights.

A list of the mean observed values at each time point for covariates and - if the outcome is of type "survival" - the risk and survival.

A list of data tables The data tables contain the observed and simulated mean values of the covariates under each time point.

For outcomes of type "survival", a list of data tables. The data tables contain the observed and simulated risks and survival under each time point. For other outcomes, a value of NA is given.

Data table containing the observed data.

Character string specifying the name of the ID variable in obs_data.

Number of time points to simulate. By default, this argument is set equal to the maximum number of records that obs_data contains for any individual plus 1.

Character string specifying the name of the time variable in obs_data.

Vector of character strings specifying the names of the time-varying covariates in obs_data.

Vector of character strings specifying the "type" of each time-varying covariate included in covnames. The possible "types" are: "binary", "normal", "categorical", "bounded normal", "zero-inflated normal", "truncated normal", "absorbing", "categorical time", and "custom".

List of vectors, where each vector contains information for one parameter used in the modeling of the time-varying covariates (e.g., model statement, family, link function, etc.). Each vector must be the same length as covnames and in the same order. If a parameter is not required for a certain covariate, it should be set to NA at that index.

Vector containing custom fit functions for time-varying covariates that do not fall within the pre-defined covariate types. It should be in the same order covnames. If a custom fit function is not required for a particular covariate (e.g., if the first covariate is of type "binary" but the second is of type "custom"), then that index should be set to NA. The default is NA.

Vector containing custom prediction functions for time-varying covariates that do not fall within the pre-defined covariate types. It should be in the same order as covnames. If a custom prediction function is not required for a particular covariate, then that index should be set to NA. The default is NA.

List of vectors. The kth vector specifies the names of the variables for which the kth history function in histories is to be applied.

Vector of history functions to apply to the variables specified in histvars. The default is NA.

Vector of character strings specifying the names of baseline covariates in obs_data. These covariates are not simulated using a model but rather carry their value over all time points from the first time point of obs_data. These covariates should not be included in covnames. The default is NA.

Character string specifying the name of the outcome variable in obs_data.

Character string specifying the "type" of outcome. The possible "types" are: "survival", "continuous_eof", and "binary_eof".

Model statement for the outcome variable.

Function specifying a custom outcome model. See the vignette "Using Custom Outcome Models in gfoRmula" for details. The default is NULL.

Function obtaining predictions from the custom outcome model specified in ymodel_fit_custom. See the vignette "Using Custom Outcome Models in gfoRmula" for details. The default is NULL.

Character string specifying the name of the competing event variable in obs_data. Only applicable for survival outcomes.

Model statement for the competing event variable. The default is NA. Only applicable for survival outcomes.

Logical scalar indicating whether to treat competing events as censoring events. This argument is only applicable for survival outcomes and when a competing even model is supplied (i.e., compevent_name and compevent_model are specified). If this argument is set to TRUE, the competing event model will only be used to construct inverse probability weights to estimate the natural course means / risk from the observed data. If this argument is set to FALSE, the competing event model will be used in the parametric g-formula estimates of the risk and will not be used to construct inverse probability weights. See "Details". The default is FALSE.

Character string specifying the name of the censoring variable in obs_data. Only applicable when using inverse probability weights to estimate the natural course means / risk from the observed data. See "Details".

Model statement for the censoring variable. Only applicable when using inverse probability weights to estimate the natural course means / risk from the observed data. See "Details".

(Deprecated. See the ... argument) List, whose elements are vectors of character strings. The kth vector in intvars specifies the name(s) of the variable(s) to be intervened on in each round of the simulation under the kth intervention in interventions.

(Deprecated. See the ... argument) List, whose elements are lists of vectors. Each list in interventions specifies a unique intervention on the relevant variable(s) in intvars. Each vector contains a function implementing a particular intervention on a single variable, optionally followed by one or more "intervention values" (i.e., integers used to specify the treatment regime).

(Deprecated. See the ... argument) List, whose elements are lists of vectors. The kth list in int_times corresponds to the kth intervention in interventions. Each vector specifies the time points in which the relevant intervention is applied on the corresponding variable in intvars. When an intervention is not applied, the simulated natural course value is used. By default, this argument is set so that all interventions are applied in all time points.

Vector of character strings, each describing an intervention. It must be in same order as the specified interventions (see the ... argument).

Integer denoting the intervention to be used as the reference for calculating the risk ratio and risk difference. 0 denotes the natural course, while subsequent integers denote user-specified interventions in the order that they are named (see the ... argument). The default is 0.

List of two numbers indicating a pair of interventions to be compared by a hazard ratio. The default is NA, resulting in no hazard ratio calculation.

List of vectors. Each vector contains as its first entry the covariate name of a visit process; its second entry the name of a covariate whose modeling depends on the visit process; and its third entry the maximum number of consecutive visits that can be missed before an individual is censored. The default is NA.

List of vectors. Each vector contains as its first entry a covariate for which a priori knowledge of its distribution is available; its second entry a condition under which no knowledge of its distribution is available and that must be TRUE for the distribution of that covariate given that condition to be estimated via a parametric model or other fitting procedure; its third entry a function for estimating the distribution of that covariate given the condition in the second entry is false such that a priori knowledge of the covariate distribution is available; and its fourth entry a value used by the function in the third entry. The default is NA.

List of vectors. Each vector contains as its first entry a condition and its second entry an integer. When the condition is TRUE, the outcome variable is simulated according to the fitted model; when the condition is FALSE, the outcome variable takes on the value in the second entry. The default is NA.

List of vectors. Each vector contains as its first entry a condition and its second entry an integer. When the condition is TRUE, the competing event variable is simulated according to the fitted model; when the condition is FALSE, the competing event variable takes on the value in the second entry. The default is NA. Only applicable for survival outcomes.

Logical scalar for specifying the convention used for lagi and lag_cumavgi terms in the model statements when pre-baseline times are not included in obs_data and when the current time index, t, is such that t < i. If this argument is set to FALSE, the value of all lagi and lag_cumavgi terms in this context are set to 0 (for non-categorical covariates) or the reference level (for categorical covariates). If this argument is set to TRUE, the value of lagi and lag_cumavgi terms are set to their values at time 0. The default is FALSE.

Number of subjects for whom to simulate data. By default, this argument is set equal to the number of subjects in obs_data.

Logical scalar indicating whether to return the simulated data set. If bootstrap samples are used (i.e., nsamples is set to a value greater than 0), this argument must be set to FALSE. The default is FALSE.

Starting seed for simulations and bootstrapping.

Integer specifying the number of bootstrap samples to generate. The default is 0.

Logical scalar indicating whether to parallelize simulations of different interventions to multiple cores.

Integer specifying the number of CPU cores to use in parallel simulation. This argument is required when parallel is set to TRUE. In many applications, users may wish to set this argument equal to parallel::detectCores() - 1.

Character string specifying the method for calculating the bootstrap 95% confidence intervals, if applicable. The options are "percentile" and "normal".

Integer specifying the number of threads to be used in data.table. See setDTthreads for further details.

Logical scalar indicating whether to return the fitted models. Note that if this argument is set to TRUE, the output of this function may use a lot of memory. The default is FALSE.

Logical scalar indicating whether to return the parametric g-formula estimates as well as the coefficients, standard errors, and variance-covariance matrices of the parameters of the fitted models in the bootstrap samples. The default is FALSE.

Logical scalar indicating whether to print a progress bar for the number of bootstrap samples completed in the R console. This argument is only applicable when parallel is set to FALSE and bootstrap samples are used (i.e., nsamples is set to a value greater than 0). The default is TRUE.

Percentile by which to truncate inverse probability weights. The default is NULL (i.e., no truncation). See "Details".

Cutoff value by which to truncate inverse probability weights. The default is NULL (i.e., no truncation). See "Details".

Vector of logicals. The kth element is a logical specifying whether to carry forward the intervened value (rather than the natural value) of the treatment variables(s) when performing a carry forward restriction type for the kth intervention in interventions. When the kth element is set to FALSE, the natural value of the treatment variable(s) in the kth intervention in interventions will be carried forward. By default, this argument is set so that the intervened value of the treatment variable(s) is carried forward for all interventions.

Logical scalar indicating whether to truncate simulated covariates to their range in the observed data set. This argument is only applicable for covariates of type "normal", "bounded normal", "truncated normal", and "zero-inflated normal". The default is TRUE.

Other arguments, including (a) those that specify the interventions and (b) those that are passed to the functions in covpredict_custom. To specify interventions, users can supply arguments with the following naming requirements

• Each intervention argument begins with a prefix of intervention.

• After the prefix, the intervention number is specified and followed by a period.

• After the period, the treatment variable name is specified.

Each intervention argument takes as input a list with the following elements:

• The first element specifies the intervention function.

• The subsequent elements specify any intervention values.

• (Optional) The named element int_times specifies the time points to apply the intervention. By default, all interventions are applied at all time points.

For example, an "always treat" intervention on A is given by
intervention1.A = list(static, rep(1, time_points))
See the vignette "A Simplified Approach for Specifying Interventions in gfoRmula" and "Examples" section for more examples.

Results table. For survival outcomes, this contains the estimated risk, risk difference, and risk ratio for all interventions (inculding the natural course) at each time point. For continuous end-of-follow-up outcomes, this contains estimated mean outcome, mean difference, and mean ratio for all interventions (inculding natural course) at the last time point. For binary end-of-follow-up outcomes, this contains the estimated outcome probability, probability difference, and probability ratio for all interventions (inculding natural course) at the last time point. For all outcome types, this also contains the "cumulative percent intervened on" and the "average percent intervened on". If bootstrapping was used, the results table includes the bootstrap risk / mean / probability difference, ratio, standard error, and 95% confidence interval.

A list of the coefficients of the fitted models.

A list of the standard errors of the coefficients of the fitted models.

A list of the variance-covariance matrices of the parameters of the fitted models.

A list of root mean square error (RMSE) values of the fitted models.

Hazard ratio between two interventions (if applicable).

A list of the fitted models for the time-varying covariates, outcome, and competing event (if applicable). If model_fits is set to FALSE, a value of NULL is given.

A list of data tables of the simulated data. Each element in the list corresponds to one of the interventions. If the argument sim_data_b is set to FALSE, a value of NA is given.

A numeric vector specifying the inverse probability weights. See "Details".

A data.table containing the bootstrap replicates of the parametric g-formula estimates. If boot_diag is set to FALSE, a value of NULL is given.

A list, where the kth element is a list containing the coefficients of the fitted models corresponding to the kth bootstrap sample. If boot_diag is set to FALSE, a value of NULL is given.

A list, where the kth element is a list containing the standard errors of the coefficients of the fitted models corresponding to the kth bootstrap sample. If boot_diag is set to FALSE, a value of NULL is given.

A list, where the kth element is a list containing the variance-covariance matrices of the parameters of the fitted models corresponding to the kth bootstrap sample. If boot_diag is set to FALSE, a value of NULL is given.

Some additional elements.

Data table containing the observed data.

Character string specifying the name of the ID variable in obs_data.

Character string specifying the name of the time variable in obs_data.

Vector of character strings specifying the names of the time-varying covariates in obs_data.

Vector of character strings specifying the "type" of each time-varying covariate included in covnames. The possible "types" are: "binary", "normal", "categorical", "bounded normal", "zero-inflated normal", "truncated normal", "absorbing", "categorical time", and "custom".

List of vectors, where each vector contains information for one parameter used in the modeling of the time-varying covariates (e.g., model statement, family, link function, etc.). Each vector must be the same length as covnames and in the same order. If a parameter is not required for a certain covariate, it should be set to NA at that index.

Vector containing custom fit functions for time-varying covariates that do not fall within the pre-defined covariate types. It should be in the same order covnames. If a custom fit function is not required for a particular covariate (e.g., if the first covariate is of type "binary" but the second is of type "custom"), then that index should be set to NA. The default is NA.

Vector containing custom prediction functions for time-varying covariates that do not fall within the pre-defined covariate types. It should be in the same order as covnames. If a custom prediction function is not required for a particular covariate, then that index should be set to NA. The default is NA.

List of vectors. The kth vector specifies the names of the variables for which the kth history function in histories is to be applied.

Vector of history functions to apply to the variables specified in histvars. The default is NA.

Vector of character strings specifying the names of baseline covariates in obs_data. These covariates are not simulated using a model but rather carry their value over all time points from the first time point of obs_data. These covariates should not be included in covnames. The default is NA.

Character string specifying the name of the censoring variable in obs_data. Only applicable when using inverse probability weights to estimate the natural course means / risk from the observed data. See "Details".

Model statement for the censoring variable. Only applicable when using inverse probability weights to estimate the natural course means / risk from the observed data. See "Details".

Character string specifying the name of the outcome variable in obs_data.

Model statement for the outcome variable.

Function specifying a custom outcome model. See the vignette "Using Custom Outcome Models in gfoRmula" for details. The default is NULL.

Function obtaining predictions from the custom outcome model specified in ymodel_fit_custom. See the vignette "Using Custom Outcome Models in gfoRmula" for details. The default is NULL.

(Deprecated. See the ... argument) List, whose elements are vectors of character strings. The kth vector in intvars specifies the name(s) of the variable(s) to be intervened on in each round of the simulation under the kth intervention in interventions.

(Deprecated. See the ... argument) List, whose elements are lists of vectors. Each list in interventions specifies a unique intervention on the relevant variable(s) in intvars. Each vector contains a function implementing a particular intervention on a single variable, optionally followed by one or more "intervention values" (i.e., integers used to specify the treatment regime).

(Deprecated. See the ... argument) List, whose elements are lists of vectors. The kth list in int_times corresponds to the kth intervention in interventions. Each vector specifies the time points in which the relevant intervention is applied on the corresponding variable in intvars. When an intervention is not applied, the simulated natural course value is used. By default, this argument is set so that all interventions are applied in all time points.

Vector of character strings, each describing an intervention. It must be in same order as the specified interventions (see the ... argument).

Integer denoting the intervention to be used as the reference for calculating the end-of-follow-up mean ratio and mean difference. 0 denotes the natural course, while subsequent integers denote user-specified interventions in the order that they are named in interventions. The default is 0.

List of vectors. Each vector contains as its first entry the covariate name of a visit process; its second entry the name of a covariate whose modeling depends on the visit process; and its third entry the maximum number of consecutive visits that can be missed before an individual is censored. The default is NA.

List of vectors. Each vector contains as its first entry a covariate for which a priori knowledge of its distribution is available; its second entry a condition under which no knowledge of its distribution is available and that must be TRUE for the distribution of that covariate given that condition to be estimated via a parametric model or other fitting procedure; its third entry a function for estimating the distribution of that covariate given the condition in the second entry is false such that a priori knowledge of the covariate distribution is available; and its fourth entry a value used by the function in the third entry. The default is NA.

List of vectors. Each vector contains as its first entry a condition and its second entry an integer. When the condition is TRUE, the outcome variable is simulated according to the fitted model; when the condition is FALSE, the outcome variable takes on the value in the second entry. The default is NA.

Logical scalar for specifying the convention used for lagi and lag_cumavgi terms in the model statements when pre-baseline times are not included in obs_data and when the current time index, t, is such that t < i. If this argument is set to FALSE, the value of all lagi and lag_cumavgi terms in this context are set to 0 (for non-categorical covariates) or the reference level (for categorical covariates). If this argument is set to TRUE, the value of lagi and lag_cumavgi terms are set to their values at time 0. The default is FALSE.

Number of subjects for whom to simulate data. By default, this argument is set equal to the number of subjects in obs_data.

Logical scalar indicating whether to return the simulated data set. If bootstrap samples are used (i.e., nsamples is set to a value greater than 0), this argument must be set to FALSE. The default is FALSE.

Starting seed for simulations and bootstrapping.

Integer specifying the number of bootstrap samples to generate. The default is 0.

Logical scalar indicating whether to parallelize simulations of different interventions to multiple cores.

Integer specifying the number of CPU cores to use in parallel simulation. This argument is required when parallel is set to TRUE. In many applications, users may wish to set this argument equal to parallel::detectCores() - 1.

Character string specifying the method for calculating the bootstrap 95% confidence intervals, if applicable. The options are "percentile" and "normal".

Integer specifying the number of threads to be used in data.table. See setDTthreads for further details.

Logical scalar indicating whether to return the fitted models. Note that if this argument is set to TRUE, the output of this function may use a lot of memory. The default is FALSE.

Logical scalar indicating whether to return the parametric g-formula estimates as well as the coefficients, standard errors, and variance-covariance matrices of the parameters of the fitted models in the bootstrap samples. The default is FALSE.

Logical scalar indicating whether to print a progress bar for the number of bootstrap samples completed in the R console. This argument is only applicable when parallel is set to FALSE and bootstrap samples are used (i.e., nsamples is set to a value greater than 0). The default is TRUE.

Percentile by which to truncate inverse probability weights. The default is NULL (i.e., no truncation). See "Details".

Cutoff value by which to truncate inverse probability weights. The default is NULL (i.e., no truncation). See "Details".

Vector of logicals. The kth element is a logical specifying whether to carry forward the intervened value (rather than the natural value) of the treatment variables(s) when performing a carry forward restriction type for the kth intervention in interventions. When the kth element is set to FALSE, the natural value of the treatment variable(s) in the kth intervention in interventions will be carried forward. By default, this argument is set so that the intervened value of the treatment variable(s) is carried forward for all interventions.

Logical scalar indicating whether to truncate simulated covariates to their range in the observed data set. This argument is only applicable for covariates of type "normal", "bounded normal", "truncated normal", and "zero-inflated normal". The default is TRUE.

Other arguments, including (a) those that specify the interventions and (b) those that are passed to the functions in covpredict_custom. To specify interventions, users can supply arguments with the following naming requirements

• Each intervention argument begins with a prefix of intervention.

• After the prefix, the intervention number is specified and followed by a period.

• After the period, the treatment variable name is specified.

Each intervention argument takes as input a list with the following elements:

• The first element specifies the intervention function.

• The subsequent elements specify any intervention values.

• (Optional) The named element int_times specifies the time points to apply the intervention. By default, all interventions are applied at all time points.

For example, an "always treat" intervention on A is given by
intervention1.A = list(static, rep(1, time_points))
See the vignette "A Simplified Approach for Specifying Interventions in gfoRmula" and "Examples" section for more examples.

Results table containing the estimated outcome probability for all interventions (inculding natural course) at the last time point as well as the "cumulative percent intervened on" and the "average percent intervened on". If bootstrapping was used, the results table includes the bootstrap end-of-follow-up mean ratio, standard error, and 95% confidence interval.

A list of the coefficients of the fitted models.

A list of the standard errors of the coefficients of the fitted models.

A list of the variance-covariance matrices of the parameters of the fitted models.

A list of root mean square error (RMSE) values of the fitted models.

A list of the fitted models for the time-varying covariates and outcome. If model_fits is set to FALSE, a value of NULL is given.

A list of data tables of the simulated data. Each element in the list corresponds to one of the interventions. If the argument sim_data_b is set to FALSE, a value of NA is given.

A numeric vector specifying the inverse probability weights. See "Details".

A data.table containing the bootstrap replicates of the parametric g-formula estimates. If boot_diag is set to FALSE, a value of NULL is given.

A list, where the kth element is a list containing the coefficients of the fitted models corresponding to the kth bootstrap sample. If boot_diag is set to FALSE, a value of NULL is given.

A list, where the kth element is a list containing the standard errors of the coefficients of the fitted models corresponding to the kth bootstrap sample. If boot_diag is set to FALSE, a value of NULL is given.

A list, where the kth element is a list containing the variance-covariance matrices of the parameters of the fitted models corresponding to the kth bootstrap sample. If boot_diag is set to FALSE, a value of NULL is given.

Some additional elements.

Data table containing the observed data.

Character string specifying the name of the ID variable in obs_data.

Character string specifying the name of the time variable in obs_data.

Vector of character strings specifying the names of the time-varying covariates in obs_data.

Vector of character strings specifying the "type" of each time-varying covariate included in covnames. The possible "types" are: "binary", "normal", "categorical", "bounded normal", "zero-inflated normal", "truncated normal", "absorbing", "categorical time", and "custom".

List of vectors, where each vector contains information for one parameter used in the modeling of the time-varying covariates (e.g., model statement, family, link function, etc.). Each vector must be the same length as covnames and in the same order. If a parameter is not required for a certain covariate, it should be set to NA at that index.

Vector containing custom fit functions for time-varying covariates that do not fall within the pre-defined covariate types. It should be in the same order covnames. If a custom fit function is not required for a particular covariate (e.g., if the first covariate is of type "binary" but the second is of type "custom"), then that index should be set to NA. The default is NA.

Vector containing custom prediction functions for time-varying covariates that do not fall within the pre-defined covariate types. It should be in the same order as covnames. If a custom prediction function is not required for a particular covariate, then that index should be set to NA. The default is NA.

List of vectors. The kth vector specifies the names of the variables for which the kth history function in histories is to be applied.

Vector of history functions to apply to the variables specified in histvars. The default is NA.

Vector of character strings specifying the names of baseline covariates in obs_data. These covariates are not simulated using a model but rather carry their value over all time points from the first time point of obs_data. These covariates should not be included in covnames. The default is NA.

Character string specifying the name of the outcome variable in obs_data.

Model statement for the outcome variable.

Function specifying a custom outcome model. See the vignette "Using Custom Outcome Models in gfoRmula" for details. The default is NULL.

Function obtaining predictions from the custom outcome model specified in ymodel_fit_custom. See the vignette "Using Custom Outcome Models in gfoRmula" for details. The default is NULL.

Character string specifying the name of the censoring variable in obs_data. Only applicable when using inverse probability weights to estimate the natural course means / risk from the observed data. See "Details".

Model statement for the censoring variable. Only applicable when using inverse probability weights to estimate the natural course means / risk from the observed data. See "Details".

(Deprecated. See the ... argument) List, whose elements are vectors of character strings. The kth vector in intvars specifies the name(s) of the variable(s) to be intervened on in each round of the simulation under the kth intervention in interventions.

(Deprecated. See the ... argument) List, whose elements are lists of vectors. Each list in interventions specifies a unique intervention on the relevant variable(s) in intvars. Each vector contains a function implementing a particular intervention on a single variable, optionally followed by one or more "intervention values" (i.e., integers used to specify the treatment regime).

(Deprecated. See the ... argument) List, whose elements are lists of vectors. The kth list in int_times corresponds to the kth intervention in interventions. Each vector specifies the time points in which the relevant intervention is applied on the corresponding variable in intvars. When an intervention is not applied, the simulated natural course value is used. By default, this argument is set so that all interventions are applied in all time points.

Vector of character strings, each describing an intervention. It must be in same order as the specified interventions (see the ... argument).

Integer denoting the intervention to be used as the reference for calculating the end-of-follow-up mean ratio and mean difference. 0 denotes the natural course, while subsequent integers denote user-specified interventions in the order that they are named in interventions. The default is 0.

List of vectors. Each vector contains as its first entry the covariate name of a visit process; its second entry the name of a covariate whose modeling depends on the visit process; and its third entry the maximum number of consecutive visits that can be missed before an individual is censored. The default is NA.

List of vectors. Each vector contains as its first entry a covariate for which a priori knowledge of its distribution is available; its second entry a condition under which no knowledge of its distribution is available and that must be TRUE for the distribution of that covariate given that condition to be estimated via a parametric model or other fitting procedure; its third entry a function for estimating the distribution of that covariate given the condition in the second entry is false such that a priori knowledge of the covariate distribution is available; and its fourth entry a value used by the function in the third entry. The default is NA.

List of vectors. Each vector contains as its first entry a condition and its second entry an integer. When the condition is TRUE, the outcome variable is simulated according to the fitted model; when the condition is FALSE, the outcome variable takes on the value in the second entry. The default is NA.

Logical scalar for specifying the convention used for lagi and lag_cumavgi terms in the model statements when pre-baseline times are not included in obs_data and when the current time index, t, is such that t < i. If this argument is set to FALSE, the value of all lagi and lag_cumavgi terms in this context are set to 0 (for non-categorical covariates) or the reference level (for categorical covariates). If this argument is set to TRUE, the value of lagi and lag_cumavgi terms are set to their values at time 0. The default is FALSE.

Number of subjects for whom to simulate data. By default, this argument is set equal to the number of subjects in obs_data.

Logical scalar indicating whether to return the simulated data set. If bootstrap samples are used (i.e., nsamples is set to a value greater than 0), this argument must be set to FALSE. The default is FALSE.

Starting seed for simulations and bootstrapping.

Integer specifying the number of bootstrap samples to generate. The default is 0.

Logical scalar indicating whether to parallelize simulations of different interventions to multiple cores.

Integer specifying the number of CPU cores to use in parallel simulation. This argument is required when parallel is set to TRUE. In many applications, users may wish to set this argument equal to parallel::detectCores() - 1.

Character string specifying the method for calculating the bootstrap 95% confidence intervals, if applicable. The options are "percentile" and "normal".

Integer specifying the number of threads to be used in data.table. See setDTthreads for further details.

Logical scalar indicating whether to return the fitted models. Note that if this argument is set to TRUE, the output of this function may use a lot of memory. The default is FALSE.

Logical scalar indicating whether to return the parametric g-formula estimates as well as the coefficients, standard errors, and variance-covariance matrices of the parameters of the fitted models in the bootstrap samples. The default is FALSE.

Logical scalar indicating whether to print a progress bar for the number of bootstrap samples completed in the R console. This argument is only applicable when parallel is set to FALSE and bootstrap samples are used (i.e., nsamples is set to a value greater than 0). The default is TRUE.

Percentile by which to truncate inverse probability weights. The default is NULL (i.e., no truncation). See "Details".

Cutoff value by which to truncate inverse probability weights. The default is NULL (i.e., no truncation). See "Details".

Vector of logicals. The kth element is a logical specifying whether to carry forward the intervened value (rather than the natural value) of the treatment variables(s) when performing a carry forward restriction type for the kth intervention in interventions. When the kth element is set to FALSE, the natural value of the treatment variable(s) in the kth intervention in interventions will be carried forward. By default, this argument is set so that the intervened value of the treatment variable(s) is carried forward for all interventions.

Logical scalar indicating whether to truncate simulated covariates to their range in the observed data set. This argument is only applicable for covariates of type "normal", "bounded normal", "truncated normal", and "zero-inflated normal". The default is TRUE.

Other arguments, including (a) those that specify the interventions and (b) those that are passed to the functions in covpredict_custom. To specify interventions, users can supply arguments with the following naming requirements

• Each intervention argument begins with a prefix of intervention.

• After the prefix, the intervention number is specified and followed by a period.

• After the period, the treatment variable name is specified.

Each intervention argument takes as input a list with the following elements:

• The first element specifies the intervention function.

• The subsequent elements specify any intervention values.

• (Optional) The named element int_times specifies the time points to apply the intervention. By default, all interventions are applied at all time points.

For example, an "always treat" intervention on A is given by
intervention1.A = list(static, rep(1, time_points))
See the vignette "A Simplified Approach for Specifying Interventions in gfoRmula" and "Examples" section for more examples.

Results table containing the estimated mean outcome for all interventions (inculding natural course) at the last time point as well as the "cumulative percent intervened on" and the "average percent intervened on". If bootstrapping was used, the results table includes the bootstrap end-of-follow-up mean ratio, standard error, and 95% confidence interval.

A list of the coefficients of the fitted models.

A list of the standard errors of the coefficients of the fitted models.

A list of the variance-covariance matrices of the parameters of the fitted models.

A list of root mean square error (RMSE) values of the fitted models.

A list of the fitted models for the time-varying covariates and outcome. If model_fits is set to FALSE, a value of NULL is given.

A list of data tables of the simulated data. Each element in the list corresponds to one of the interventions. If the argument sim_data_b is set to FALSE, a value of NA is given.

A numeric vector specifying the inverse probability weights. See "Details".

A data.table containing the bootstrap replicates of the parametric g-formula estimates. If boot_diag is set to FALSE, a value of NULL is given.

A list, where the kth element is a list containing the coefficients of the fitted models corresponding to the kth bootstrap sample. If boot_diag is set to FALSE, a value of NULL is given.

A list, where the kth element is a list containing the standard errors of the coefficients of the fitted models corresponding to the kth bootstrap sample. If boot_diag is set to FALSE, a value of NULL is given.

A list, where the kth element is a list containing the variance-covariance matrices of the parameters of the fitted models corresponding to the kth bootstrap sample. If boot_diag is set to FALSE, a value of NULL is given.

Some additional elements.

Data table containing the observed data.

Character string specifying the name of the ID variable in obs_data.

Number of time points to simulate. By default, this argument is set equal to the maximum number of records that obs_data contains for any individual.

Character string specifying the name of the time variable in obs_data.

Vector of character strings specifying the names of the time-varying covariates in obs_data.

Vector of character strings specifying the "type" of each time-varying covariate included in covnames. The possible "types" are: "binary", "normal", "categorical", "bounded normal", "zero-inflated normal", "truncated normal", "absorbing", "categorical time", and "custom".

List of vectors, where each vector contains information for one parameter used in the modeling of the time-varying covariates (e.g., model statement, family, link function, etc.). Each vector must be the same length as covnames and in the same order. If a parameter is not required for a certain covariate, it should be set to NA at that index.

Vector containing custom fit functions for time-varying covariates that do not fall within the pre-defined covariate types. It should be in the same order covnames. If a custom fit function is not required for a particular covariate (e.g., if the first covariate is of type "binary" but the second is of type "custom"), then that index should be set to NA. The default is NA.

Vector containing custom prediction functions for time-varying covariates that do not fall within the pre-defined covariate types. It should be in the same order as covnames. If a custom prediction function is not required for a particular covariate, then that index should be set to NA. The default is NA.

List of vectors. The kth vector specifies the names of the variables for which the kth history function in histories is to be applied.

Vector of history functions to apply to the variables specified in histvars. The default is NA.

Vector of character strings specifying the names of baseline covariates in obs_data. These covariates are not simulated using a model but rather carry their value over all time points from the first time point of obs_data. These covariates should not be included in covnames. The default is NA.

Character string specifying the name of the outcome variable in obs_data.

Model statement for the outcome variable.

Function specifying a custom outcome model. See the vignette "Using Custom Outcome Models in gfoRmula" for details. The default is NULL.

Function obtaining predictions from the custom outcome model specified in ymodel_fit_custom. See the vignette "Using Custom Outcome Models in gfoRmula" for details. The default is NULL.

Character string specifying the name of the competing event variable in obs_data.

Model statement for the competing event variable. The default is NA.

Logical scalar indicating whether to treat competing events as censoring events. This argument is only applicable for survival outcomes and when a competing even model is supplied (i.e., compevent_name and compevent_model are specified). If this argument is set to TRUE, the competing event model will only be used to construct inverse probability weights to estimate the natural course means / risk from the observed data. If this argument is set to FALSE, the competing event model will be used in the parametric g-formula estimates of the risk and will not be used to construct inverse probability weights. See "Details". The default is FALSE.

Character string specifying the name of the censoring variable in obs_data. Only applicable when using inverse probability weights to estimate the natural course means / risk from the observed data. See "Details".

Model statement for the censoring variable. Only applicable when using inverse probability weights to estimate the natural course means / risk from the observed data. See "Details".

(Deprecated. See the ... argument) List, whose elements are vectors of character strings. The kth vector in intvars specifies the name(s) of the variable(s) to be intervened on in each round of the simulation under the kth intervention in interventions.

(Deprecated. See the ... argument) List, whose elements are lists of vectors. Each list in interventions specifies a unique intervention on the relevant variable(s) in intvars. Each vector contains a function implementing a particular intervention on a single variable, optionally followed by one or more "intervention values" (i.e., integers used to specify the treatment regime).

(Deprecated. See the ... argument) List, whose elements are lists of vectors. The kth list in int_times corresponds to the kth intervention in interventions. Each vector specifies the time points in which the relevant intervention is applied on the corresponding variable in intvars. When an intervention is not applied, the simulated natural course value is used. By default, this argument is set so that all interventions are applied in all time points.

Vector of character strings, each describing an intervention. It must be in same order as the specified interventions (see the ... argument).

Integer denoting the intervention to be used as the reference for calculating the risk ratio and risk difference. 0 denotes the natural course, while subsequent integers denote user-specified interventions in the order that they are named in interventions. The default is 0.

List of two numbers indicating a pair of interventions to be compared by a hazard ratio. The default is NA, resulting in no hazard ratio calculation.

List of vectors. Each vector contains as its first entry the covariate name of a visit process; its second entry the name of a covariate whose modeling depends on the visit process; and its third entry the maximum number of consecutive visits that can be missed before an individual is censored. The default is NA.

List of vectors. Each vector contains as its first entry a covariate for which a priori knowledge of its distribution is available; its second entry a condition under which no knowledge of its distribution is available and that must be TRUE for the distribution of that covariate given that condition to be estimated via a parametric model or other fitting procedure; its third entry a function for estimating the distribution of that covariate given the condition in the second entry is false such that a priori knowledge of the covariate distribution is available; and its fourth entry a value used by the function in the third entry. The default is NA.

List of vectors. Each vector contains as its first entry a condition and its second entry an integer. When the condition is TRUE, the outcome variable is simulated according to the fitted model; when the condition is FALSE, the outcome variable takes on the value in the second entry. The default is NA.

List of vectors. Each vector contains as its first entry a condition and its second entry an integer. When the condition is TRUE, the competing event variable is simulated according to the fitted model; when the condition is FALSE, the competing event variable takes on the value in the second entry. The default is NA.

Logical scalar for specifying the convention used for lagi and lag_cumavgi terms in the model statements when pre-baseline times are not included in obs_data and when the current time index, t, is such that t < i. If this argument is set to FALSE, the value of all lagi and lag_cumavgi terms in this context are set to 0 (for non-categorical covariates) or the reference level (for categorical covariates). If this argument is set to TRUE, the value of lagi and lag_cumavgi terms are set to their values at time 0. The default is FALSE.

Number of subjects for whom to simulate data. By default, this argument is set equal to the number of subjects in obs_data.

Logical scalar indicating whether to return the simulated data set. If bootstrap samples are used (i.e., nsamples is set to a value greater than 0), this argument must be set to FALSE. The default is FALSE.

Starting seed for simulations and bootstrapping.

Integer specifying the number of bootstrap samples to generate. The default is 0.

Logical scalar indicating whether to parallelize simulations of different interventions to multiple cores.

Integer specifying the number of CPU cores to use in parallel simulation. This argument is required when parallel is set to TRUE. In many applications, users may wish to set this argument equal to parallel::detectCores() - 1.

Character string specifying the method for calculating the bootstrap 95% confidence intervals, if applicable. The options are "percentile" and "normal".

Integer specifying the number of threads to be used in data.table. See setDTthreads for further details.

Logical scalar indicating whether to return the fitted models. Note that if this argument is set to TRUE, the output of this function may use a lot of memory. The default is FALSE.

Logical scalar indicating whether to return the parametric g-formula estimates as well as the coefficients, standard errors, and variance-covariance matrices of the parameters of the fitted models in the bootstrap samples. The default is FALSE.

Logical scalar indicating whether to print a progress bar for the number of bootstrap samples completed in the R console. This argument is only applicable when parallel is set to FALSE and bootstrap samples are used (i.e., nsamples is set to a value greater than 0). The default is TRUE.

Percentile by which to truncate inverse probability weights. The default is NULL (i.e., no truncation). See "Details".

Cutoff value by which to truncate inverse probability weights. The default is NULL (i.e., no truncation). See "Details".

Vector of logicals. The kth element is a logical specifying whether to carry forward the intervened value (rather than the natural value) of the treatment variables(s) when performing a carry forward restriction type for the kth intervention in interventions. When the kth element is set to FALSE, the natural value of the treatment variable(s) in the kth intervention in interventions will be carried forward. By default, this argument is set so that the intervened value of the treatment variable(s) is carried forward for all interventions.

Logical scalar indicating whether to truncate simulated covariates to their range in the observed data set. This argument is only applicable for covariates of type "normal", "bounded normal", "truncated normal", and "zero-inflated normal". The default is TRUE.

Other arguments, including (a) those that specify the interventions and (b) those that are passed to the functions in covpredict_custom. To specify interventions, users can supply arguments with the following naming requirements

• Each intervention argument begins with a prefix of intervention.

• After the prefix, the intervention number is specified and followed by a period.

• After the period, the treatment variable name is specified.

Each intervention argument takes as input a list with the following elements:

• The first element specifies the intervention function.

• The subsequent elements specify any intervention values.

• (Optional) The named element int_times specifies the time points to apply the intervention. By default, all interventions are applied at all time points.

For example, an "always treat" intervention on A is given by
intervention1.A = list(static, rep(1, time_points))
See the vignette "A Simplified Approach for Specifying Interventions in gfoRmula" and "Examples" section for more examples.

Results table containing the estimated risk and risk ratio for all interventions (inculding the natural course) at each time point as well as the "cumulative percent intervened on" and the "average percent intervened on". If bootstrapping was used, the results table includes the bootstrap mean risk ratio, standard error, and 95% confidence interval.

A list of the coefficients of the fitted models.

A list of the standard errors of the coefficients of the fitted models.

A list of the variance-covariance matrices of the parameters of the fitted models.

A list of root mean square error (RMSE) values of the fitted models.

Hazard ratio between two interventions (if applicable).

A list of the fitted models for the time-varying covariates, outcome, and competing event (if applicable). If model_fits is set to FALSE, a value of NULL is given.

A list of data tables of the simulated data. Each element in the list corresponds to one of the interventions. If the argument sim_data_b is set to FALSE, a value of NA is given.

A numeric vector specifying the inverse probability weights. See "Details".

A data.table containing the bootstrap replicates of the parametric g-formula estimates. If boot_diag is set to FALSE, a value of NULL is given.

A list, where the kth element is a list containing the coefficients of the fitted models corresponding to the kth bootstrap sample. If boot_diag is set to FALSE, a value of NULL is given.

A list, where the kth element is a list containing the standard errors of the coefficients of the fitted models corresponding to the kth bootstrap sample. If boot_diag is set to FALSE, a value of NULL is given.

A list, where the kth element is a list containing the variance-covariance matrices of the parameters of the fitted models corresponding to the kth bootstrap sample. If boot_diag is set to FALSE, a value of NULL is given.

Some additional elements.

Integer specifying the index intcomp.

List of two numbers indicating a pair of interventions to be compared by a hazard ratio.

Character string specifying the name of the time variable in pools.

Data table containing the simulated values for the covariates, outcome probabilities, competing event probabilities, outcomes, and competing events.

Data table containing the simulated data at time t.

Data table containing the simulated data at times before t.

List, whose elements are lists of vectors. Each vector contains a function implementing a particular intervention on a single variable, optionally followed by one or more "intervention values" (i.e., integers used to specify the treatment regime).

Character string specifying the name of the variable to be intervened on in each round of the simulation.

Vector specifying the time points in which the intervention is applied.

Character string specifying the name of the time variable in pool and newdf.

Integer specifying the current time index.

Data table containing all information prior to time t (t noninclusive).

Vector of character strings specifying the names of the variables for which history functions are to be applied.

For lagged, this argument is a vector specifying the lags used in the model statements (e.g., if lag1_varname and lag2_varname were included in the model statements, this vector would be c(1,2)). For lagavg, this argument is a numeric vector specifying the lag averages used in the model statements.

Character string specifying the name of the time variable in pool.

Integer specifying the current time index.

Character string specifying the name of the ID variable in pool.

Logical scalar for specifying the convention used for lagi and lag_cumavgi terms in the model statements when pre-baseline times are not included in obs_data and when the current time index, t, is such that t < i. If this argument is set to FALSE, the value of all lagi and lag_cumavgi terms in this context are set to 0 (for non-categorical covariates) or the reference level (for categorical covariates). If this argument is set to TRUE, the value of lagi and lag_cumavgi terms are set to their values at time 0. The default is FALSE.

Logical scalar indicating whether the observed data set contains rows for time t < 0.

Data table containing all information prior to time t (t noninclusive).

List of vectors. The kth vector specifies the names of the variables for which the kth history function in histories is to be applied.

List of length two. The first element is a numeric vector specifying the lags used in the model statements (e.g., if lag1_varname and lag2_varname were included in the model statements, this vector would be c(1,2)). The second element is a numeric vector specifying the lag averages used in the model statements.

Vector of history functions to apply to the variables specified in histvars.

Character string specifying the name of the time variable in pool.

Integer specifying the current time index.

Character string specifying the name of the ID variable in pool.

A vector of one or more values denoting the maximum number of times a binary covariate representing a visit process may be missed before the individual is censored from the data (in the observed data) or a visit is forced (in the simulated data). Multiple values exist in the vector when the modeling of more than covariate is attached to a visit process. A value of NA should be provided when there is no visit process.

Logical scalar for specifying the convention used for lagi and lag_cumavgi terms in the model statements when pre-baseline times are not included in obs_data and when the current time index, t, is such that t < i. If this argument is set to FALSE, the value of all lagi and lag_cumavgi terms in this context are set to 0 (for non-categorical covariates) or the reference level (for categorical covariates). If this argument is set to TRUE, the value of lagi and lag_cumavgi terms are set to their values at time 0. The default is FALSE.

Logical scalar indicating whether the observed data set contains rows for time t < 0.

Data table containing the simulated data at time t.

Data table containing the simulated data at times before t.

Character string specifying the name of the variable to be intervened on in each round of the simulation.

A list of user-specified values for the intervention.

Character string specifying the name of the time variable in pool and newdf.

Integer specifying the current time index.

Character string specifying the name of the outcome variable in obs_data.

Character string specifying the name of the competing event variable in obs_data.

Character string specifying the name of the competing event variable in obs_data if competing events are treated as censoring events.

Character string specifying the name of the censoring variable in obs_data.

Character string specifying the name of the time variable in obs_data.

Character string specifying the name of the ID variable in obs_data.

Vector of character strings specifying the names of the time-varying covariates in obs_data.

Vector of character strings specifying the "type" of each time-varying covariate included in covnames. The possible "types" are: "binary", "normal", "categorical", "bounded normal", "zero-inflated normal", "truncated normal", "absorbing", "categorical time", and "custom".

Logical scalar indicating the presence of a competing event.

Logical scalar indicating whether competing events are treated as censoring events.

Logical scalar indicating the presence of a censoring variable in obs_data.

Model fit for the competing event variable if competing events are treated as censoring events.

Model fit for the censoring variable.

Character string specifying the "type" of the outcome. The possible "types" are: "survival", "continuous_eof", and "binary_eof".

Data table containing the observed data.

Percentile by which to truncate inverse probability weights.

Cutoff value by which to truncate inverse probability weights.

Object of class "gformula_binary_eof".

Vector of character strings specifying the names of the time-varying covariates to be plotted. The ordering of covariates given here is used in the plot grid. Time-varying covariates of type "categorical time" cannot be included. By default, this argument is set equal to the covnames argument used in gformula_binary_eof, where covariates of type "categorical time" are removed.

Number of columns in the plot grid. By default, two columns are used when there is at least two plots.

Number of rows in the plot grid. By default, a maximum of six rows is used and additional plots are included in subsequent pages.

Logical scalar indicating whether to include a legend. The default is TRUE.

Character string specifying the legend position. Valid values are "top", "bottom", "left", "right", and "none". The default is "bottom".

Character string for the x axes of all plots. By default, this argument is set to the time_name argument specified in gformula_binary_eof.

Vector of character strings for the y axes of the plots for the covariates. This argument must be the same length as covnames. The i-th element of this argument corresponds to the plot for the i-th element of covnames.

Other arguments, which are passed to ggarrange.

Object of class "gformula_continuous_eof".

Vector of character strings specifying the names of the time-varying covariates to be plotted. The ordering of covariates given here is used in the plot grid. Time-varying covariates of type "categorical time" cannot be included. By default, this argument is set equal to the covnames argument used in gformula_continuous_eof, where covariates of type "categorical time" are removed.

Number of columns in the plot grid. By default, two columns are used when there is at least two plots.

Number of rows in the plot grid. By default, a maximum of six rows is used and additional plots are included in subsequent pages.

Logical scalar indicating whether to include a legend. The default is TRUE.

Character string specifying the legend position. Valid values are "top", "bottom", "left", "right", and "none". The default is "bottom".

Character string for the x axes of all plots. By default, this argument is set to the time_name argument specified in gformula_continuous_eof.

Vector of character strings for the y axes of the plots for the covariates. This argument must be the same length as covnames. The i-th element of this argument corresponds to the plot for the i-th element of covnames.

Other arguments, which are passed to ggarrange.

Object of class "gformula_survival".

Vector of character strings specifying the names of the time-varying covariates to be plotted. The ordering of covariates given here is used in the plot grid. Time-varying covariates of type "categorical time" cannot be included. To plot none of the time-varying covariates, set this argument to NA. By default, this argument is set equal to the covnames argument used in gformula_survival, where covariates of type 'categorical time' are removed.

Logical scalar indicating whether to include a plot for the risk. The default is TRUE.

Logical scalar indicating whether to include a plot for the survival. The default is FALSE.

Number of columns in the plot grid. By default, two columns are used when there is at least two plots.

Number of rows in the plot grid. By default, a maximum of six rows is used and additional plots are included in subsequent pages.

Logical scalar indicating whether to include a legend. The default is TRUE.

Character string specifying the legend position. Valid values are "top", "bottom", "left", "right", and "none". The default is "bottom".

Character string for the x axes of all plots. By default, this argument is set to the time_name argument specified in gformula_survival.

Vector of character strings for the y axes of the plots for the covariates. This argument must be the same length as covnames. The i-th element of this argument corresponds to the plot for the i-th element of covnames.

Character string for the y axis of the plot for the risk (if applicable). The default is "risk".

Character string for the y axis of the plot for the survival (if applicable). The default is "survival".

Integer specifying the position at which to order the risk plot (if applicable). By default, this argument is set to the number of plots in the grid minus one (i.e., orders the risk plot second last).

Integer specifying the position at which to order the survival plot (if applicable). By default, this argument is set to the number of plots in the grid (i.e., orders the survival plot last).

Logical scalar specifying whether to include error bars for the 95% confidence intervals of the estimated risk under the natural course. This argument is only effective if the argument nsamples was set to a positive value in gformula_survival. The default is TRUE.

Other arguments, which are passed to ggarrange.

Model statement for competing event variable.

List of vectors. Each vector containins as its first entry a condition and its second entry an integer. When the condition is TRUE, the competing event variable is simulated according to the fitted model; when the condition is FALSE, the competing event variable takes on the value in the second entry.

Data on which the model is fit.

Logical scalar indicating whether to return the fitted models. The default is FALSE.

Model statement for the outcome variable.

List of vectors. Each vector containins as its first entry a condition and its second entry an integer. When the condition is TRUE, the outcome variable is simulated according to the fitted model; when the condition is FALSE, the outcome variable takes on the value in the second entry.

Character string specifying the "type" of the outcome. The possible "types" are: "survival", "continuous_eof", and "binary_eof".

Character string specifying the name of the outcome variable in obs_data.

Character string specifying the name of the time variable in obs_data.

Data on which the model is fit.

Logical scalar indicating whether to return the fitted models. The default is FALSE.

Function specifying a custom outcome model. See the vignette "Using Custom Outcome Models in gfoRmula" for details.

List of vectors, where each vector contains information for one parameter used in the modeling of the time-varying covariates (e.g., model statement, family, link function, etc.). Each vector must be the same length as covnames and in the same order.

Vector of character strings specifying the names of the time-varying covariates in obs_data.

Vector of character strings specifying the "type" of each time-varying covariate included in covnames. The possible "types" are: "binary", "normal", "categorical", "bounded normal", "zero-inflated normal", "truncated normal", "absorbing", "categorical time", and "custom".

Vector containing custom fit functions for time-varying covariates that do not fall within the pre-defined covariate types. It should be in the same order covnames. If a custom fit function is not required for a particular covariate (e.g., if the first covariate is of type "binary" but the second is of type "custom"), then that index should be set to NA.

List of vectors. Each vector contains as its first entry a covariate for which a priori knowledge of its distribution is available; its second entry a condition under which no knowledge of its distribution is available and that must be TRUE for the distribution of that covariate given that condition to be estimated via a parametric model or other fitting procedure; its third entry a function for estimating the distribution of that covariate given the condition in the second entry is false such that a priori knowledge of the covariate distribution is available; and its fourth entry a value used by the function in the third entry. The default is NA.

Character string specifying the name of the time variable in obs_data.

Data on which the models are fit.

Logical scalar indicating whether to return the fitted models. The default is FALSE.

Integer specifying the number of observations to be simulated.

Integer specifying the number of trials.

Numeric vector specifying the probabilities.

Integer specifying the number of observations to be simulated.

Numeric scalar specifying the mean of the distribution.

Numeric scalar specifying the standard deviation of the distribution.

Integer specifying the number of observations to be simulated.

Numeric scalar specifying the mean of the distribution.

Numeric scalar specifying the standard deviation of the distribution.

Numeric scalar specifying the lower bound of truncation.

Numeric scalar specifying the upper bound of truncation.

Object of class "gformula_survival", "gformula_continuous_eof", "gformula_binary_eof", or "summary.gformula" (for print).

Logical scalar indicating whether to print the results for all time points. This argument is only applicable to objects of class "gformula_survival". If this argument is set to FALSE, the results are only shown for the final time point. The default is FALSE for print and TRUE for summary.

Logical scalar indicating whether to print the model coefficients. The default is FALSE.

Logical scalar indicating whether to print the standard error of the model coefficients. The default is FALSE.

Logical scalar indicating whether to print the model root mean square errors (RMSEs). The default is FALSE.

Logical scalar indicating whether to print the hazard ratio between two interventions (if computed). If bootstrapping was used, 95% confidence intervals will be given. This argument is only applicable to objects of class "gformula_survival". The default is FALSE.

Logical scalar indicating whether to print summaries of the fitted models for the time-varying covariates, outcome, and competing event (if applicable). This argument is only effective if the argument model_fits was set to TRUE in gformula. The default is FALSE for print and TRUE for summary.

Other arguments.

Object of class "gformula" (for summary).

Integer specifying the index of fits.

List of fitted models.

Vector of character strings specifying the names of the time-varying covariates in obs_data.

Vector of character strings specifying the "type" of each time-varying covariate included in covnames. The possible "types" are: "binary", "normal", "categorical", "bounded normal", "zero-inflated normal", "truncated normal", "absorbing", "categorical time", and "custom".

Data table containing the simulated data at time t.

Data table containing the simulated data at times before t.

List of vectors. Each vector contains as its first entry the covariate affected by the restriction; its second entry the condition that must be TRUE for the covariate to be modeled; its third entry a function that executes other specific actions based on the condition (in this case, this function); and its fourth entry some value used by the function (in this case, the value the user desires to assign to the covariate when it is not modeled).

Character string specifying the name of the time variable in pool and newdf.

Integer specifying the current time index.

This argument is not used in this function.

Integer specifying the index of the current intervention.

List of model fits for the time-varying covariates.

Model fit for the outcome variable.

Model fit for the competing event variable, if any.

Function obtaining predictions from the custom outcome model specified in ymodel_fit_custom. See the vignette "Using Custom Outcome Models in gfoRmula" for details.

List of vectors. Each vector containins as its first entry a condition and its second entry an integer. When the condition is TRUE, the outcome variable is simulated according to the fitted model; when the condition is FALSE, the outcome variable takes on the value in the second entry.

List of vectors. Each vector containins as its first entry a condition and its second entry an integer. When the condition is TRUE, the competing event variable is simulated according to the fitted model; when the condition is FALSE, the competing event variable takes on the value in the second entry.

List of vectors. Each vector contains as its first entry a covariate for which a priori knowledge of its distribution is available; its second entry a condition under which no knowledge of its distribution is available and that must be TRUE for the distribution of that covariate given that condition to be estimated via a parametric model or other fitting procedure; its third entry a function for estimating the distribution of that covariate given the condition in the second entry is false such that a priori knowledge of the covariate distribution is available; and its fourth entry a value used by the function in the third entry. The default is NA.

Character string specifying the name of the outcome variable in obs_data.

Character string specifying the name of the competing event variable in obs_data.

Character string specifying the name of the time variable in obs_data.

List, whose elements are vectors of character strings. The kth vector in intvars specifies the name(s) of the variable(s) to be intervened on in each round of the simulation under the kth intervention in interventions.

List, whose elements are lists of vectors. Each list in interventions specifies a unique intervention on the relevant variable(s) in intvars. Each vector contains a function implementing a particular intervention on a single variable, optionally followed by one or more "intervention values" (i.e., integers used to specify the treatment regime).

List, whose elements are lists of vectors. The kth list in int_times corresponds to the kth intervention in interventions. Each vector specifies the time points in which the relevant intervention is applied on the corresponding variable in intvars. When an intervention is not applied, the simulated natural course value is used. By default, this argument is set so that all interventions are applied in all time points.

List of vectors. The kth vector specifies the names of the variables for which the kth history function in histories is to be applied.

List of length two. The first element is a numeric vector specifying the lags used in the model statements (e.g., if lag1_varname and lag2_varname were included in the model statements, this vector would be c(1,2)). The second element is a numeric vector specifying the lag averages used in the model statements.

Vector of history functions to apply to the variables specified in histvars.

Logical scalar indicating the presence of a competing event.

List of vectors. Each vector contains the minimum and maximum values of one of the covariates in covnames.

Character string specifying the "type" of the outcome. The possible "types" are: "survival", "continuous_eof", and "binary_eof".

Integer specifying the seed for this simulation.

Data table containing the observed data.

Number of time points to simulate.

Logical scalar indicating whether to parallelize simulations of different interventions to multiple cores.

Character string specifying the name of the competing event variable in obs_data.

Vector of character strings specifying the "type" of each time-varying covariate included in covnames. The possible "types" are: "binary", "normal", "categorical", "bounded normal", "zero-inflated normal", "truncated normal", "absorbing", "categorical time", and "custom".

List of vectors, where each vector contains information for one parameter used in the modeling of the time-varying covariates (e.g., model statement, family, link function, etc.). Each vector must be the same length as covnames and in the same order. If a parameter is not required for a certain covariate, it should be set to NA at that index.

Vector containing custom prediction functions for time-varying covariates that do not fall within the pre-defined covariate types. It should be in the same order as covnames. If a custom prediction function is not required for a particular covariate, then that index should be set to NA.

Vector of character strings specifying the names of baseline covariates in obs_data.

A vector of one or more values denoting the maximum number of times a binary covariate representing a visit process may be missed before the individual is censored from the data (in the observed data) or a visit is forced (in the simulated data). Multiple values exist in the vector when the modeling of more than covariate is attached to a visit process.

Logical scalar for specifying the convention used for lagi and lag_cumavgi terms in the model statements when pre-baseline times are not included in obs_data and when the current time index, t, is such that t < i. If this argument is set to FALSE, the value of all lagi and lag_cumavgi terms in this context are set to 0 (for non-categorical covariates) or the reference level (for categorical covariates). If this argument is set to TRUE, the value of lagi and lag_cumavgi terms are set to their values at time 0. The default is FALSE.

Logical scalar indicating whether the observed data set contains rows for time t < 0.

Numeric scalar specifying lowest value of time t in the observed data set.

Logical scalar indicating whether to print a progress bar for the number of bootstrap samples completed in the R console. This argument is only applicable when parallel is set to FALSE and bootstrap samples are used (i.e., nsamples is set to a value greater than 0). The default is TRUE.

Progress bar R6 object. See progress_bar for further details.

Vector of logicals. The kth element is a logical specifying whether to carry forward the intervened value (rather than the natural value) of the treatment variables(s) when performing a carry forward restriction type for the kth intervention in interventions. When the kth element is set to FALSE, the natural value of the treatment variable(s) in the kth intervention in interventions will be carried forward. By default, this argument is set so that the intervened value of the treatment variable(s) is carried forward for all interventions.

Logical scalar indicating whether to truncate simulated covariates to their range in the observed data set. This argument is only applicable for covariates of type "normal", "bounded normal", "truncated normal", and "zero-inflated normal".

Other arguments, which are passed to the functions in covpredict_custom.

Data table containing the simulated data at time t.

Data table containing the simulated data at times before t.

Character string specifying the name of the variable to be intervened on in each round of the simulation.

A list of length 1. The entry is the value of static treatment to be assigned to intvar.

Character string specifying the name of the time variable in pool and newdf.

Integer specifying the current time index.

Data table containing the simulated data at time t.

Data table containing the simulated data at times before t.

Character string specifying the name of the variable to be intervened on in each round of the simulation.

A list of length 2. The first entry is lower bound of the threshold, and the second entry is the upper bound.

Character string specifying the name of the time variable in pool and newdf.

Integer specifying the current time index.

Object of class "gformula".

Other arguments.

Data table containing all information prior to time t (t noninclusive).

Vector of character strings specifying the names of the variables for which lagged cumulative averages are to be created.

Character string specifying the name of the time variable in pool.

Integer specifying the current time index.

Character string specifying the name of the ID variable in pool.

A vector of one or more values denoting the maximum number of times a binary covariate representing a visit process may be missed before the individual is censored from the data (in the observed data) or a visit is forced (in the simulated data). Multiple values exist in the vector when the modeling of more than covariate is attached to a visit process.