The 'morseTKTD' package.

Description

Advanced methods for a valuable quantitative environmental risk assessment using Bayesian inference of survival Data with toxicokinetics toxicodynamics (TKTD) models. Among others, it facilitates Bayesian inference of the general unified threshold model of survival (GUTS).

References

Stan Development Team (NA). RStan: the R interface to Stan. R package version 2.32.7. https://mc-stan.org

Set of function to test conformity of data

Description

• check_time: check if the time within a time serie is (1) numeric, (2) unique, (3) minimal value is 0.

• check_concentration: check if the concentration is numeric and always positive.

• check_Nsurv: check if the Nsurv is (1) integer and (2) always positive (3) can be NA.

• check_TimeNsurv: check if the pair time - Nsurv within a time serie satisfies (1) Nsurv at t=0 is >0, (2) decreasing.

• check_concNsurv: check if the pair conc - Nsurv within a time serie satisfies that the timeline of concentration covers timeline of Nsurv.

• checking_table: add msg in a data.frame data if check are not all TRUE.

• is_exposure_constant: Test in a well-formed argument to function SurvData if the concentration is constant and different from NA for each replicate (each time-serie).

• is.between: Test if x is between min and max

Usage

check_time(data)

check_concentration(data)

check_Nsurv(data)

check_TimeNsurv(data)

check_concNsurv(data)

checking_table(data, check, msg)

is_exposure_constant(data)

is.between(x, min, max)

Arguments

Value

a boolean TRUE if concentration in replicate is constant, or FALSE if the concentration in at least one of the replicates is time-variable, and/or if NA occurs.

Compute post value on object

Description

compute_Nsurv: compute the number of survival Nsurv

Usage

compute_Nsurv(x, ...)

compute_Ninit(x, ...)

## S3 method for class 'SurvPredict'
compute_Nsurv(x, Ninit = NULL, ...)

Arguments

Value

No return value, called for side effects. Return the same object after computing Number of survivor (Nsurv column) and number of initial individuals (Ninit column).

Extraction methods to recover output of fit object.

Description

• extract_Nsurv_ppc: extract the Nsurv generated with the sampler. To be used for the Posterior Predictive Check (PPC).

• extract_Nsurv_sim: extract the Nsurv generated with the sampler. To be used for the Simulation (sim).

• extract_param: extract parameters of SD or IT models.

• priors_distribution: Return a data.frame with prior density distributions of parameters used in the model.

Usage

extract_Nsurv_ppc(fit)

extract_Nsurv_sim(fit)

extract_param(fit)

priors_distribution(fit, ...)

## S3 method for class 'SurvFit'
priors_distribution(fit, size_sample = 1000, ...)

Arguments

Value

a data.frame with the extracted object from stanfit.

A simulated exposure profile with 11641 time points using FOCUS model.

Description

• FOCUSprofile: A simulated exposure profile with 11641 time points. Exposure profile of 11641 time points used for prediction. A data frame with 11641 observations on the following two variables: time, a vector of class numeric, conc, a vector of class numeric with exposure concentrations, and replicate, a vector of class factor.

Usage

data(FOCUSprofile)

Predict Lethal Concentration at any specified time point.

Description

Predict the Lethal Concentration at any specified time point for a SurvFit object.

The function LCx, x\ the dose required to kill x\ after a specified test duration (time_LCx) (default is the maximum time point of the experiment).

Mathematical definition of x\ denoted LC(x,t), is:

S(LC(x,t), t) = S(0, t)*(1- x/100),

where S(LC(x,t), t) is the survival probability at concentration LC(x,t) at time t, and S(0,t) is the survival probability at no concentration (i.e. concentration is 0) at time t which reflect the background mortality h_b:

S(0, t) = exp(-hb* t).

In the function LCx, we use the median of S(0,t) to rescale the x\

Usage

lcxt(fit, x, t, ...)

## S3 method for class 'SurvFit'
lcxt(
  fit,
  x = 0.5,
  t = NULL,
  exposure_range = NULL,
  interpolate_length = 50,
  ...
)

Arguments

Value

The function returns an object of class LCx, which is a list with the following information:

• X_propSurvival probability of individuals surviving considering the median of the background mortality (i.e. S(0, t)*(1- x/100)).

• X_prop_providedSurvival probability of individuals surviving as provided in arguments (i.e. (100-X)/100).

• time_LCxA number giving the time at which LC_{x} has to be estimated as provided in arguments or if NULL, the latest time point of the experiment is used.

• df_LCxA data.frame with quantiles (median, 2.5\ of LC_{X} at time time_LCx for X\

• df_doseA data.frame with four columns: concentration, and median q50 and 95\ (qinf95 and qsup95) of the survival probability at time time_LCx.

Lethal Profile calculation

Description

Predict the Lethal Profile factor leading to $x$ % of reduction in survival at a specific time $t$.

Generic method for LPxt, a function denoted LP(x,t) for x\

Usage

lpxt(fit, x, ...)

## S3 method for class 'SurvFit'
lpxt(
  fit,
  x = 0.5,
  t = NULL,
  display.exposure = NULL,
  interpolate_length = NULL,
  max.steps = 100,
  accuracy = 0.01,
  ...
)

## S3 method for class 'LPxt'
update(object, accuracy = 0.01, max.steps = 100, ...)

Arguments

Value

returns an object of class LPxt

Create a list giving data to use in Bayesian inference.

Description

Function to build the data list to give to stan

1. Order the data set in replicate and then in time to create a new column i_row used to delimited replicates.

2. Create a matrix of replicate and index "id_row"

3. Compute Nprec = lag of Nsurv

4. return a list of element to be passed to Stan sampler

Create a list of scalars giving priors to use in Bayesian inference.

Usage

modelData(data, model_type, ...)

## S3 method for class 'SurvData'
modelData(data, model_type = c("SD", "IT"), hb_value = NULL, ...)

build_stanData(x)

build_priors(x, model_type = c("SD", "IT"), hb_value = NULL)

Arguments

Value

A list for parameterization of priors for Bayesian inference.

A list for parameterization of priors for Bayesian inference with JAGS.

Posterior predictive check methods

Description

This is the generic ppc S3 method for computing Posterior predictive check. It predicts values with 95 \ values for SurvFit objects.

Usage

ppc(fit, ...)

## S3 method for class 'SurvFit'
ppc(fit, ...)

Arguments

Value

a data.frame of class PPC with the original data point and the response of simulation and 95\ indicates if the observation fall within (green) or outside (red) of the 95\ credible interval.

Plotting method for survDataVar objects

Description

This is the generic plot S3 method for the survDataVar class. It plots the number of survivors as a function of time.

Usage

## S3 method for class 'SurvDataVarExp'
plot(
  x,
  xlab = "Time",
  ylab = "Number of survivors",
  main = NULL,
  one_plot = FALSE,
  add_legend = FALSE,
  ...
)

## S3 method for class 'SurvDataCstExp'
plot(
  x,
  xlab = "Time",
  ylab = "Number of survivors",
  main = NULL,
  one_plot = FALSE,
  ...
)

Arguments

Value

an object of class ggplot, see function ggplot

Plot of the LCxt object

Description

Method for plotting output of lcxt function returning object of class LCxt.

Usage

## S3 method for class 'LCxt'
plot(
  x,
  xlab = "Concentration",
  ylab = "Survival probability",
  main = NULL,
  ...
)

Arguments

Value

an object of class ggplot, see function ggplot

Plot of the LPxt object

Description

Method for plotting output of loxt function returning object of class LPxt.

Usage

## S3 method for class 'LPxt'
plot(
  x,
  plot = "curve",
  xlab = "Time",
  ylab = "Survival probability",
  main = NULL,
  ...
)

Arguments

Value

an object of class ggplot, see function ggplot

Plot an object PPC

Description

The coordinates of black points are the observed values of the number of survivors (pooled replicates) for a given concentration (X-axis) and the corresponding predicted values (Y-axis). 95\ value, colored in green if this interval contains the observed value and in red otherwise. The bisecting line (y = x) is added to the plot in order to see if each prediction interval contains each observed value. As replicates are shifted on the x-axis, this line is represented by steps.

Usage

## S3 method for class 'PPC'
plot(
  x,
  xlab = "Observation",
  ylab = "Prediction",
  main = NULL,
  dodge.width = 0,
  ...
)

Arguments

Value

an object of class ggplot, see function ggplot

Plotting method for SurvPredict objects

Description

This is the generic plot S3 method for the SurvPredict class. It plots concentration-response fit under target time survival analysis.

Usage

## S3 method for class 'SurvPredict'
plot(
  x,
  xlab = "Time",
  ylab = "Number of Survival",
  main = "Survival Probability with 95% Credible Interval",
  background_concentration = FALSE,
  add_legend = FALSE,
  ...
)

Arguments

Value

an object of class ggplot, see function ggplot

Plot of Prior and Posterior distributions

Description

A function to plot priors and posteriors distribution after using the priorPosterior function on a SurvFit object.

Usage

## S3 method for class 'PriorPosterior'
plot(x, ...)

Arguments

Value

an object of class ggplot, see function ggplot

Prediction base on SurvFit objects

Description

This is the generic predict S3 method for the SurvFit class. It provides predicted survival rate for "SD" or "IT" models under constant or time-variable exposure. prediction on constant exposure profile

Note: On constant exposure profiles, the results is explicit (exact), so you don't have to profile

Usage

predict_SurvFitCstExp(
  fit,
  display.exposure = NULL,
  hb_value = NULL,
  interpolate_length = NULL,
  ...
)

predict_cstSD(
  display.exposure = NULL,
  display.parameters = NULL,
  hb_value = NULL,
  interpolate_length = NULL
)

predict_cstIT(
  display.exposure = NULL,
  display.parameters = NULL,
  hb_value = NULL,
  interpolate_length = NULL
)

predict_SurvFitVarExp(
  fit,
  display.exposure = NULL,
  hb_value = NULL,
  interpolate_length = NULL,
  interpolate_method = "linear",
  ...
)

predict_varSD(
  display.exposure = NULL,
  display.parameters = NULL,
  hb_value = NULL,
  interpolate_length = NULL,
  interpolate_method = NULL
)

predict_varIT(
  display.exposure = NULL,
  display.parameters = NULL,
  hb_value = NULL,
  interpolate_length = NULL,
  interpolate_method = NULL
)

predict(fit, ...)

## S3 method for class 'SurvFit'
predict(
  fit,
  display.exposure = NULL,
  hb_value = NULL,
  interpolate_length = NULL,
  interpolate_method = "linear",
  ...
)

Arguments

Value

a list of data.frame with the quantiles of outputs in df_quantiles or all the MCMC chains df_spaghetti

Return Prior and Posterior density of parameters of SurvFit object

Description

This is the generic pp S3 method for the survFitTT class. It plots the predicted values with 95 \ values for SurvFit objects.

The coordinates of black points are the observed values of the number of survivors (pooled replicates) for a given concentration (X-axis) and the corresponding predicted values (Y-axis). 95\ value, colored in green if this interval contains the observed value and in red otherwise. The bisecting line (y = x) is added to the plot in order to see if each prediction interval contains each observed value. As replicates are shifted on the x-axis, this line is represented by steps.

Usage

priorPosterior(fit, ...)

## S3 method for class 'SurvFit'
priorPosterior(fit, ...)

Arguments

Value

a plot of class ggplot

Creates a data set for survival analysis

Description

This function creates a SurvData object from experimental data provided as a data.frame. The resulting object can then be used for plotting and model fitting. It can also be used to generate individual-time estimates.

The x argument describes experimental results from a survival toxicity test. Each line of the data.frame corresponds to one experimental measurement, that is a number of alive individuals at a given concentration at a given time point and in a given replicate. Note that either the concentration or the number of alive individuals may be missing. The data set is inferred to be under constant exposure if the concentration is constant for each replicate and systematically available. The function survData fails if x does not meet the expected requirements. Please run survDataCheck to ensure x is well-formed.

Usage

survData(data, ...)

## S3 method for class 'data.frame'
survData(data, ...)

Arguments

Value

A dataframe of class survData and column replicate as factor.

See Also

survDataCheck

Checks if an object can be used to perform survival analysis

Description

The survDataCheck function can be used to check if an object containing survival data is formatted according to the expectations of the survData function.

Usage

survDataCheck(data, quiet = FALSE)

Arguments

Value

The function returns a dataframe with message describting the error in the formatting of the data. When no error is detected the object is empty.

Fits a TKTD model for survival analysis using Bayesian inference

Description

This function estimates the parameters of a TKTD model ('SD' or 'IT') for survival analysis using Bayesian inference. In this model, the survival rate of individuals is modeled as a function of the chemical compound concentration with a mechanistic description of the effects on survival over time.

The function returns the parameter estimates of Toxicokinetic-toxicodynamic (TKTD) models SD for 'Stochastic Death' or IT fo 'Individual Tolerance'. TKTD models, and particularly the General Unified Threshold model of Survival (GUTS), provide a consistent process-based framework to analyse both time and concentration dependent datasets. In GUTS-SD, all organisms are assumed to have the same internal concentration threshold (denoted z), and, once exceeded, the instantaneous probability to die increases linearly with the internal concentration. In GUTS-IT, the threshold concentration is distributed among all the organisms, and once exceeded in one individual, this individual dies immediately.

This is the generic plot S3 method for the SurvFit class. It plots concentration-response fit under target time survival analysis.

Usage

fit(data, model_type, hb_value, ...)

## S3 method for class 'SurvDataCstExp'
fit(data, model_type, hb_value = NULL, ...)

## S3 method for class 'SurvDataVarExp'
fit(data, model_type, hb_value = NULL, ...)

## S3 method for class 'SurvFit'
plot(
  x,
  xlab = "Time",
  ylab = "Number of Survival",
  main = NULL,
  add_data = TRUE,
  add_legend = FALSE,
  ...
)

Arguments

Value

An object of class stanfit returned by rstan::sampling

an object of class ggplot, see function ggplot

References

Jager, T., Albert, C., Preuss, T. G. and Ashauer, R. (2011) General unified threshold model of survival-a toxicokinetic-toxicodynamic framework for ecotoxicology, Environmental Science and Technology, 45, 2529-2540. 303-314.

Internal predict function

Description

Survival function for "IT" model with external concentration changing with time

Usage

SurvIT_cst(Cw, time, kd, hb, alpha, beta, interpolate_length = NULL)

Arguments

Value

A data.frame with exposure columns time and conc and the resulting probabilisty of survival in Psurv_XX column where XX refer to an MCMC iteration

Internal predict function

Description

Survival function for "IT" model with external concentration changing with time

Usage

SurvIT_var(
  Cw,
  time,
  kd,
  hb,
  alpha,
  beta,
  interpolate_length = NULL,
  interpolate_method = c("linear", "constant")
)

Arguments

Value

A data.frame with exposure columns time and conc and the resulting probabilisty of survival in Psurv_XX column where XX refer to an MCMC iteration

Internal predict function

Description

Survival function for "SD" model with external concentration changing with time

Usage

SurvSD_cst(Cw, time, kd, hb, z, kk, interpolate_length = NULL)

Arguments

Value

A data.frame with exposure columns time and conc and the resulting probabilisty of survival in Psurv_XX column where XX refer to an MCMC iteration

Internal predict function

Description

Survival function for "SD" model with external concentration changing with time

Usage

SurvSD_var(
  Cw,
  time,
  kd,
  hb,
  z,
  kk,
  interpolate_length = NULL,
  interpolate_method = c("linear", "constant")
)

Arguments

Value

A data.frame with exposure columns time and conc and the resulting probabilisty of survival in Psurv_XX column where XX refer to an MCMC iteration

build sub-dataframe of Nsurv without NA

Description

internal function to remove NA in 'replicate', 'time' and 'Nsurv' columns and building 'Nprec' variable. Removing 'conc" column.

Usage

build_dN(subdata)

Arguments

build sub-dataframe of concentration without NA

Description

internal function to remove NA in 'replicate', 'time' and 'conc' columns, remove 'Nsurv' column to only have concentration matrix

Usage

build_dX(subdata)

Arguments

Reproduction and survival data sets of chronic laboratory toxicity tests of cadmium with Daphnia

Description

• cadmium1: Reproduction and survival data sets of chronic laboratory toxicity tests with Daphnia magna freshwater invertebrate exposed to five concentrations of cadmium during 21 days. Five concentrations were tested, with four replicates per concentration. Each replicate contained 10 organisms. Reproduction and survival were monitored at 10 time points.

Usage

data(cadmium1)

References

Billoir, E., Delhaye, H., Forfait, C., Clement, B., Triffault-Bouchet, G., Charles, S. and Delignette-Muller, M.L. (2012) Comparison of toxicity tests with different exposure time patterns: The added value of dynamic modelling in predictive ecotoxicology, Ecotoxicology and Environmental Safety, 75, 80-86.

Reproduction and survival data sets of chronic laboratory toxicity tests of cadmium with snails

Description

• cadmium2: Reproduction and survival data sets of chronic laboratory toxicity tests with snails (Lymnaea stagnalis) exposed to six concentrations of cadmium during 28 days. Six concentrations were tested, with six replicates per concentration. Each replicate contained five organisms. Reproduction and survival were monitored at 17 time points.

Usage

data(cadmium2)

References

Ducrot, V., Askem, C., Azam, D., Brettschneider, D., Brown, R., Charles, S., Coke, M., Collinet, M., Delignette-Muller, M.L., Forfait-Dubuc, C., Holbech, H., Hutchinson, T., Jach, A., Kinnberg, K.L., Lacoste, C., Le Page, G., Matthiessen, P., Oehlmann, J., Rice, L., Roberts, E., Ruppert, K., Davis, J.E., Veauvy, C., Weltje, L., Wortham, R. and Lagadic, L. (2014) Development and validation of an OECD reproductive toxicity test guideline with the pond snail Lymnaea stagnalis (Mollusca, Gastropoda), Regulatory Toxicology and Pharmacology, 70(3), 605-14.

Charles, S., Ducrot, V., Azam, D., Benstead, R., Brettschneider, D., De Schamphelaere, K., Filipe Goncalves, S., Green, J.W., Holbech, H., Hutchinson, T.H., Faber, D., Laranjeiro, F., Matthiessen, P., Norrgren, L., Oehlmann, J., Reategui-Zirena, E., Seeland-Fremer, A., Teigeler, M., Thome, J.P., Tobor Kaplon, M., Weltje, L., Lagadic, L. (2016) Optimizing the design of a reproduction toxicity test with the pond snail Lymnaea stagnalis, Regulatory Toxicology and Pharmacology, vol. 81 pp.47-56.

Reproduction and survival data sets of chronic laboratory toxicity tests of chlordan with Daphnia

Description

• chlordan: Reproduction and survival data sets of chronic laboratory toxicity tests with Daphnia magna freshwater invertebrate exposed to six concentrations of one organochlorine insecticide (chlordan) during 21 days. Six concentrations were tested, with 10 replicates per concentration. Each replicate contained one organism. Reproduction and survival were monitored at 22 time points. See Manar et al. (2009).

Usage

data(chlordan)

References

Manar, R., Bessi, H. and Vasseur, P. (2009) Reproductive effects and bioaccumulation of chlordan in Daphnia magna, Environmental Toxicology and Chemistry, 28(10), 2150-2159.

Reproduction and survival data sets of chronic laboratory toxicity tests of copper on Daphnia

Description

• copper: Reproduction and survival data sets of chronic laboratory toxicity tests with Daphnia magna freshwater invertebrate exposed to five concentrations of copper during 21 days. Five concentrations were tested, with three replicates per concentration. Each replicate contained 20 organisms. Reproduction and survival were monitored at 16 time points.

Usage

data(copper)

References

Billoir, E., Delignette-Muller, M.L., Pery, A.R.R. and Charles, S. (2008) A Bayesian Approach to Analyzing Ecotoxicological Data, Environmental Science & Technology, 42 (23), 8978-8984.

Survival data set of chronic laboratory toxicity tests of dichromate with Daphnia

Description

• dichromate: Survival data set of chronic laboratory toxicity tests with Daphnia magna freshwater invertebrate exposed to six concentrations of one oxidizing agent (potassium dichromate) during 21 days. Six concentrations were tested with one replicate of 50 organisms per concentration. Survival is monitored at 10 time points.

Usage

data(dichromate)

References

Bedaux, J., Kooijman, SALM (1994) Statistical analysis of toxicity tests, based on hazard modeling, Environmental and Ecological Statistics, 1, 303-314.

build array with indices of rows

Description

internal function to build an array from a data-frame to have the indices of rows

Usage

group_array(d)

Arguments

Survival data set of chronic laboratory toxicity tests of propiconazole with Gammarus pulex

Description

• propiconazole: Survival data set of chronic laboratory toxicity tests with Gammarus pulex freshwater invertebrate exposed to eight concentrations of one fungicide (propiconazole) during four days. Eight concentrations were tested with two replicates of 10 organisms per concentration. Survival is monitored at five time points.

Usage

data(propiconazole)

References

Nyman, A.-M., Schirmer, K., Ashauer, R., (2012) Toxicokinetic-toxicodynamic modelling of survival of Gammarus pulex in multiple pulse exposures to propiconazole: model assumptions, calibration data requirements and predictive power, Ecotoxicology, (21), 1828-1840.

Survival data set of chronic laboratory toxicity tests of propiconazole with Gammarus pulex

Description

• propiconazole_pulse_exposure: Survival data set for Gammarus pulex exposed to propiconazole during 10 days with time-variable exposure concentration (non-standard pulsed toxicity experiments). Survival data set of laboratory toxicity tests with Gammarus pulex freshwater invertebrates exposed to several profiles of concentrations (time-variable concentration for each time series) of one fungicide (propiconazole) during 10 days.

Usage

data(propiconazole_pulse_exposure)

References

Nyman, A.-M., Schirmer, K., Ashauer, R., (2012) Toxicokinetic-toxicodynamic modelling of survival of Gammarus pulex in multiple pulse exposures to propiconazole: model assumptions, calibration data requirements and predictive power, Ecotoxicology, (21), 1828-1840.

Table of posterior estimated parameters

Description

create the table of posterior estimated parameters for the survival analyses

Usage

survFit_TKTD_params(mcmc, model_type, hb_value = TRUE)

Arguments

Value

a data.frame with 3 columns (values, CIinf, CIsup) and 3-4rows (the estimated parameters)

Reproduction and survival data sets of a chronic laboratory toxicity tests of zinc with Daphnia

Description

• zinc: Reproduction and survival data sets of a chronic laboratory toxicity tests with Daphnia magna freshwater invertebrate exposed to four concentrations of zinc during 21 days. Four concentrations were tested with three replicates per concentration. Each replicate contained 20 organisms. Reproduction and survival were monitored at 15 time points.

Usage

data(zinc)

References

Billoir, E., Delignette-Muller, M.L., Pery, A.R.R. and Charles, S. (2008) A Bayesian Approach to Analyzing Ecotoxicological Data, Environmental Science & Technology, 42 (23), 8978-8984.