Pseudo values for survival.

Description

Produce pseudo values from a survival curve.

Usage

pseudo(fit, times, type, collapse= TRUE, data.frame=FALSE, ...) 

Arguments

Details

This function computes pseudo values based on a first order Taylor series, also known as the "infinitesimal jackknife" (IJ) or "dfbeta" residuals. To be completely correct the results of this function could perhaps be called ‘IJ pseudo values’ or even pseudo psuedo-values to distinguish them from Andersen and Pohar-Perme. For moderate to large data, however, the result will be almost identical, numerically, to the ordinary jackknife psuedovalues.

A primary advantage of this approach is computational speed. Two other features, neither good nor bad, are that they will agree with robust standard errors of other survival package estimates, which are based on the IJ, and that the mean of the estimates, over subjects, is exactly the underlying survival estimate.

For the type variable, surv is an acceptable synonym for pstate, chaz for cumhaz, and rmst,rmts and auc are equivalent to sojourn. All of these are case insensitive.

If the orginal survfit call produced multiple curves, the internal computations are done separately for each curve. The result from this routine is the IJ (as computed by resid.survfit) scaled by n and then recentered. If the the survfit call included an id option, n is the number of unique id values, otherwise the number of rows in the data set. If the original survfit call used case weights, those weights are part of the IJ residuals, but are not used to compute the rescaling factor n.

IJ values are well defined for all variants of the Aalen-Johansen estimate; indeed, they are the basis for standard errors of the result. However, understanding properties of the pseudovalues is still evolving. Validity has been verified for the probability in state and sojourn times whenever all subjects start in the same state; this includes for instance the usual Kaplan-Meier and competing risks cases. On the other hand, regression results based on pseudovalues from left-truncated data will be biased (Parner); and pseudo-values for the cumulative hazard have not been widely explored. When a given subject is spread across multiple (time1, time2) windows, e.g., a data set with a time-dependent covariate, the IJ values from a simple survival (without TD variables) will sum to the overall IJ for that subject; however, whether and how these partial pseudovalues can be directly used in a model is still uncertain. As understanding evolves, treat this routine's results as a reseach tool, not production, for these more complex cases.

Value

A vector, matrix, or array. The first dimension is always the number of observations in the data object, in the same order as the original data set (less any missing values that were removed when creating the survfit object); the second dimension, if applicable, corresponds to fit$states, e.g., multi-state survival, and the last dimension to the selected time points. (If there are multiple rows for a given id and collapse=TRUE, there is only one row per unique id.)

For the data.frame option, a data frame containing values for id, time, and pseudo. If the original survfit call contained an id statement, then the values in the id column will be taken from that variable. If the id statement has a simple form, e.g., id = patno, then the name of the id column will be ‘patno’, otherwise it will be named ‘(id)’.

Note

The code will be slightly faster if the model=TRUE option is used in the survfit call. It may be essential if the survfit/pseudo pair is used inside another function.

References

PK Andersen and M Pohar-Perme, Pseudo-observations in surivival analysis, Stat Methods Medical Res, 2010; 19:71-99

ET Parner, PK Andersen and M Overgaard, Regression models for censored time-to-event data using infinitesimal jack-knife pseudo-observations, with applications to left-truncation, Lifetime Data Analysis, 2023, 29:654-671

See Also

residuals.survfit

Examples

fit1 <- survfit(Surv(time, status) ~ 1, data=lung)
yhat <- pseudo(fit1, times=c(365, 730))
dim(yhat)
lfit <- lm(yhat[,1] ~ ph.ecog + age + sex, data=lung)

# Restricted Mean Time in State (RMST) 
rms <- pseudo(fit1, times= 730, type='RMST') # 2 years
rfit <- lm(rms ~ ph.ecog + sex, data=lung)
rhat <- predict(rfit, newdata=expand.grid(ph.ecog=0:3, sex=1:2), se.fit=TRUE)
# print it out nicely
temp1 <- cbind(matrix(rhat$fit, 4,2))
temp2 <- cbind(matrix(rhat$se.fit, 4, 2))
temp3 <- cbind(temp1[,1], temp2[,1], temp1[,2], temp2[,2])
dimnames(temp3) <- list(paste("ph.ecog", 0:3), 
                        c("Male RMST", "(se)", "Female RMST", "(se)"))

round(temp3, 1)
# compare this to the fully non-parametric estimate
fit2 <- survfit(Surv(time, status) ~ ph.ecog, data=lung)
print(fit2, rmean=730)
# the estimate for ph.ecog=3 is very unstable (n=1), pseudovalues smooth it.
#
# In all the above we should be using the robust variance, e.g., svyglm, but
#  a recommended package can't depend on external libraries.
# See the vignette for a more complete exposition.