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. For moderate to large data, however, the resulta will be almost identical, numerically, to the ordinary jackknife.

A primary advantage of this approach is computational speed. 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 simply n times the IJ value, where n is the number of uniue subjects in the respective curve. (If the the survfit call included and id option, n is the number of unique id values, otherwise the number of rows in the data set.) IJ values are well defined for all variants of the Aalen-Johansen estimate, as computed by the survfit function; indeed, they are the basis for standard errors of the result.

Understanding of the properties of the pseudo-values 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, one must be cautious when the data includes left-truncation (Parner); and pseudo-values for the cumulative hazard have not been widely explored. When a given subject is spread across multiple (time1, time2) windows with different weights for each of those portions, which can happen with time-dependent inverse probability of censoring (IPW) weights for instance, the current thought is to set both collapse and weight to FALSE, with clustering and weighting as part of the subsequent GEE model; but this is quite tentative. As understanding evolves, treat this routine's results as a reseach tool, not production, for these more complex models.

Value

A vector, matrix, or array. The first dimension is always the number of observations in fit object, in the same order as the original data set (less any missing values that were removed when creating the survfit object); the second, 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, there is only one pseudovalue 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.