RISCA (version 0.8)

ipw.survival: Adjusted Survival Curves by Using IPW.

Description

This function allows to estimate confounder-adjusted survival curves by weighting the individual contributions by the inverse of the probability to be in the group (IPW).

Usage

ipw.survival(times, failures, variable, weights)

Arguments

times

A numeric vector with the follow up times.

failures

A numeric vector with the event indicators (0=right censored, 1=event).

variable

A numeric vector with the binary variable under interest (only two groups).

weights

The weights for correcting the contribution of each individual. By default, the weights are all equaled to 1 and the survival curves correspond to the usual Kaplan-Meier estimator.

Value

table

This data frame presents the survival probabilities (survival) in each group (variable) according to the times. The number of individuals at risk (n.risk) and the number of observed events are also provided (n.event).

Details

For instance, the weights may be equal to 1/p, where p is the estimated probability of the individual to be in its group. The probabilities p are often estimated by a logistic regression in which the dependent binary variable is the group. The possible confounding factors are the covariates of this model.

References

Le Borgne et al. Comparisons of the performances of different statistical tests for time-to-event analysis with confounding factors: practical illustrations in kidney transplantation. Statistics in medicine. 30;35(7):1103-16, 2016. <doi:10.1002/ sim.6777>

Examples

# NOT RUN {
data(dataDIVAT2)

# Kaplan-Meier estimator
res.km <- ipw.survival(times=dataDIVAT2$times, failures=dataDIVAT2$failures,
  variable=dataDIVAT2$ecd, weights=NULL)
plot(NULL,xlim=c(0,13),ylim=c(0,1),ylab="Graft and patient survival",
 xlab="Time post-transplantation (years)")
lines(res.km$times[res.km$variable==1], res.km$survival[res.km$variable==1],
type="s",col=2,lty=2,lwd=2)
lines(res.km$times[res.km$variable==0], res.km$survival[res.km$variable==0],
type="s",col=1,lty=2,lwd=2)

# adjusted Kaplan-Meier estimator by IPW
Pr0 <- glm(ecd ~ 1, family = binomial(link="logit"), data=dataDIVAT2)$fitted.values[1]
Pr1 <- glm(ecd ~ age + hla + retransplant, data=dataDIVAT2,
 family=binomial(link = "logit"))$fitted.values
W <- (dataDIVAT2$ecd==1) * (1/Pr1) + (dataDIVAT2$ecd==0) * (1)/(1-Pr1)
res.akm <-ipw.survival(times=dataDIVAT2$times, failures=dataDIVAT2$failures,
 variable=dataDIVAT2$ecd, weights=W)
lines(res.akm$times[res.akm$variable==1], res.akm$survival[res.akm$variable==1],
 type="s",col=2,lwd=2)
lines(res.akm$times[res.akm$variable==0], res.akm$survival[res.akm$variable==0],
 type="s",col=1,lwd=2)

nb.risk1<-function(x) {sum(dataDIVAT2$times[dataDIVAT2$ecd==0]>x)}
nb.risk2<-function(x) {sum(dataDIVAT2$times[dataDIVAT2$ecd==1]>x)}
segments(x0=0, y0=0.1, x1=13, y1=0.1) 
text(x=6, y=0.12, "number of at-risk patients", cex=0.8)
tps <- seq(1,12,by=1)
text(x=tps, y=rep(0.07,length(tps)), as.character(sapply(tps, FUN="nb.risk1")),
 cex=0.8, col=1)
text(x=tps, y=rep(0.02,length(tps)), as.character(sapply(tps, FUN="nb.risk2")),
 cex=0.8, col=2)
legend("topright", legend=c("Unadjusted estimator for SCD",
 "Adjusted estimator for SCD", "Unadjusted estimator for ECD",
 "Adjusted estimator for ECD"), col=c(1,1,2,2),
 lty=c(2,1,2,1), lwd=2, cex=0.8)
# }