# Survival analysis mostly censored data

I have (another) question regarding survival analysis: If I had two groups of participants (rather small, less than 100, well-matched apart for one or two covariates) exposed to treatments A and B respectively (say, a cancer drug) in a time period of about 5 years, with similar distribution (i.e. similar number of participants recruited each month). A year or two later, in both groups some, but few, have died (say, 2 in group A, but 15 in group B), but most are still alive. In both groups, the majority of individuals have only been followed for 2-3 years.

Given the fact that most of the data is censored, is there a way to estimate the survival function and its CI, as well as compare survival in both groups? Essentially, how would I estimate how likely it is, given current, data that treatment A is or is not more effective than treatment B? Thank you!

Everything you want to do is theoretically possible, following the same procedures as usual for survival analysis. In practice, however, you have very little information, so the conclusion is likely to be that you can't tell which treatment is more effective (e.g. wide confidence intervals on (e.g.) the coefficient giving you the log-hazard difference between the groups).

On the other hand, this quick summary suggests that you might actually have enough information if your numbers of deaths are really approx 2 vs 10.

dd <- data.frame(trt = rep(c("A", "B"), each=100))
set.seed(101)
dd$$time <- rexp(200, rate = ifelse(dd$$trt == "A", 0.02, 0.1))
dd$$death <- dd$$time < 1
dd$$time[!dd$$death] <- 1.0
library(survival)
cc <- coxph(Surv(time, event = death) ~ trt, dd)
> summary(cc)
Call:
coxph(formula = Surv(time, event = death) ~ trt, data = dd)

n= 200, number of events= 13

coef exp(coef) se(coef)    z Pr(>|z|)
trtB 1.7451    5.7267   0.7687 2.27   0.0232 *

• i see, thank you so much! This really helps me! Apr 26, 2022 at 19:09