cumulative survival rate after weighting using survey::svykm() - r

Question

I used the survey package to draw a weighted Kaplan Meier survival plot, like this:
library(survey)
data(pbc, package="survival")
pbc$randomized <- with(pbc, !is.na(trt) & trt>0)
biasmodel <- glm(randomized~age*edema,data=pbc)
pbc$randprob <- fitted(biasmodel)
dpbc<-svydesign(id=~1, prob=~randprob, strata=~edema, data=subset(pbc,randomized))
s2 <-svykm(Surv(time,status>0) ~ sex, design = dpbc)
svyjskm(s2, pval = T, table = T, design = dpbc)
Now I would like to calculate the survival rates in the two groups, similar to what I would get when using summary(x, times = c(1:5)) on a survfit object. Does anybody know how I can extract these values?
Many thanks in advance!

Answer 1

Saving survival probabilities to data frames
The time and survival probability values can be extracted from the svykm object ("s2") and saved in separate data frames for females ("s2_data_f") and males ("s2_data_m") using the following codes:
s2_data_f <- data.frame(time = s2[["f"]][["time"]], surv = s2[["f"]][["surv"]])
s2_data_m <- data.frame(time = s2[["m"]][["time"]], surv = s2[["m"]][["surv"]])
Note that not all time values will be available in the data (e.g. no one has time = 5) and for these values the nearest smaller value should be taken (e.g. for time = 5 the value for time = 0 should be used which is 100% survival).
Functions to extract survival probabilities or time values from data frames
Below is a function that locates the row in "s2_data_f" with a specified time value (or the nearest smaller time value) and returns the corresponding survival probability value.
return_surv_f <- function(x) {
time <- max(s2_data_f$time[s2_data_f$time <= x])
return(s2_data_f$surv[s2_data_f$time==time])
}
Similarly, for males ("s2_data_m") the function would be:
return_surv_m <- function(x) {
time <- max(s2_data_m$time[s2_data_m$time <= x])
return(s2_data_m$surv[s2_data_m$time==time])
}
These functions can then be used with "sapply" to return survival probability results for one or more chosen time values.
sapply(c(1:5), return_surv_f)
sapply(c(1:5), return_surv_m)
If you need to get the results in reverse (i.e. find the time corresponding with a specific survival probability) the "quantile" function can be used. For example, if you want to know at what time 75% of participants were alive then:
quantile(s2[["f"]], probs = 0.75)
quantile(s2[["m"]], probs = 0.75)
Confidence intervals or standard errors for survival probabilities
If you wish to calculate confidence intervals or standard errors for the survival probabilities then "se = TRUE" must be added to the svykm function.
s2 <- svykm(Surv(time,status>0) ~ sex, design = dpbc, se = TRUE)
Note however that this changes the statistical method with the R survey package documentation stating that:
"When standard errors are computed, the survival curve is actually the
Aalen (hazard-based) estimator rather than the Kaplan-Meier estimator."
Confidence intervals can then be obtained using "confint" with one or more time values specified in "parm =".
confint(s2[["f"]], parm = c(1000:1005), level = 0.95)
confint(s2[["m"]], parm = c(1000:1005), level = 0.95)
Standard errors can be obtained from the "varlog" values.
s2_data_f <- data.frame(varlog = s2[["f"]][["varlog"]])
s2_data_m <- data.frame(varlog = s2[["m"]][["varlog"]])
Example of a data frame including survival probabilities and their confidence intervals:
s2_results_f <- data.frame(
time = c(1000:1005),
surv = sapply(c(1000:1005), return_surv_f),
CI = confint(s2[["f"]], parm = c(1000:1005), level = 0.95)
)
s2_results_f[2:4] <- round(s2_results_f[2:4], 2)*100
s2_results_f[2:4] <- paste0(unlist(s2_results_f[2:4]), "%")
names(s2_results_f)[1:4] <- c("Follow-up time", "Survival probability", "95% CI lower", "95% CI upper")