Log-rank test with time-dependent variable [duplicate] - r

Question

Background: at half-year follow up times for 4y, patients may switch to a different medication group. To account for this, I've converted survival data into counting process form. I want to compare survival curves for medication groups A, B, and C. I am using an extended Cox model but want to do pairwise comparisons of each hazard function or do stratified log-rank tests. pairwise_survdiff throws an error because of the form of my data, I think.
Example data:
x<-data.frame(tstart=rep(seq(0,18,6),3),tstop=rep(seq(6,24,6),3), rx = rep(c("A","B","C"),4), death=c(rep(0,11),1))
x
Problem:
When using survdiff in the survival package,
survdiff(Surv(tstart,tstop,death) ~ rx, data = x)
I get the error:
Error in survdiff(Surv(tstart, tstop, death) ~ rx, data = x) :
Right censored data only
I think this stems from the counting process form, since I can't find an example online that compares survival curves for time-varying covariates.
Question: is there a quick fix to this problem? Or, is there an alternative package/function with the same versatility to compare survival curves, namely using different methods? How can I implement stratified log-rank tests using survidff on counting process form data?
NOTE: this was marked as a known issue in the survminer package, see github issue here, but updating survminer did not solve my issue, and using one time interval, tstop-tstart wouldn't be correct, since that would leave, e.g., multiple entries at 6 months rather than out to the actual interval of risk.

Answer 1

So, here is an example of fitting the model and making the multiple comparisons using multcomp package. Note that this implicitly assumes that administration of treatments A-C is random. Depending on the assumptions about the process, it might be better to fit a multistate model with transitions between treatments and outcome.
library(purrr)
library(dplyr)
#>
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#>
#> filter, lag
#> The following objects are masked from 'package:base':
#>
#> intersect, setdiff, setequal, union
library(survival)
library(multcomp)
#> Loading required package: mvtnorm
#> Loading required package: TH.data
#> Loading required package: MASS
#>
#> Attaching package: 'MASS'
#> The following object is masked from 'package:dplyr':
#>
#> select
#>
#> Attaching package: 'TH.data'
#> The following object is masked from 'package:MASS':
#>
#> geyser
# simulate survival data
set.seed(123)
n <- 200
df <- data.frame(
id = rep(1:n, each = 8),
start = rep(seq(0, 42, by = 6), times = 8),
stop = rep(seq(6, 48, by = 6), times = 8),
rx = sample(LETTERS[1:3], n * 8, replace = T))
df$hazard <- exp(-3.5 -1 * (df$rx == "A") + .5 * (df$rx == "B") +
.5 * (df$rx == "C"))
df_surv <- data.frame(id = 1:n)
df_surv$time <- split(df, f = df$id) %>%
map_dbl(~msm::rpexp(n = 1, rate = .x$hazard, t = .x$start))
df <- df %>% left_join(df_surv)
#> Joining, by = "id"
df <- df %>%
mutate(status = 1L * (time <= stop)) %>%
filter(start <= time)
df %>% head()
#> id start stop rx hazard time status
#> 1 1 0 6 A 0.01110900 13.78217 0
#> 2 1 6 12 C 0.04978707 13.78217 0
#> 3 1 12 18 B 0.04978707 13.78217 1
#> 4 2 0 6 B 0.04978707 22.37251 0
#> 5 2 6 12 B 0.04978707 22.37251 0
#> 6 2 12 18 C 0.04978707 22.37251 0
# fit the model
model <- coxph(Surv(start, stop, status)~rx, data = df)
# define pairwise comparison
glht_rx <- multcomp::glht(model, linfct=multcomp::mcp(rx="Tukey"))
glht_rx
#>
#> General Linear Hypotheses
#>
#> Multiple Comparisons of Means: Tukey Contrasts
#>
#>
#> Linear Hypotheses:
#> Estimate
#> B - A == 0 1.68722
#> C - A == 0 1.60902
#> C - B == 0 -0.07819
# perform multiple comparisons
# (adjusts for multiple comparisons + takes into account correlation of coefficients -> more power than e.g. bonferroni)
smry_rx <- summary(glht_rx)
smry_rx # -> B and C different to A, but not from each other
#>
#> Simultaneous Tests for General Linear Hypotheses
#>
#> Multiple Comparisons of Means: Tukey Contrasts
#>
#>
#> Fit: coxph(formula = Surv(start, stop, status) ~ rx, data = df)
#>
#> Linear Hypotheses:
#> Estimate Std. Error z value Pr(>|z|)
#> B - A == 0 1.68722 0.28315 5.959 <1e-05 ***
#> C - A == 0 1.60902 0.28405 5.665 <1e-05 ***
#> C - B == 0 -0.07819 0.16509 -0.474 0.88
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> (Adjusted p values reported -- single-step method)
# confidence intervals
plot(smry_rx)
Created on 2019-04-01 by the reprex package (v0.2.1)