Stratified log-rank test in R for counting process form data?

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)}