Anchored Survival Analysis
In maicplus: Matching Adjusted Indirect Comparison

knitr::opts_chunk$set(warning = FALSE, message = FALSE)

Loading R packages

# install.packages("maicplus")
library(maicplus)

Additional R packages for this vignette:

library(dplyr)

Illustration using example data

This example reads in centered_ipd_twt data that was created in calculating_weights vignette and uses adtte_twt and pseudo_ipd_twt datasets to run survival analysis using the maic_anchored function by specifying endpoint_type = "tte".

Set up is very similar to unanchored_survival vignette, except now that we have a common treatment between two trials. Common treatment has to have same name in the data and we need to specify additional parameter, trt_common, in maic_unanchored.

data(centered_ipd_twt)
data(adtte_twt)
data(pseudo_ipd_twt)

centered_colnames <- c("AGE", "AGE_SQUARED", "SEX_MALE", "ECOG0", "SMOKE", "N_PR_THER_MEDIAN")
centered_colnames <- paste0(centered_colnames, "_CENTERED")

#### derive weights
weighted_data <- estimate_weights(
  data = centered_ipd_twt,
  centered_colnames = centered_colnames
)

# inferential result
result <- maic_anchored(
  weights_object = weighted_data,
  ipd = adtte_twt,
  pseudo_ipd = pseudo_ipd_twt,
  trt_ipd = "A",
  trt_agd = "B",
  trt_common = "C",
  normalize_weight = FALSE,
  endpoint_name = "Overall Survival",
  endpoint_type = "tte",
  eff_measure = "HR",
  time_scale = "month",
  km_conf_type = "log-log"
)

There are two summaries available in the result: descriptive and inferential. In the descriptive section, we have summaries from fitting survfit function. Note that restricted mean (rmean), median, and 95% CI are summarized in the time_scale specified.

result$descriptive$summary

# Not shown due to long output
# result$descriptive$survfit_ipd_before
# result$descriptive$survfit_ipd_after
# result$descriptive$survfit_pseudo

In the inferential section, we have the fitted models stored (i.e. survfit and coxph) and the results from the coxph models (i.e. hazard ratios and CI). Note that the p-values summarized are from coxph model Wald test and not from a log-rank test. Here is the overall summary.

result$inferential$summary

Here are models and results before adjustment.

result$inferential$fit$km_before
result$inferential$fit$model_before
result$inferential$fit$res_AC_unadj
result$inferential$fit$res_AB_unadj

Here are models and results after adjustment.

result$inferential$fit$km_after
result$inferential$fit$model_after
result$inferential$fit$res_AC
result$inferential$fit$res_AB

# heuristic check
# merge in adtte with ipd_matched

ipd <- adtte_twt
ipd$weights <- weighted_data$data$weights[match(ipd$USUBJID, weighted_data$data$USUBJID)]

pseudo_ipd <- pseudo_ipd_twt
pseudo_ipd$weights <- 1

# Change the reference treatment to C
ipd$ARM <- stats::relevel(as.factor(ipd$ARM), ref = "C")
pseudo_ipd$ARM <- stats::relevel(as.factor(pseudo_ipd$ARM), ref = "C")

# Fit a Cox model with/without weights to estimate the HR
unweighted_cox <- coxph(Surv(TIME, EVENT == 1) ~ ARM, data = ipd)
weighted_cox <- coxph(Surv(TIME, EVENT == 1) ~ ARM,
  data = ipd, weights = weights, robust = TRUE
)
coxobj_agd <- coxph(Surv(TIME, EVENT) ~ ARM, pseudo_ipd)

unweighted_cox
weighted_cox
coxobj_agd

res_AC_unadj <- as.list(summary(unweighted_cox)$coef)[c(1, 3)] # est, se
res_AC <- as.list(summary(weighted_cox)$coef)[c(1, 4)] # est, robust se
res_BC <- as.list(summary(coxobj_agd)$coef)[c(1, 3)] # est, se

names(res_AC_unadj) <- names(res_AC) <- names(res_BC) <- c("est", "se")

res_AB_unadj <- bucher(res_AC_unadj, res_BC, conf_lv = 0.95)
res_AB <- bucher(res_AC, res_BC, conf_lv = 0.95)

res_AB_unadj
res_AB

kmobj <- survfit(Surv(TIME, EVENT) ~ ARM, ipd, conf.type = "log-log")
kmobj_adj <- survfit(Surv(TIME, EVENT) ~ ARM,
  ipd,
  weights = ipd$weights, conf.type = "log-log"
)

# Derive median survival time
medSurv <- medSurv_makeup(kmobj, legend = "before matching", time_scale = "day")
medSurv_adj <- medSurv_makeup(kmobj_adj, legend = "after matching", time_scale = "day")
medSurv_out <- rbind(medSurv, medSurv_adj)
medSurv_out

Using bootstrap to calculate standard errors

If bootstrap standard errors are preferred, we need to specify the number of bootstrap iteration (n_boot_iteration) in estimate_weights function and proceed fitting maic_anchored function. Now, the outputs include bootstrapped CI. Different types of bootstrap CI can be found by using parameter boot_ci_type.

weighted_data2 <- estimate_weights(
  data = centered_ipd_twt,
  centered_colnames = centered_colnames,
  n_boot_iteration = 100,
  set_seed_boot = 1234
)

result_boot <- maic_anchored(
  weights_object = weighted_data2,
  ipd = adtte_twt,
  pseudo_ipd = pseudo_ipd_twt,
  trt_ipd = "A",
  trt_agd = "B",
  trt_common = "C",
  normalize_weight = FALSE,
  endpoint_name = "Overall Survival",
  endpoint_type = "tte",
  eff_measure = "HR",
  boot_ci_type = "perc",
  time_scale = "month",
  km_conf_type = "log-log"
)

result_boot$inferential$fit$boot_res_AB