Unanchored Survival Analysis

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_sat data that was created in calculating_weights vignette and uses adtte_sat and pseudo_ipd_sat outcome datasets to run survival analysis using the maic_unanchored function by specifying endpoint_type = "tte".

Note that parameters ipd and pseudo_ipd in the maic_unanchored function for survival data analysis needs to have the following columns: USUBJID, ARM, EVENT, and TIME. USUBJID in ipd needs to match USUBJID in weights_object. USUBJID in pseudo_ipd is not strictly required, as if left unspecified, subject numbers are assigned using the row indexes.

Furthermore, TIME in both these datasets have to be in days. For instance, when we digitize a KM plot where time is recorded in months, we need to multiply the months by the appropriate factor (i.e. 30.4375) to get the time in days.

If you would like to run an analysis using scaled weights, set normalize_weight to TRUE. One clear benefit of using scaled weights is that the risk table at time = 0 in the Kaplan-Meier curve will match the IPD sample size.

data(centered_ipd_sat)
data(adtte_sat)
data(pseudo_ipd_sat)

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

weighted_data <- estimate_weights(
  data = centered_ipd_sat,
  centered_colnames = centered_colnames
)

result <- maic_unanchored(
  weights_object = weighted_data,
  ipd = adtte_sat,
  pseudo_ipd = pseudo_ipd_sat,
  trt_ipd = "A",
  trt_agd = "B",
  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

##   trt_ind treatment            type records    n.max  n.start    events
## 1       B         B Before matching     300 300.0000 300.0000 178.00000
## 2       A         A Before matching     500 500.0000 500.0000 190.00000
## 3       B         B  After matching     300 300.0000 300.0000 178.00000
## 4       A         A  After matching     500 199.4265 199.4265  65.68878
##       rmean se(rmean)    median  0.95LCL   0.95UCL
## 1  4.303551 0.3367260  2.746131 2.261125  3.320857
## 2  8.709690 0.3551477  7.587627 6.278691 10.288538
## 3  4.303551 0.3367260  2.746131 2.261125  3.320857
## 4 10.166029 0.5499915 11.900015 7.815275 14.873786

# Not shown due to long output
# result$descriptive$survfit_before
# result$descriptive$survfit_after

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

##          case        HR       LCL       UCL         pval
## 1          AB 0.3748981 0.3039010 0.4624815 5.245204e-20
## 2 adjusted_AB 0.2834780 0.2074664 0.3873387 2.473442e-15

Here are models and results before adjustment.

result$inferential$fit$km_before

## Call: survfit(formula = Surv(TIME, EVENT) ~ ARM, data = dat, conf.type = km_conf_type)
## 
##         n events median 0.95LCL 0.95UCL
## ARM=B 300    178   83.6    68.8     101
## ARM=A 500    190  230.9   191.1     313

result$inferential$fit$model_before

## Call:
## coxph(formula = Surv(TIME, EVENT) ~ ARM, data = dat)
## 
##         coef exp(coef) se(coef)      z      p
## ARMA -0.9811    0.3749   0.1071 -9.159 <2e-16
## 
## Likelihood ratio test=80.62  on 1 df, p=< 2.2e-16
## n= 800, number of events= 368

result$inferential$fit$res_AB_unadj

## $est
## [1] 0.3748981
## 
## $se
## [1] 0.0405065
## 
## $ci_l
## [1] 0.303901
## 
## $ci_u
## [1] 0.4624815
## 
## $pval
## [1] 5.245204e-20

Here are models and results after adjustment.

result$inferential$fit$km_after

## Call: survfit(formula = Surv(TIME, EVENT) ~ ARM, data = dat, weights = dat$weights, 
##     conf.type = km_conf_type)
## 
##       records   n events median 0.95LCL 0.95UCL
## ARM=B     300 300  178.0   83.6    68.8     101
## ARM=A     500 199   65.7  362.2   237.9     453

result$inferential$fit$model_after

## Call:
## coxph(formula = Surv(TIME, EVENT) ~ ARM, data = dat, weights = weights, 
##     robust = TRUE)
## 
##         coef exp(coef) se(coef) robust se      z        p
## ARMA -1.2606    0.2835   0.1504    0.1593 -7.915 2.47e-15
## 
## Likelihood ratio test=80.4  on 1 df, p=< 2.2e-16
## n= 800, number of events= 368

result$inferential$fit$res_AB

## $est
## [1] 0.283478
## 
## $se
## [1] 0.04601759
## 
## $ci_l
## [1] 0.2074664
## 
## $ci_u
## [1] 0.3873387
## 
## $pval
## [1] 2.473442e-15

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_unanchored function. Then, the outputs include bootstrapped CI. Different types of bootstrap CI can be found by specifying the parameter boot_ci_type. See boot.ci in boot package for more details.

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

result_boot <- maic_unanchored(
  weights_object = weighted_data2,
  ipd = adtte_sat,
  pseudo_ipd = pseudo_ipd_sat,
  trt_ipd = "A",
  trt_agd = "B",
  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

## $est
## [1] 0.283478
## 
## $se
## [1] NA
## 
## $ci_l
## [1] 0.2144978
## 
## $ci_u
## [1] 0.3740624
## 
## $pval
## [1] NA