Unanchored Binary 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_sat data that was created in calculating_weights vignette and uses adrs_sat dataset to run binary outcome analysis using the maic_unanchored function by specifying endpoint_type = "binary".

Note that parameters ipd and pseudo_ipd in the maic_unanchored function for binary data analysis needs to have the following columns: USUBJID, ARM, RESPONSE. USUBJID in ipd needs to match USUBJID in weights_object. pseudo_ipd for binary data can be conveniently generated using get_pseudo_ipd_binary function.

Robust standard error for the adjusted result are calculated by sandwich variance estimator in sandwich package with the function vcovHC. Default type of variance estimator (specified by parameter binary_robust_cov_type) is HC3, but other types can be specified. For more information on different types, see vcovHC.

data(centered_ipd_sat)
data(adrs_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
)

# get dummy binary pseudo IPD
pseudo_adrs <- get_pseudo_ipd_binary(
  binary_agd = data.frame(
    ARM = "B",
    RESPONSE = c("YES", "NO"),
    COUNT = c(280, 120)
  ),
  format = "stacked"
)

result <- maic_unanchored(
  weights_object = weighted_data,
  ipd = adrs_sat,
  pseudo_ipd = pseudo_adrs,
  trt_ipd = "A",
  trt_agd = "B",
  normalize_weight = FALSE,
  endpoint_type = "binary",
  endpoint_name = "Binary Endpoint",
  eff_measure = "OR",
  # binary specific args
  binary_robust_cov_type = "HC3"
)

There are two summaries available in the result: descriptive and inferential. In the descriptive section, we have summaries of events.

result$descriptive

In the inferential section, we have the fitted models stored (i.e. logistic regression) and the results from the glm models (i.e. odds ratios and CI). If other effect measures are needed besides odds ratios, we have an option to fit risk ratios or risk differences via eff_measure parameter. Here is the overall summary.

result$inferential$summary

Here are model and results before adjustment.

result$inferential$fit$model_before
result$inferential$fit$res_AB_unadj

Here are model and results after adjustment.

result$inferential$fit$model_after
result$inferential$fit$res_AB

# heuristic check
# merge in adrs with ipd_matched
ipd_matched <- weighted_data$data
combined_data_binary <- ipd_matched %>%
  left_join(adrs_sat, by = c("USUBJID", "ARM"))
pseudo_adrs$weights <- 1

combined_data_binary <- rbind(
  combined_data_binary[, colnames(pseudo_adrs)],
  pseudo_adrs
)

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

binobj_dat <- glm(RESPONSE ~ ARM, combined_data_binary, family = binomial(link = "logit"))
binobj_dat_adj <- suppressWarnings(
  glm(RESPONSE ~ ARM, combined_data_binary,
    weights = weights,
    family = binomial(link = "logit")
  )
)

bin_robust_cov <- sandwich::vcovHC(binobj_dat_adj, type = "HC3")
bin_robust_coef <- lmtest::coeftest(binobj_dat_adj, vcov. = bin_robust_cov)
bin_robust_ci <- lmtest::coefci(binobj_dat_adj, vcov. = bin_robust_cov)

bin_robust_ci
exp(bin_robust_ci)

exp(summary(binobj_dat)$coef[2, "Estimate"])
exp(summary(binobj_dat_adj)$coef[2, "Estimate"])

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 using 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 = adrs_sat,
  pseudo_ipd = pseudo_adrs,
  trt_ipd = "A",
  trt_agd = "B",
  normalize_weight = FALSE,
  endpoint_type = "binary",
  endpoint_name = "Binary Endpoint",
  eff_measure = "OR",
  boot_ci_type = "perc",
  # binary specific args
  binary_robust_cov_type = "HC3"
)

result_boot$inferential$fit$boot_res_AB

Note that the bootstrap in unanchored analysis only uses resampling of internal IPD trial population and assumes there is no uncertainty in the comparator trial population (i.e. estimated mean outcomes). [@chandler] Therefore, we recommend the use of sandwich estimators for the variance calculation in the unanchored analysis.