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 adrs_twt dataset to run binary outcome analysis using the maic_anchored function by specifying endpoint_type = "binary".

data(centered_ipd_twt)
data(adrs_twt)

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_twt,
  centered_colnames = centered_colnames
)

# get dummy binary IPD
pseudo_adrs <- get_pseudo_ipd_binary(
  binary_agd = data.frame(
    ARM = c("B", "C", "B", "C"),
    RESPONSE = c("YES", "YES", "NO", "NO"),
    COUNT = c(280, 120, 200, 200)
  ),
  format = "stacked"
)

result <- maic_anchored(
  weights_object = weighted_data,
  ipd = adrs_twt,
  pseudo_ipd = pseudo_adrs,
  trt_ipd = "A",
  trt_agd = "B",
  trt_common = "C",
  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

## $summary
##   trt_ind treatment                 type   n   events events_pct
## 1       C         C IPD, before matching 500 338.0000   67.60000
## 2       A         A IPD, before matching 500 390.0000   78.00000
## 3       C         C  IPD, after matching 500 131.2892   26.25784
## 4       A         A  IPD, after matching 500 142.8968   28.57935
## 5       C         C        AgD, external 320 120.0000   37.50000
## 6       B         B        AgD, external 480 280.0000   58.33333

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).

result$inferential$summary

##          case        OR       LCL       UCL         pval
## 1          AC 1.6993007 1.2809976 2.2541985 2.354448e-04
## 2 adjusted_AC 1.3119021 0.8210000 2.0963303 2.562849e-01
## 3          BC 2.3333333 1.7458092 3.1185794 1.035032e-08
## 4          AB 0.7282717 0.4857575 1.0918611 1.248769e-01
## 5 adjusted_AB 0.5622438 0.3239933 0.9756933 4.061296e-02

Here are model and results before adjustment.

result$inferential$fit$model_before

## 
## Call:  glm(formula = RESPONSE ~ ARM, family = glm_link, data = ipd)
## 
## Coefficients:
## (Intercept)         ARMA  
##      0.7354       0.5302  
## 
## Degrees of Freedom: 999 Total (i.e. Null);  998 Residual
## Null Deviance:       1170 
## Residual Deviance: 1157  AIC: 1161

result$inferential$fit$res_AC_unadj

## $est
## [1] 1.699301
## 
## $se
## [1] 0.2488482
## 
## $ci_l
## [1] 1.280998
## 
## $ci_u
## [1] 2.254199
## 
## $pval
## [1] 0.0002354448

result$inferential$fit$res_AB_unadj

##             result             pvalue 
## "0.73[0.49; 1.09]"            "0.125"

Here are model and results after adjustment.

result$inferential$fit$model_after

## 
## Call:  glm(formula = RESPONSE ~ ARM, family = glm_link, data = ipd, 
##     weights = weights)
## 
## Coefficients:
## (Intercept)         ARMA  
##      0.6559       0.2715  
## 
## Degrees of Freedom: 999 Total (i.e. Null);  998 Residual
## Null Deviance:       495.5 
## Residual Deviance: 493.9     AIC: 454.5

result$inferential$fit$res_AC

## $est
## [1] 1.311902
## 
## $se
## [1] 0.3275028
## 
## $ci_l
## [1] 0.821
## 
## $ci_u
## [1] 2.09633
## 
## $pval
## [1] 0.2562849

result$inferential$fit$res_AB

##             result             pvalue 
## "0.56[0.32; 0.98]"            "0.041"

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. Then, 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 = adrs_twt,
  pseudo_ipd = pseudo_adrs,
  trt_ipd = "A",
  trt_agd = "B",
  trt_common = "C",
  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

## $est
## [1] 0.5622438
## 
## $se
## [1] NA
## 
## $ci_l
## [1] 0.3228615
## 
## $ci_u
## [1] 0.9791133
## 
## $pval
## [1] NA