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 500.0000 338.0000 67.60000
## 2 A A IPD, before matching 500.0000 390.0000 78.00000
## 3 C C IPD, after matching 199.4265 134.0364 67.21094
## 4 A A IPD, after matching 199.4265 142.8968 71.65386
## 5 C C AgD, external 320.0000 120.0000 37.50000
## 6 B B AgD, external 480.0000 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 1.2332036 0.7710134 1.9724576 3.817109e-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 0.5285158 0.3043103 0.9179084 2.356848e-02

Here are model and results before adjustment.

result$inferential$fit$model_before

## 
## Call: glm(formula = RESPONSE ~ ARM, family = binomial(link = 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 = binomial(link = glm_link), 
## data = ipd, weights = weights)
## 
## Coefficients:
## (Intercept) ARMA 
## 0.7177 0.2096 
## 
## Degrees of Freedom: 999 Total (i.e. Null); 998 Residual
## Null Deviance: 491.1 
## Residual Deviance: 490.1 AIC: 458.4

result$inferential$fit$res_AC

## $est
## [1] 1.233204
## 
## $se
## [1] 0.3085377
## 
## $ci_l
## [1] 0.7710134
## 
## $ci_u
## [1] 1.972458
## 
## $pval
## [1] 0.3817109

result$inferential$fit$res_AB

## result pvalue 
## "0.53[0.30; 0.92]" "0.024"

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] 0.5285158
## 
## $se
## [1] NA
## 
## $ci_l
## [1] 0.3034937
## 
## $ci_u
## [1] 0.9203782
## 
## $pval
## [1] NA