# Storing and Analyzing Imputed Data with rbmiUtils

#### 2025-09-13

# 1 Introduction

This vignette demonstrates how to:

- Perform multiple imputation using the `{rbmi}` package.

- Store and modify the imputed data using `{rbmiUtils}`.

- Analyze the imputed data using:

  - A standard ANCOVA on a continuous endpoint (`CHG`)
  - A binary responder analysis on `CRIT1FLN` using `{beeca}`

This pattern enables reproducible workflows where imputation and analysis can be separated and revisited independently.

# 2 Statistical Context

This approach applies Rubin’s Rules for inference after multiple imputation:

> We fit a model to each imputed dataset, dervive a response variable on the CHG score, extract marginal effects or other statistics of interest, and combine the results into a single inference using Rubin’s combining rules.

# 3 Step 1: Setup and Data Preparation

    library(dplyr)
    library(tidyr)
    library(readr)
    library(purrr)
    library(rbmi)
    library(beeca)
    library(rbmiUtils)

    set.seed(1974)

    data("ADEFF")

    ADEFF <- ADEFF %>%
      mutate(
        TRT = factor(TRT01P, levels = c("Placebo", "Drug A")),
        USUBJID = factor(USUBJID),
        AVISIT = factor(AVISIT)
      )

# 4 Step 2: Define Imputation Model

    vars <- set_vars(
      subjid = "USUBJID",
      visit = "AVISIT",
      group = "TRT",
      outcome = "CHG",
      covariates = c("BASE", "STRATA", "REGION")
    )

    method <- method_bayes(
      n_samples = 100,
      control = control_bayes(warmup = 200, thin = 2)
    )

    dat <- ADEFF %>%
      select(USUBJID, STRATA, REGION, REGIONC, TRT, BASE, CHG, AVISIT)

    draws_obj <- draws(data = dat, vars = vars, method = method)
    #>
    #> SAMPLING FOR MODEL 'rbmi_mmrm' NOW (CHAIN 1).
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    impute_obj <- impute(draws_obj, references = c("Placebo" = "Placebo", "Drug A" = "Placebo"))

    ADMI <- get_imputed_data(impute_obj)

# 5 Step 3: Add Responder Variables

    ADMI <- ADMI %>%
      mutate(
        CRIT1FLN = ifelse(CHG > 3, 1, 0),
        CRIT1FL = ifelse(CRIT1FLN == 1, "Y", "N"),
        CRIT = "CHG > 3"
      )

# 6 Step 4: Continuous Endpoint Analysis (CHG)

    ana_obj_ancova <- analyse_mi_data(
      data = ADMI,
      vars = vars,
      method = method,
      fun = ancova
    )

    pool_obj_ancova <- pool(ana_obj_ancova)
    print(pool_obj_ancova)
    #>
    #> Pool Object
    #> -----------
    #> Number of Results Combined: 100
    #> Method: rubin
    #> Confidence Level: 0.95
    #> Alternative: two.sided
    #>
    #> Results:
    #>
    #>   ========================================================
    #>       parameter      est     se     lci     uci     pval
    #>   --------------------------------------------------------
    #>      trt_Week 24    -2.177  0.182  -2.535  -1.819  <0.001
    #>    lsm_ref_Week 24  0.077   0.131  -0.18   0.334   0.558
    #>    lsm_alt_Week 24   -2.1   0.125  -2.347  -1.854  <0.001
    #>      trt_Week 48    -3.806  0.256  -4.309  -3.304  <0.001
    #>    lsm_ref_Week 48  0.044   0.185  -0.319  0.408   0.811
    #>    lsm_alt_Week 48  -3.762  0.176  -4.107  -3.417  <0.001
    #>   --------------------------------------------------------

    tidy_pool_obj(pool_obj_ancova)
    #> # A tibble: 6 × 10
    #>   parameter       description visit parameter_type lsm_type     est    se    lci
    #>   <chr>           <chr>       <chr> <chr>          <chr>      <dbl> <dbl>  <dbl>
    #> 1 trt_Week 24     Treatment … Week… trt            <NA>     -2.18   0.182 -2.53
    #> 2 lsm_ref_Week 24 Least Squa… Week… lsm            ref       0.0766 0.131 -0.180
    #> 3 lsm_alt_Week 24 Least Squa… Week… lsm            alt      -2.10   0.125 -2.35
    #> 4 trt_Week 48     Treatment … Week… trt            <NA>     -3.81   0.256 -4.31
    #> 5 lsm_ref_Week 48 Least Squa… Week… lsm            ref       0.0442 0.185 -0.319
    #> 6 lsm_alt_Week 48 Least Squa… Week… lsm            alt      -3.76   0.176 -4.11
    #> # ℹ 2 more variables: uci <dbl>, pval <dbl>

# 7 Step 5: Responder Endpoint Analysis (CRIT1FLN)

## 7.1 Define Analysis Function

    gcomp_responder <- function(data, ...) {
      model <- glm(CRIT1FLN ~ TRT + BASE + STRATA + REGION, data = data, family = binomial)

      marginal_fit <- get_marginal_effect(
        model,
        trt = "TRT",
        method = "Ge",
        type = "HC0",
        contrast = "diff",
        reference = "Placebo"
      )

      res <- marginal_fit$marginal_results
      list(
        trt = list(
          est = res[res$STAT == "diff", "STATVAL"][[1]],
          se = res[res$STAT == "diff_se", "STATVAL"][[1]],
          df = NA
        )
      )
    }

## 7.2 Define Variables and Run Analysis

    vars_binary <- set_vars(
      subjid = "USUBJID",
      visit = "AVISIT",
      group = "TRT",
      outcome = "CRIT1FLN",
      covariates = c("BASE", "STRATA", "REGION")
    )

    ana_obj_prop <- analyse_mi_data(
      data = ADMI,
      vars = vars_binary,
      method = method,
      fun = gcomp_responder
    )

    pool_obj_prop <- pool(ana_obj_prop)
    print(pool_obj_prop)
    #>
    #> Pool Object
    #> -----------
    #> Number of Results Combined: 100
    #> Method: rubin
    #> Confidence Level: 0.95
    #> Alternative: two.sided
    #>
    #> Results:
    #>
    #>   ==================================================
    #>    parameter   est     se     lci     uci     pval
    #>   --------------------------------------------------
    #>       trt     -0.063  0.012  -0.087  -0.039  <0.001
    #>   --------------------------------------------------

# 8 Final Notes

- The `ADMI` object can be saved for later reuse.
- Analyses can be modularly applied using custom functions.
- The tidy output from `tidy_pool_obj()` is helpful for reporting and review.