# Storing and Analyzing Imputed Data with rbmiUtils

#### 2026-02-16

# 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.

Related vignettes:

- Data Preparation and Validation - Validate data before imputation
- Efficient Storage of Imputed Data - Reduce storage for large imputations

# 2 Statistical Context

This approach applies Rubin’s Rules for inference after multiple imputation (see the rbmi quickstart vignette for background on the draws/impute/analyse/pool pipeline):

> We fit a model to each imputed dataset, derive 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

We use `rbmi::set_vars()` to specify the key variable roles:

    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)
    #>
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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)
    #>        parameter   visit   est   lci   uci    pval
    #>      trt_Week 24 Week 24 -2.18 -2.53 -1.82 < 0.001
    #>  lsm_ref_Week 24 Week 24  0.08 -0.18  0.33   0.560
    #>  lsm_alt_Week 24 Week 24 -2.10 -2.35 -1.85 < 0.001
    #>      trt_Week 48 Week 48 -3.81 -4.31 -3.30 < 0.001
    #>  lsm_ref_Week 48 Week 48  0.04 -0.32  0.41   0.814
    #>  lsm_alt_Week 48 Week 48 -3.76 -4.11 -3.42 < 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       0.0764 0.131 -0.181
    #> 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       0.0436 0.185 -0.320
    #> 6 lsm_alt_Week 48 Least Squa… Week… lsm            alt      -3.76   0.175 -4.11
    #> # ℹ 2 more variables: uci <dbl>, pval <dbl>

# 7 Step 5: Responder Endpoint Analysis (CRIT1FLN)

## 7.1 Define Analysis Function

We use `beeca::get_marginal_effect()` for robust variance estimation of marginal treatment effects from the logistic model:

    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)
    #>  parameter visit   est   lci   uci    pval
    #>        trt  <NA> -0.06 -0.09 -0.04 < 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

## 8.1 Efficient Storage

When working with many imputations, consider using `reduce_imputed_data()` to store only the imputed values:

    # Reduce for efficient storage
    reduced <- reduce_imputed_data(ADMI, ADEFF, vars)

    # Later, expand back for analysis
    ADMI_restored <- expand_imputed_data(reduced, ADEFF, vars)

See the Efficient Storage vignette for details.

## 8.2 See Also

For a guided tutorial walking through the complete pipeline from raw data to regulatory tables, see `vignette('pipeline')`.