1 Introduction

Once the rbmi pipeline has been run and imputed datasets are available, the same imputed data can be reused to analyse derived endpoints without re-running the computationally expensive draws() and impute() steps. This is particularly useful for binary responder endpoints, where the response is defined by whether a subject’s outcome crosses a pre-specified threshold.

This vignette demonstrates how to define binary responder endpoints from imputed continuous data and analyse them using rbmi’s analyse() / pool() machinery via rbmiUtils helper functions. Two types of responder definitions are covered:

Threshold-based responder – using the pre-derived CRIT1FLN column (CHG > 3) already present in the imputed data.
Clinical cutoff responder – deriving a new binary variable from the continuous CHG column using a higher threshold (CHG > 5), demonstrating the flexibility of imputed data reuse.

For the full rbmi workflow including draws(), impute(), and continuous ANCOVA analysis, see the pipeline vignette. This vignette assumes familiarity with rbmi core concepts (draws, impute, analyse, pool).

2 Prerequisites and Setup

We need rbmi for the analysis/pool infrastructure, rbmiUtils for the analysis helpers and reporting functions, and dplyr for data manipulation.

library(rbmi)
library(rbmiUtils)
library(dplyr)

Next, we load the pre-built ADMI dataset bundled with rbmiUtils. This dataset contains 100 imputed copies of a simulated two-arm clinical trial, with continuous change-from-baseline outcomes (CHG) and a pre-derived binary responder variable (CRIT1FLN, defined as CHG > 3).

data("ADMI", package = "rbmiUtils")

Before analysis, we convert the key grouping columns to factors. Factor levels control the ordering of treatment arms and visits, so it is important to set them explicitly.

ADMI <- ADMI |>
  mutate(
    TRT = factor(TRT, levels = c("Placebo", "Drug A")),
    USUBJID = factor(USUBJID),
    AVISIT = factor(AVISIT),
    STRATA = factor(STRATA),
    REGION = factor(REGION)
  )

We also define the analysis variables for the binary responder endpoint. The outcome is CRIT1FLN (the numeric 0/1 responder flag), and we adjust for baseline, stratification, and region.

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

Finally, we specify the method object. This must match the imputation method originally used to create the imputed datasets – here, Bayesian MI with 100 samples.

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

3 Threshold-Based Responder (CHG > 3)

The ADMI dataset already contains the CRIT1FLN column, which flags subjects as responders (1) if their change from baseline exceeds 3, and non-responders (0) otherwise. We can verify this:

Interpreting the results: In this simulated dataset, positive CHG values represent worsening (an increase in symptom score). Therefore CHG > 3 defines “worsening responders” – subjects whose symptoms deteriorated by more than 3 points. A lower responder rate for Drug A compared to Placebo indicates that fewer patients on the active treatment experienced clinically meaningful worsening, which is evidence of drug efficacy.

# The responder criterion is pre-derived
ADMI |>
  distinct(CRIT) |>
  pull(CRIT)
#> [1] "CHG > 3"
#> attr(,"label")
#> [1] "Responder criteria (definition)"

3.1 Analyse

We use analyse_mi_data() with gcomp_responder_multi() as the analysis function. This applies g-computation via logistic regression at each visit, estimating covariate-adjusted marginal treatment effects using the method of Ge et al. (implemented in the beeca package).

ana_obj <- analyse_mi_data(
  data = ADMI,
  vars = vars_binary,
  method = method,
  fun = gcomp_responder_multi,
  reference_levels = "Placebo"
)

3.2 Pool

Pool the per-imputation results using Rubin’s rules:

pool_obj <- pool(ana_obj)

3.3 Results

The tidy_pool_obj() function converts the pool object into a tidy tibble with clearly labelled columns for estimates, standard errors, confidence intervals, and p-values.

tidy_pool_obj(pool_obj)
#> # A tibble: 6 × 10
#>   parameter  description visit parameter_type lsm_type      est      se      lci
#>   <chr>      <chr>       <chr> <chr>          <chr>       <dbl>   <dbl>    <dbl>
#> 1 trt_Drug … Treatment … Week… trt            <NA>     -3.08e-2 1.15e-2 -0.0534 
#> 2 lsm_Drug … Least Squa… Week… lsm            Drug A    7.79e-5 7.85e-4 -0.00146
#> 3 lsm_Place… Least Squa… Week… lsm            Placebo   3.09e-2 1.15e-2  0.00843
#> 4 trt_Drug … Treatment … Week… trt            <NA>     -9.57e-2 2.10e-2 -0.137  
#> 5 lsm_Drug … Least Squa… Week… lsm            Drug A    7.27e-3 5.04e-3 -0.00262
#> 6 lsm_Place… Least Squa… Week… lsm            Placebo   1.03e-1 2.06e-2  0.0627 
#> # ℹ 2 more variables: uci <dbl>, pval <dbl>

The efficacy table presents the results in a regulatory-style format:

efficacy_table(
  pool_obj,
  title = "Responder Analysis: CHG > 3",
  subtitle = "G-computation with Marginal Effects (Ge et al.)",
  arm_labels = c(ref = "Placebo", alt = "Drug A")
)

	Estimate	Std. Error	95% CI	P-value
Responder Analysis: CHG > 3
G-computation with Marginal Effects (Ge et al.)
Week 24
LS Mean (Drug A)	0.00	0.00	(-0.00, 0.00)	0.921
LS Mean (Placebo)	0.03	0.01	(0.01, 0.05)	0.007
Treatment Difference	−0.03	0.01	(-0.05, -0.01)	0.007
Week 48
LS Mean (Drug A)	0.01	0.01	(-0.00, 0.02)	0.150
LS Mean (Placebo)	0.10	0.02	(0.06, 0.14)	< 0.001
Treatment Difference	−0.10	0.02	(-0.14, -0.05)	< 0.001
Pooling method: rubin
Number of imputations: 100
Confidence level: 95%

4 Clinical Cutoff Responder (CHG > 5)

The key advantage of working with imputed continuous data is the flexibility to derive new binary endpoints without re-running the imputation model. Here, we define a more stringent “clinically meaningful improvement” threshold of CHG > 5.

4.1 Derive the New Endpoint

We create a new binary column RESP5 directly from the continuous CHG values in the imputed data:

ADMI_cutoff <- ADMI |>
  mutate(RESP5 = as.numeric(CHG > 5))

We can inspect the responder rates by treatment arm and visit:

ADMI_cutoff |>
  group_by(TRT, AVISIT) |>
  summarise(
    n = n(),
    responders = sum(RESP5),
    rate = mean(RESP5),
    .groups = "drop"
  )
#> # A tibble: 4 × 5
#>   TRT     AVISIT      n responders    rate
#>   <fct>   <fct>   <int>      <dbl>   <dbl>
#> 1 Placebo Week 24 23900        105 0.00439
#> 2 Placebo Week 48 23900        941 0.0394 
#> 3 Drug A  Week 24 26100          0 0      
#> 4 Drug A  Week 48 26100          0 0

4.2 Analyse

We define new analysis variables pointing to the RESP5 outcome and repeat the analysis:

vars_cutoff <- set_vars(
  subjid = "USUBJID",
  visit = "AVISIT",
  group = "TRT",
  outcome = "RESP5",
  covariates = c("BASE", "STRATA", "REGION")
)

ana_obj_cutoff <- analyse_mi_data(
  data = ADMI_cutoff,
  vars = vars_cutoff,
  method = method,
  fun = gcomp_responder_multi,
  reference_levels = "Placebo"
)

4.3 Pool and Display

pool_obj_cutoff <- pool(ana_obj_cutoff)

tidy_pool_obj(pool_obj_cutoff)
#> # A tibble: 6 × 10
#>   parameter         description visit parameter_type lsm_type       est       se
#>   <chr>             <chr>       <chr> <chr>          <chr>        <dbl>    <dbl>
#> 1 trt_Drug A-Place… Treatment … Week… trt            <NA>     -4.39e- 3 4.28e- 3
#> 2 lsm_Drug A_Week … Least Squa… Week… lsm            Drug A    1.58e-11 9.51e-12
#> 3 lsm_Placebo_Week… Least Squa… Week… lsm            Placebo   4.39e- 3 4.28e- 3
#> 4 trt_Drug A-Place… Treatment … Week… trt            <NA>     -4.30e- 2 1.39e- 2
#> 5 lsm_Drug A_Week … Least Squa… Week… lsm            Drug A    4.35e-10 3.45e-11
#> 6 lsm_Placebo_Week… Least Squa… Week… lsm            Placebo   4.30e- 2 1.39e- 2
#> # ℹ 3 more variables: lci <dbl>, uci <dbl>, pval <dbl>

efficacy_table(
  pool_obj_cutoff,
  title = "Responder Analysis: CHG > 5",
  subtitle = "G-computation with Marginal Effects (Ge et al.)",
  arm_labels = c(ref = "Placebo", alt = "Drug A")
)

	Estimate	Std. Error	95% CI	P-value
Responder Analysis: CHG > 5
G-computation with Marginal Effects (Ge et al.)
Week 24
LS Mean (Drug A)	0.00	0.00	(-0.00, 0.00)	0.098
LS Mean (Placebo)	0.00	0.00	(-0.00, 0.01)	0.304
Treatment Difference	0.00	0.00	(-0.01, 0.00)	0.304
Week 48
LS Mean (Drug A)	0.00	0.00	(0.00, 0.00)	< 0.001
LS Mean (Placebo)	0.04	0.01	(0.02, 0.07)	0.002
Treatment Difference	−0.04	0.01	(-0.07, -0.02)	0.002
Pooling method: rubin
Number of imputations: 100
Confidence level: 95%

5 Storing Results as ARD

The Analysis Results Dataset (ARD) format from the pharmaverse provides a standardised long-format representation suitable for downstream use with tools like gtsummary. The pool_to_ard() function converts a pool object into this format:

ard <- pool_to_ard(pool_obj)
print(ard)
#>    group1 group1_level         group2 group2_level   group3 group3_level
#> 1   visit      Week 24 parameter_type          trt lsm_type           NA
#> 2   visit      Week 24 parameter_type          trt lsm_type           NA
#> 3   visit      Week 24 parameter_type          trt lsm_type           NA
#> 4   visit      Week 24 parameter_type          trt lsm_type           NA
#> 5   visit      Week 24 parameter_type          trt lsm_type           NA
#> 6   visit      Week 24 parameter_type          trt lsm_type           NA
#> 7   visit      Week 24 parameter_type          lsm lsm_type       Drug A
#> 8   visit      Week 24 parameter_type          lsm lsm_type       Drug A
#> 9   visit      Week 24 parameter_type          lsm lsm_type       Drug A
#> 10  visit      Week 24 parameter_type          lsm lsm_type       Drug A
#>                      variable variable_level stat_name stat_label   stat
#> 1  trt_Drug A-Placebo_Week 24             NA  estimate   Estimate -0.031
#> 2  trt_Drug A-Placebo_Week 24             NA std.error  Std. Err…  0.012
#> 3  trt_Drug A-Placebo_Week 24             NA  conf.low  95% CI L… -0.053
#> 4  trt_Drug A-Placebo_Week 24             NA conf.high  95% CI U… -0.008
#> 5  trt_Drug A-Placebo_Week 24             NA   p.value    p-value  0.007
#> 6  trt_Drug A-Placebo_Week 24             NA    method     Method  rubin
#> 7          lsm_Drug A_Week 24             NA  estimate   Estimate      0
#> 8          lsm_Drug A_Week 24             NA std.error  Std. Err…  0.001
#> 9          lsm_Drug A_Week 24             NA  conf.low  95% CI L… -0.001
#> 10         lsm_Drug A_Week 24             NA conf.high  95% CI U…  0.002

Each row in the ARD represents a single statistic (estimate, standard error, confidence interval bound, or p-value) for a given parameter, with grouping columns for visit, parameter type, and least-squares-mean type. This format integrates directly into pharmaverse reporting workflows.

6 Caveats

When deriving binary responder endpoints from multiply imputed continuous data, keep the following considerations in mind:

Imputation model assumptions carry forward. The binary endpoints are derived from continuous values that were imputed under a specific model (e.g., Bayesian MMRM with jump-to-reference). The validity of the responder analysis depends on the appropriateness of that continuous imputation model.
Pre-specify responder thresholds. Responder definitions and their thresholds should be documented in the statistical analysis plan before unblinding. Post-hoc threshold selection risks inflating type I error.
Results are conditional on reference-based assumptions. The imputed values – and therefore the derived responder status – reflect the chosen reference-based assumption (e.g., jump-to-reference, copy-reference). Different assumptions will produce different responder rates.

Deriving Endpoints from Imputed Data

2026-02-16