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---
title: FEV1 data comparison between Bayesian and frequentist MMRMs
date: "2024-31-05"
output:
rmarkdown::html_document:
theme: spacelab
highlight: default
toc: yes
toc_float: yes
number_sections: true
vignette: >
%\VignetteIndexEntry{FEV1 data comparison between Bayesian and frequentist MMRMs}
%\VignetteEngine{knitr::rmarkdown}
%\VignetteEncoding{UTF-8}
editor_options:
chunk_output_type: console
markdown:
wrap: 72
---
# About {.unnumbered}
This vignette provides an example comparison of a Bayesian MMRM fit,
obtained by `brms.mmrm::brm_model()`, and a frequentist MMRM fit,
obtained by `mmrm::mmrm()`. An overview of parameter estimates and
differences by type of MMRM is given in the [summary (Tables 4 and 5)](#Summary)
at the end.
# Prerequisites
This comparison workflow requires the following packages.
```r
> packages <- c(
+ "dplyr",
+ "tidyr",
+ "ggplot2",
+ "gt",
+ "gtsummary",
+ "purrr",
+ "parallel",
+ "brms.mmrm",
+ "mmrm",
+ "posterior"
+ )
> invisible(lapply(packages, library, character.only = TRUE))
```
We set a seed for the random number generator to ensure statistical reproducibility.
```r
> set.seed(123L)
```
# Data
## Pre-processing
This analysis exercise uses the `fev_dat` dataset contained in the `mmrm`-package:
```r
> data(fev_data, package = "mmrm")
```
It is an artificial (simulated) dataset of a clinical trial investigating the
effect of an active treatment on `FEV1` (forced expired volume in one second),
compared to placebo. `FEV1` is a measure of how quickly the lungs can be
emptied and low levels may indicate chronic obstructive pulmonary disease
(COPD).
The dataset is a `tibble` with 800 rows and 7 variables:
* `USUBJID` (subject ID),
* `AVISIT` (visit number),
* `ARMCD` (treatment, `TRT` or `PBO`),
* `RACE` (3-category race),
* `SEX` (sex),
* `FEV1_BL` (FEV1 at baseline, %),
* `FEV1` (FEV1 at study visits),
* `WEIGHT` (weighting variable).
The primary endpoint for the analysis is change from baseline in `FEV1`, which we derive below and denote `FEV1_CHG`.
```r
> fev_data <- fev_data |>
+ mutate("FEV1_CHG" = FEV1 - FEV1_BL)
```
The rest of the pre-processing steps create factors for the study arm and visit and apply the usual checking and standardization steps of `brms.mmrm::brm_data()`.
```r
> fev_data <- brm_data(
+ data = fev_data,
+ outcome = "FEV1_CHG",
+ role = "change",
+ group = "ARMCD",
+ time = "AVISIT",
+ patient = "USUBJID",
+ baseline = "FEV1_BL",
+ reference_group = "PBO",
+ covariates = c("RACE", "SEX")
+ ) |>
+ mutate(ARMCD = factor(ARMCD), AVISIT = factor(AVISIT))
```
The following table shows the first rows of the dataset.
```r
> head(fev_data) |>
+ gt() |>
+ tab_caption(caption = md("Table 1. First rows of the pre-processed `fev_dat` dataset."))
```
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<table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
<!--/html_preserve--><caption class='gt_caption'>Table 1. First rows of the pre-processed <code>fev_dat</code> dataset.</caption><!--html_preserve-->
<thead>
<tr class="gt_col_headings">
<th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="FEV1_CHG">FEV1_CHG</th>
<th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1" scope="col" id="FEV1_BL">FEV1_BL</th>
<th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="ARMCD">ARMCD</th>
<th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="AVISIT">AVISIT</th>
<th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="USUBJID">USUBJID</th>
<th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="RACE">RACE</th>
<th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="SEX">SEX</th>
</tr>
</thead>
<tbody class="gt_table_body">
<tr><td headers="FEV1_CHG" class="gt_row gt_right">NA</td>
<td headers="FEV1_BL" class="gt_row gt_right">45.02477</td>
<td headers="ARMCD" class="gt_row gt_center">PBO</td>
<td headers="AVISIT" class="gt_row gt_center">VIS1</td>
<td headers="USUBJID" class="gt_row gt_center">PT2</td>
<td headers="RACE" class="gt_row gt_center">Asian</td>
<td headers="SEX" class="gt_row gt_center">Male</td></tr>
<tr><td headers="FEV1_CHG" class="gt_row gt_right">-13.569552</td>
<td headers="FEV1_BL" class="gt_row gt_right">45.02477</td>
<td headers="ARMCD" class="gt_row gt_center">PBO</td>
<td headers="AVISIT" class="gt_row gt_center">VIS2</td>
<td headers="USUBJID" class="gt_row gt_center">PT2</td>
<td headers="RACE" class="gt_row gt_center">Asian</td>
<td headers="SEX" class="gt_row gt_center">Male</td></tr>
<tr><td headers="FEV1_CHG" class="gt_row gt_right">-8.145878</td>
<td headers="FEV1_BL" class="gt_row gt_right">45.02477</td>
<td headers="ARMCD" class="gt_row gt_center">PBO</td>
<td headers="AVISIT" class="gt_row gt_center">VIS3</td>
<td headers="USUBJID" class="gt_row gt_center">PT2</td>
<td headers="RACE" class="gt_row gt_center">Asian</td>
<td headers="SEX" class="gt_row gt_center">Male</td></tr>
<tr><td headers="FEV1_CHG" class="gt_row gt_right">3.783324</td>
<td headers="FEV1_BL" class="gt_row gt_right">45.02477</td>
<td headers="ARMCD" class="gt_row gt_center">PBO</td>
<td headers="AVISIT" class="gt_row gt_center">VIS4</td>
<td headers="USUBJID" class="gt_row gt_center">PT2</td>
<td headers="RACE" class="gt_row gt_center">Asian</td>
<td headers="SEX" class="gt_row gt_center">Male</td></tr>
<tr><td headers="FEV1_CHG" class="gt_row gt_right">NA</td>
<td headers="FEV1_BL" class="gt_row gt_right">43.50070</td>
<td headers="ARMCD" class="gt_row gt_center">PBO</td>
<td headers="AVISIT" class="gt_row gt_center">VIS1</td>
<td headers="USUBJID" class="gt_row gt_center">PT3</td>
<td headers="RACE" class="gt_row gt_center">Black or African American</td>
<td headers="SEX" class="gt_row gt_center">Female</td></tr>
<tr><td headers="FEV1_CHG" class="gt_row gt_right">-7.513705</td>
<td headers="FEV1_BL" class="gt_row gt_right">43.50070</td>
<td headers="ARMCD" class="gt_row gt_center">PBO</td>
<td headers="AVISIT" class="gt_row gt_center">VIS2</td>
<td headers="USUBJID" class="gt_row gt_center">PT3</td>
<td headers="RACE" class="gt_row gt_center">Black or African American</td>
<td headers="SEX" class="gt_row gt_center">Female</td></tr>
</tbody>
</table>
</div><!--/html_preserve-->
## Descriptive statistics
Table of baseline characteristics:
```{.r .fold-hide}
> fev_data |>
+ select(ARMCD, USUBJID, SEX, RACE, FEV1_BL) |>
+ distinct() |>
+ select(-USUBJID) |>
+ tbl_summary(
+ by = c(ARMCD),
+ statistic = list(
+ all_continuous() ~ "{mean} ({sd})",
+ all_categorical() ~ "{n} / {N} ({p}%)"
+ )
+ ) |>
+ modify_caption("Table 2. Baseline characteristics.")
```
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