MMRM Analysis with zzlongplot

Introduction

Mixed models for repeated measures (MMRM) are the standard primary analysis method for continuous longitudinal endpoints in clinical trials. Regulatory agencies (FDA, EMA) routinely expect MMRM as the primary or sensitivity analysis in confirmatory studies. The zzlongplot package integrates MMRM model fitting (via the mmrm package) with emmeans pairwise contrasts, embedding the results directly into longitudinal plots as significance annotations.

This vignette demonstrates the test_method = "mmrm" option and its interaction with covariance structure selection, p-value adjustment, and visualization.

Simulated clinical trial data

We simulate a two-arm parallel-group trial with four post-baseline visits. The active arm shows a treatment effect emerging at visit 2.

set.seed(42)
n_subj <- 80

df <- data.frame(
  subject_id = rep(1:n_subj, each = 5),
  visit = rep(c(0, 4, 8, 12, 16), times = n_subj),
  group = rep(
    c("Placebo", "Active"), each = 5,
    length.out = n_subj * 5
  )
)

df$measure <- rnorm(nrow(df), mean = 50, sd = 10)
df$measure[df$group == "Active" & df$visit >= 8] <-
  df$measure[df$group == "Active" & df$visit >= 8] - 7

Basic MMRM plot

Setting test_method = "mmrm" fits a mixed model for repeated measures with an interaction between treatment group and visit, then extracts pairwise contrasts at each timepoint via emmeans. Significance stars appear above points where the adjusted p-value crosses the standard thresholds.

lplot(df, measure ~ visit | group,
  baseline_value = 0,
  cluster_var = "subject_id",
  statistical_annotations = TRUE,
  test_method = "mmrm",
  title = "MMRM: Unstructured Covariance (default)")

By default (cov_struct = "auto"), the package selects unstructured covariance for studies with 10 or fewer timepoints and compound symmetry otherwise. If the chosen structure fails to converge, it falls back through progressively simpler structures (heterogeneous Toeplitz, heterogeneous AR(1), compound symmetry) before giving up.

Covariance structure selection

The covariance structure models the within-subject correlation pattern across visits. The choice can affect both model fit and inference. Common options:

• "us" (unstructured): estimates a separate variance for each visit and a separate correlation for each visit pair. The most flexible option and the regulatory default. Requires the most parameters: t(t+1)/2 for t timepoints.

• "cs" (compound symmetry): assumes equal variance across visits and equal correlation between all visit pairs. Only 2 parameters. Appropriate when all timepoints are exchangeable.

• "ar1" (first-order autoregressive): assumes equal variance and exponentially decaying correlation with increasing time lag. Only 2 parameters. Appropriate for equally spaced visits where nearby measurements are more correlated.

• "ar1h" (heterogeneous AR(1)): AR(1) correlation structure but allows each visit to have its own variance. Good when variability changes over time (common in dose-titration studies).

• "toep" / "toeph" (Toeplitz / heterogeneous Toeplitz): correlation depends only on the lag between visits, not which specific visits are compared. A middle ground between AR(1) and unstructured.

• "sp_exp" (spatial exponential): similar to AR(1) but accommodates unequally spaced visits naturally.

lplot(df, measure ~ visit | group,
  baseline_value = 0,
  cluster_var = "subject_id",
  statistical_annotations = TRUE,
  test_method = "mmrm",
  cov_struct = "ar1",
  title = "MMRM: AR(1) Covariance")

lplot(df, measure ~ visit | group,
  baseline_value = 0,
  cluster_var = "subject_id",
  statistical_annotations = TRUE,
  test_method = "mmrm",
  cov_struct = "cs",
  title = "MMRM: Compound Symmetry")

P-value adjustment

The p_adjust_method parameter controls multiple comparison correction. For MMRM, this is passed to emmeans::contrast() as the adjust argument.

lplot(df, measure ~ visit | group,
  baseline_value = 0,
  cluster_var = "subject_id",
  statistical_annotations = TRUE,
  test_method = "mmrm",
  p_adjust_method = "none",
  title = "MMRM: No p-value Adjustment")

lplot(df, measure ~ visit | group,
  baseline_value = 0,
  cluster_var = "subject_id",
  statistical_annotations = TRUE,
  test_method = "mmrm",
  p_adjust_method = "bonferroni",
  title = "MMRM: Bonferroni Adjustment")

Three-arm trial

MMRM with emmeans handles multi-arm trials naturally. For three or more groups, the omnibus test (via emmeans::joint_tests()) is reported at each timepoint, and pairwise contrasts are drawn as bracket annotations below the omnibus p-value. Only significant pairs (after any multiplicity adjustment) are displayed, keeping the figure uncluttered when many comparisons are non-significant.

set.seed(123)
n3 <- 90
df3 <- data.frame(
  subject_id = rep(1:n3, each = 5),
  visit = rep(c(0, 4, 8, 12, 16), times = n3),
  group = rep(
    c("Placebo", "Low Dose", "High Dose"), each = 5,
    length.out = n3 * 5
  )
)
df3$measure <- rnorm(nrow(df3), mean = 50, sd = 10)
df3$measure[df3$group == "Low Dose" & df3$visit >= 8] <-
  df3$measure[df3$group == "Low Dose" & df3$visit >= 8] - 4
df3$measure[df3$group == "High Dose" & df3$visit >= 8] <-
  df3$measure[df3$group == "High Dose" & df3$visit >= 8] - 9

lplot(df3, measure ~ visit | group,
  baseline_value = 0,
  cluster_var = "subject_id",
  statistical_annotations = TRUE,
  test_method = "mmrm",
  title = "Three-Arm MMRM: Dose Response")

Combined with sample size table

The MMRM annotations pair naturally with the below-axis sample size table for a publication-ready figure.

lplot(df, measure ~ visit | group,
  baseline_value = 0,
  cluster_var = "subject_id",
  statistical_annotations = TRUE,
  test_method = "mmrm",
  show_sample_sizes = TRUE,
  sample_size_opts = list(position = "table"),
  theme = "nejm",
  title = "Efficacy Endpoint: MMRM Analysis")

Comparison with pointwise tests

The table below summarizes the three test_method options and their appropriate use cases.

Method	Model	Two groups	Three+ groups	Use case
"parametric"	Independent tests per visit	Welch t-test	ANOVA (omnibus) + pairwise t-tests	Exploratory, descriptive
"nonparametric"	Independent tests per visit	Wilcoxon rank-sum	Kruskal-Wallis (omnibus) + pairwise Wilcoxon	Non-normal data, ordinal endpoints
"mmrm"	Joint model across visits	Pairwise emmeans	Joint test (omnibus) + pairwise emmeans	Primary efficacy analysis, regulatory submissions

Key advantages of MMRM over pointwise tests:

• Borrows information across timepoints through the covariance model, yielding more precise estimates.
• Handles missing data under the missing-at-random (MAR) assumption without imputation.
• Produces valid inference when the dropout pattern depends on observed (but not unobserved) outcomes.
• Aligns with ICH E9(R1) guidance on estimands in clinical trials.

Requirements

The MMRM option requires two additional packages (listed in Suggests, not Imports):

• mmrm: model fitting (Satterthwaite degrees of freedom by default)
• emmeans: estimated marginal means and pairwise contrasts

Install with:

pak::pak(c("mmrm", "emmeans"))

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Rendered on 2026-03-17 at 11:58 PDT. Source: ~/prj/sfw/01-zzlongplot/zzlongplot/vignettes/mmrm-analysis.Rmd