mmrm

Mixed models for repeated measures (MMRM) are a popular choice for analyzing longitudinal continuous outcomes in randomized clinical trials and beyond; see Cnaan, Laird and Slasor (1997) for a tutorial and Mallinckrodt, Lane and Schnell (2008) for a review. This package implements MMRM based on the marginal linear model without random effects using Template Model Builder (TMB) which enables fast and robust model fitting. Users can specify a variety of covariance matrices, weight observations, fit models with restricted or standard maximum likelihood inference, perform hypothesis testing with Satterthwaite or Kenward-Roger adjustment, and extract least square means estimates by using emmeans.

Scope:

• Continuous responses with normal (but potentially heteroscedastic) residuals.
• Marginal linear models (no individual-level random effects).

Main Features:

• Flexible covariance specification:
  • Structures: unstructured, Toeplitz, AR1, compound symmetry, ante-dependence, and spatial exponential.
  • Groups: shared covariance structure for all subjects or group-specific covariance estimates.
  • Variances: homogeneous or heterogeneous across time points.
• Hypothesis testing:
  • Least square means: can be obtained with the emmeans package
  • One- and multi-dimensional linear contrasts of model parameters can be tested.
  • Satterthwaite adjusted degrees of freedom.
  • Kenward-Roger adjusted degrees of freedom and coefficients covariance matrix.
• Model inference:
  • Supports REML and ML.
  • Supports weights.
• Fast implementation using C++ and automatic differentiation to obtain precise gradient information for model fitting. See here for details of the model fitting algorithm used in mmrm.

Installation

CRAN

You can install the current stable version from CRAN with:

install.packages("mmrm")

GitHub

You can install the current development version from GitHub with:

if (!require("remotes")) {
  install.packages("remotes")
}
remotes::install_github("openpharma/mmrm")

Getting Started

See also the introductory vignette or get started by trying out the example:

library(mmrm)
fit <- mmrm(
  formula = FEV1 ~ RACE + SEX + ARMCD * AVISIT + us(AVISIT | USUBJID),
  data = fev_data
)

The code specifies an MMRM with the given covariates and an unstructured covariance matrix for the timepoints (also called visits in the clinical trial context, here given by AVISIT) within the subjects (here USUBJID). While by default this uses restricted maximum likelihood (REML), it is also possible to use ML, see ?mmrm.

You can look at the results high-level:

fit
#> mmrm fit
#> 
#> Formula:     FEV1 ~ RACE + SEX + ARMCD * AVISIT + us(AVISIT | USUBJID)
#> Data:        fev_data (used 537 observations from 197 subjects with maximum 4 
#> timepoints)
#> Covariance:  unstructured (10 variance parameters)
#> Method:      REML
#> Deviance:    3386.45
#> 
#> Coefficients: 
#>                   (Intercept) RACEBlack or African American 
#>                   30.77747548                    1.53049977 
#>                     RACEWhite                     SEXFemale 
#>                    5.64356535                    0.32606192 
#>                      ARMCDTRT                    AVISITVIS2 
#>                    3.77423004                    4.83958845 
#>                    AVISITVIS3                    AVISITVIS4 
#>                   10.34211288                   15.05389826 
#>           ARMCDTRT:AVISITVIS2           ARMCDTRT:AVISITVIS3 
#>                   -0.04192625                   -0.69368537 
#>           ARMCDTRT:AVISITVIS4 
#>                    0.62422703 
#> 
#> Model Inference Optimization:
#> Converged with code 0 and message: convergence: rel_reduction_of_f <= factr*epsmch

The summary() method then provides the coefficients table with Satterthwaite degrees of freedom as well as the covariance matrix estimate:

summary(fit)
#> mmrm fit
#> 
#> Formula:     FEV1 ~ RACE + SEX + ARMCD * AVISIT + us(AVISIT | USUBJID)
#> Data:        fev_data (used 537 observations from 197 subjects with maximum 4 
#> timepoints)
#> Covariance:  unstructured (10 variance parameters)
#> Method:      Satterthwaite
#> Inference:   REML
#> 
#> Model selection criteria:
#>      AIC      BIC   logLik deviance 
#>   3406.4   3439.3  -1693.2   3386.4 
#> 
#> Coefficients: 
#>                                Estimate Std. Error        df t value Pr(>|t|)
#> (Intercept)                    30.77748    0.88656 218.80000  34.715  < 2e-16
#> RACEBlack or African American   1.53050    0.62448 168.67000   2.451 0.015272
#> RACEWhite                       5.64357    0.66561 157.14000   8.479 1.56e-14
#> SEXFemale                       0.32606    0.53195 166.13000   0.613 0.540744
#> ARMCDTRT                        3.77423    1.07415 145.55000   3.514 0.000589
#> AVISITVIS2                      4.83959    0.80172 143.88000   6.037 1.27e-08
#> AVISITVIS3                     10.34211    0.82269 155.56000  12.571  < 2e-16
#> AVISITVIS4                     15.05390    1.31281 138.47000  11.467  < 2e-16
#> ARMCDTRT:AVISITVIS2            -0.04193    1.12932 138.56000  -0.037 0.970439
#> ARMCDTRT:AVISITVIS3            -0.69369    1.18765 158.17000  -0.584 0.559996
#> ARMCDTRT:AVISITVIS4             0.62423    1.85085 129.72000   0.337 0.736463
#>                                  
#> (Intercept)                   ***
#> RACEBlack or African American *  
#> RACEWhite                     ***
#> SEXFemale                        
#> ARMCDTRT                      ***
#> AVISITVIS2                    ***
#> AVISITVIS3                    ***
#> AVISITVIS4                    ***
#> ARMCDTRT:AVISITVIS2              
#> ARMCDTRT:AVISITVIS3              
#> ARMCDTRT:AVISITVIS4              
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Covariance estimate:
#>         VIS1    VIS2    VIS3    VIS4
#> VIS1 40.5537 14.3960  4.9747 13.3867
#> VIS2 14.3960 26.5715  2.7855  7.4745
#> VIS3  4.9747  2.7855 14.8979  0.9082
#> VIS4 13.3867  7.4745  0.9082 95.5568

Citing mmrm

To cite mmrm please see here.