Comparison of bias-corrected covariance estimators for MMRM analysis in longitudinal data with dropouts

Masahiko Gosho, Akihiro Hirakawa, Hisashi Noma, Kazushi Maruo, Yasunori Sato

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


In longitudinal clinical trials, some subjects will drop out before completing the trial, so their measurements towards the end of the trial are not obtained. Mixed-effects models for repeated measures (MMRM) analysis with "unstructured" (UN) covariance structure are increasingly common as a primary analysis for group comparisons in these trials. Furthermore, model-based covariance estimators have been routinely used for testing the group difference and estimating confidence intervals of the difference in the MMRM analysis using the UN covariance. However, using the MMRM analysis with the UN covariance could lead to convergence problems for numerical optimization, especially in trials with a small-sample size. Although the so-called sandwich covariance estimator is robust to misspecification of the covariance structure, its performance deteriorates in settings with small-sample size. We investigated the performance of the sandwich covariance estimator and covariance estimators adjusted for small-sample bias proposed by Kauermann and Carroll (J Am Stat Assoc 2001; 96: 1387-1396) and Mancl and DeRouen (Biometrics 2001; 57: 126-134) fitting simpler covariance structures through a simulation study. In terms of the type 1 error rate and coverage probability of confidence intervals, Mancl and DeRouen's covariance estimator with compound symmetry, first-order autoregressive (AR(1)), heterogeneous AR(1), and antedependence structures performed better than the original sandwich estimator and Kauermann and Carroll's estimator with these structures in the scenarios where the variance increased across visits. The performance based on Mancl and DeRouen's estimator with these structures was nearly equivalent to that based on the Kenward-Roger method for adjusting the standard errors and degrees of freedom with the UN structure. The model-based covariance estimator with the UN structure under unadjustment of the degrees of freedom, which is frequently used in applications, resulted in substantial inflation of the type 1 error rate. We recommend the use of Mancl and DeRouen's estimator in MMRM analysis if the number of subjects completing is (n + 5) or less, where n is the number of planned visits. Otherwise, the use of Kenward and Roger's method with UN structure should be the best way.

Original languageEnglish
Pages (from-to)2389-2406
Number of pages18
JournalStatistical Methods in Medical Research
Issue number5
Publication statusPublished - 2017 Oct 1
Externally publishedYes


  • Covariance structure
  • missingness
  • mixed-effects model
  • robust covariance estimator
  • small sample

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability
  • Health Information Management


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