Practical Review and Comparison of Modified Covariance Estimators for Linear Mixed Models in Small‐sample Longitudinal Studies with Missing Data

Masahiko Gosho, Hisashi Noma and Kazushi Maruo

International Statistical Review, 2021, vol. 89, issue 3, 550-572

Abstract: Mixed‐effects models for repeated measures (MMRMs) with an ‘unstructured’ (UN) covariance structure are frequently used in primary analyses for group comparisons of incomplete continuous longitudinal data from drug development trials. However, MMRM‐UN analysis could lead to convergence problems in numerical optimisation, especially in trials with a small sample size or high dropout rate. Although the so‐called sandwich covariance estimator is robust against the misspecification of the covariance structure, its performance deteriorates for small sample sizes. We review eight modified covariance estimators adjusted for small‐sample bias and compare their performances in the framework of MMRM analysis through simulations. In terms of the type 1 error rate and coverage probability of confidence intervals for group comparisons, Mancl and DeRouen's covariance estimator (MD) shows the best performance among the modified covariance estimators, followed by Fay and Graubard's estimator. The performance of MD is nearly equivalent to that of the Kenward–Roger method with a UN structure. The Kenward–Roger method with first‐order autoregressive structure results in substantial inflation of the type 1 error rate in the scenario where the variance of measurements increases across visits. In summary, we recommend the use of MD in MMRM analysis if the convergence problem involving a UN structure occurs in small clinical trials.

Date: 2021
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