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The New England Journal of Statistics in Data Science


Modeling the Mean with Time as a Categorical Variable in Longitudinal Designs for Smaller-Sized Clinical Trials: A Case Studies Approach Based on Three Phase 3 Clinical Trials in Rare Diseases
Pub. online: 28 January 2026      Type: Case Study, Application, And/or Practice Article      Open accessOpen Access
Area: Biomedical Research

1 Contributed equally.
Accepted
8 December 2025
Published
28 January 2026

Abstract

Background: Generalized estimating equations (GEE) and mixed-model repeated measures (MMRM) can handle longitudinal continuous outcomes when modeling the mean with time included categorically. Due to small sample sizes in rare diseases, a compound symmetry (CS) covariance pattern is sometimes adopted. In this setting, there is scant literature in the rare disease community that provide practical advice about the use of both methods based on real datasets from trials conducted in rare diseases, including when to use the sandwich variance estimator with or without a bias correction.
Methods: To fill this gap, we simulated data from three longitudinal, phase 3 trials conducted in rare diseases to jointly review the operating characteristics: a randomized trial in GNE myopathy (N = 44 placebo; N = 45 treatment) and pediatric X-linked hypophosphatemia (XLH) (N = 32 control; N = 29 treatment), and a single-arm in adult XLH (N = 14).
Results: In each trial, few participants discontinued; furthermore, <1.5% of the measurement occasions were missing outcome data, no missing outcome data pattern occurred in >1 participant, and the missing completely at random (MCAR) assumption was clinically justified. In the two trials with nonconstant variances/covariances over time, bias-corrected sandwich variance estimators with t-based inference was needed with MMRM and GEE. If the CS pattern was a good approximation, as seen in the pediatric XLH trial, then model-based standard errors with t-based inference performed well with both methods
Conclusion: Based on a review of three case studies, the MCAR assumption was plausible and missingness low. When modeling the mean response with time included categorically and with a parsimonious CS covariance structure, each method required careful consideration with its use.

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© 2026 New England Statistical Society
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Keywords
Generalized estimating equations Longitudinal designs Mixed model repeated measures Rare diseases Sandwich variance estimator Small-sample correction

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