Power for balanced linear mixed models with complex missing data processes

Abstract

When designing repeated measures studies, both the amount and the pattern of missing outcome data can affect power. The chance that an observation is missing may vary across measurements, and missingness may be correlated across measurements. For example, in a physiotherapy study of patients with Parkinson’s disease, increasing intermittent dropout over time yielded missing measurements of physical function. In this example, we assume data are missing completely at random, since the chance that a data point was missing appears to be unrelated to either outcomes or covariates. For data missing completely at random, we propose noncentral F power approximations for the Wald test for balanced linear mixed models with Gaussian responses. The power approximations are based on moments of missing data summary statistics. The moments were derived assuming a conditional linear missingness process. The approach provides approximate power for both complete-case analyses, which include independent sampling units where all measurements are present, and observed-case analyses, which include all independent sampling units with at least one measurement. Monte Carlo simulations demonstrate the accuracy of the method in small samples. We illustrate the utility of the method by computing power for proposed replications of the Parkinson’s study.

Keywords:

• Power
• missing data
• mixed model
• multilevel
• longitudinal

Additional information

Funding

KAS and DD were supported by NIH R01DK076645 (Dabelea), NIH UG3OD023248 (Dabelea) and AHA16MCPRP29710005 (Sauder). MS was supported by NIH R01 HD043770 (Schenkman), CCTSI TL1RR025778 (Schenkman), NIH P30 DK048520 (Hill), K23 NS052487 (Hall), and the Parkinson’s Disease Foundation. DHG and KEM were supported by NIH R01GM121081 (Glueck, Dabelea, Muller), NIH R25GM111901 (Glueck, Muller) and NIH G13LM011879 (Glueck, Muller). BMR and KPJ were supported by NIH R01GM121081 (Glueck, Dabelea, Muller).