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Sample sizes required to detect interactions between two binary fixed-effects in a mixed-effects linear regression model

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  • Leon, Andrew C.
  • Heo, Moonseong

Abstract

Mixed-effects linear regression models have become more widely used for analysis of repeatedly measured outcomes in clinical trials over the past decade. There are formulae and tables for estimating sample sizes required to detect the main effects of treatment and the treatment by time interactions for those models. A formula is proposed to estimate the sample size required to detect an interaction between two binary variables in a factorial design with repeated measures of a continuous outcome. The formula is based, in part, on the fact that the variance of an interaction is fourfold that of the main effect. A simulation study examines the statistical power associated with the resulting sample sizes in a mixed-effects linear regression model with a random intercept. The simulation varies the magnitude ([Delta]) of the standardized main effects and interactions, the intraclass correlation coefficient ([rho]), and the number (k) of repeated measures within-subject. The results of the simulation study verify that the sample size required to detect a 22 interaction in a mixed-effects linear regression model is fourfold that to detect a main effect of the same magnitude.

Suggested Citation

  • Leon, Andrew C. & Heo, Moonseong, 2009. "Sample sizes required to detect interactions between two binary fixed-effects in a mixed-effects linear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 603-608, January.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:3:p:603-608
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    2. Meager, Rachael, 2022. "Aggregating distributional treatment effects: a Bayesian hierarchical analysis of the microcredit literature," LSE Research Online Documents on Economics 115559, London School of Economics and Political Science, LSE Library.
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    4. Quinn A. W. Keefer, 2022. "Sex Differences in High-Level Managerial Jobs: Evidence From Professional Basketball," Journal of Sports Economics, , vol. 23(3), pages 301-328, April.

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