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Adjusting power for a baseline covariate in linear models.

Deborah H Glueck1, Keith E Muller

  • 1Department of Preventive Medicine and Biometrics, University of Colorado Health Sciences Center, Denver, CO 80262, U.S.A.

Statistics in Medicine
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Summary

Adjusting for baseline covariates in medical research using analysis of covariance is common. However, random covariates complicate power analysis, requiring new methods for accurate sample size determination in studies.

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Area of Science:

  • Biostatistics
  • Medical Research Methodology

Background:

  • Analysis of covariance (ANCOVA) is standard for adjusting baseline covariates in medical research.
  • While ANCOVA computations are unaffected by random covariates with Gaussian errors, power analysis theory and computation are significantly impacted.
  • Existing methods often fail to fully address the complexities introduced by random covariates in study planning.

Purpose of the Study:

  • To address the underestimation of sample size in power analysis due to random covariates.
  • To provide a comprehensive review and taxonomy of general linear multivariate models and hypotheses relevant to this problem.
  • To develop and present novel methods for power analysis that account for random covariates.

Main Methods:

  • A review of existing literature to highlight the problem's significance and limitations of current approaches.
  • Development of a taxonomy for general linear multivariate models to identify specific issues.
  • Derivation of new exact and approximate methods for power analysis in multivariate models with Gaussian baseline covariates.
  • Application of these techniques to specific tests like the Hotelling-Lawley test and repeated measures analyses.

Main Results:

  • New exact and approximate methods for power analysis are presented for both small and large sample sizes.
  • The developed techniques are applicable to a range of multivariate models, including Hotelling-Lawley and repeated measures tests.
  • The methods facilitate rapid calculations and an interactive, graphical approach to sample size selection.

Conclusions:

  • Random covariates necessitate careful consideration of quantiles and conditional power in study design.
  • The new methods offer improved accuracy for power analysis in the presence of random covariates.
  • Quantile power, particularly with a Satterthwaite-style approximation, is recommended for clinical trial power calculations, as illustrated in a bone density study.