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Sample size and power determination for multiparameter evaluation in nonlinear regression models with potential stratification

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  • Michael J. Martens
  • Soyoung Kim
  • Kwang Woo Ahn

Abstract

Sample size and power determination are crucial design considerations for biomedical studies intending to formally test the effects of key variables on an outcome. Other known prognostic factors may exist, necessitating the use of techniques for covariate adjustment when conducting this evaluation. Moreover, the main interest often includes assessing the impact of more than one variable on an outcome, such as multiple treatments or risk factors. Regression models are frequently employed for these purposes, formalizing this assessment as a test of multiple regression parameters. But, the presence of multiple variables of primary interest and correlation between covariates can complicate sample size/power calculation. Given the paucity of available sample size formulas for this context, these calculations are often performed via simulation, which can be both time‐consuming as well as demanding extensive probability modeling. We propose a simpler, general approach to sample size and power determination that may be applied when testing multiple parameters in commonly used regression models, including generalized linear models as well as ordinary and stratified versions of the Cox and Fine–Gray models. Through both rigorous simulations and theoretical derivations, we demonstrate the formulas' accuracy in producing sample sizes that will meet the type I error rate and power specifications of the study design.

Suggested Citation

  • Michael J. Martens & Soyoung Kim & Kwang Woo Ahn, 2023. "Sample size and power determination for multiparameter evaluation in nonlinear regression models with potential stratification," Biometrics, The International Biometric Society, vol. 79(4), pages 3916-3928, December.
  • Handle: RePEc:bla:biomet:v:79:y:2023:i:4:p:3916-3928
    DOI: 10.1111/biom.13897
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    References listed on IDEAS

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    1. Gwowen Shieh, 2000. "On Power and Sample Size Calculations for Likelihood Ratio Tests in Generalized Linear Models," Biometrics, The International Biometric Society, vol. 56(4), pages 1192-1196, December.
    2. Michael J. Martens & Brent R. Logan, 2018. "A group sequential test for treatment effect based on the Fine–Gray model," Biometrics, The International Biometric Society, vol. 74(3), pages 1006-1013, September.
    3. Bingqing Zhou & Aurelien Latouche & Vanderson Rocha & Jason Fine, 2011. "Competing Risks Regression for Stratified Data," Biometrics, The International Biometric Society, vol. 67(2), pages 661-670, June.
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