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A Step-Wise Multiple Testing for Linear Regression Models with Application to the Study of Resting Energy Expenditure

Author

Listed:
  • Junyi Zhang

    (Baruch College)

  • Zimian Wang

    (Columbia University)

  • Zhezhen Jin

    (Columbia University)

  • Zhiliang Ying

    (Columbia University)

Abstract

Motivated by the mechanistic model of the resting energy expenditure, we present a new multiple hypothesis testing approach to evaluate organ/tissue-specific resting metabolic rates. The approach is based on generalized marginal regression estimates for a subset of coefficients along with a stepwise multiple testing procedure with a minimization–maximization of the normalized estimates (maximization over all its components and minimization over all possible choices of the subset). The approach offers a valid way to address challenges in multiple hypothesis testing on regression coefficients in linear regression analysis especially when covariates are highly correlated. Importantly, the approach yields estimates that are conditionally unbiased. In addition, the approach controls a family-wise error rate in the strong sense. The approach was used to analyze a real study on resting energy expenditure in 131 healthy adults, which yielded an interesting and surprising result of age-related decrease in resting metabolic rate of kidneys. Simulation studies were also presented with various strengths of multi-collinearity induced by pre-specified correlation in covariates.

Suggested Citation

  • Junyi Zhang & Zimian Wang & Zhezhen Jin & Zhiliang Ying, 2023. "A Step-Wise Multiple Testing for Linear Regression Models with Application to the Study of Resting Energy Expenditure," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 163-192, April.
    • Handle: RePEc:spr:stabio:v:15:y:2023:i:1:d:10.1007_s12561-022-09355-5
    DOI: 10.1007/s12561-022-09355-5
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    References listed on IDEAS

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    1. Shao, Qi-Man, 2003. "A Gaussian correlation inequality and its applications to the existence of small ball constant," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 269-287, October.
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