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Interpretable inference on the mixed effect model with the Box–Cox transformation
Author(s) -
Maruo K.,
Yamaguchi Y.,
Noma H.,
Gosho M.
Publication year - 2017
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.7279
Subject(s) - power transform , estimator , inference , interpretability , type i and type ii errors , context (archaeology) , statistics , mixed model , mathematics , marginal model , transformation (genetics) , computer science , proportional hazards model , econometrics , artificial intelligence , regression analysis , paleontology , biochemistry , chemistry , consistency (knowledge bases) , gene , biology
We derived results for inference on parameters of the marginal model of the mixed effect model with the Box–Cox transformation based on the asymptotic theory approach. We also provided a robust variance estimator of the maximum likelihood estimator of the parameters of this model in consideration of the model misspecifications. Using these results, we developed an inference procedure for the difference of the model median between treatment groups at the specified occasion in the context of mixed effects models for repeated measures analysis for randomized clinical trials, which provided interpretable estimates of the treatment effect. From simulation studies, it was shown that our proposed method controlled type I error of the statistical test for the model median difference in almost all the situations and had moderate or high performance for power compared with the existing methods. We illustrated our method with cluster of differentiation 4 (CD4) data in an AIDS clinical trial, where the interpretability of the analysis results based on our proposed method is demonstrated. Copyright © 2017 John Wiley & Sons, Ltd.