Generalized Quasi-Likelihood Ratio Tests for Semiparametric Analysis of Covariance Models in Longitudinal Data

ABSTRACT

We model generalized longitudinal data from multiple treatment groups by a class of semiparametric analysis of covariance models, which take into account the parametric effects of time dependent covariates and the nonparametric time effects. In these models, the treatment effects are represented by nonparametric functions of time and we propose a generalized quasi-likelihood ratio test procedure to test if these functions are identical. Our estimation procedure is based on profile estimating equations combined with local linear smoothers. We find that the much celebrated Wilks phenomenon which is well established for independent data still holds for longitudinal data if a working independence correlation structure is assumed in the test statistic. However, this property does not hold in general, especially when the working variance function is misspecified. Our empirical study also shows that incorporating correlation into the test statistic does not necessarily improve the power of the test. The proposed methods are illustrated with simulation studies and a real application from opioid dependence treatments. Supplementary materials for this article are available online.

KEYWORDS:

• Analysis of variance
• Functional data
• Hypothesis testing
• Kernel smoothing
• Longitudinal data
• Semiparametric

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Supplementary Materials

The online supplementary material contains technical proofs for the theoretical results and additional simulation results.

Acknowledgments

We thank the Associate Editor and an anonymous referee for their helpful and constructive comments, which lead to significant improvement in this article. This article is based on the first author's Ph.D. dissertation under Li's supervision.

Funding

Li’s research was supported by the National Science Foundation awards DMS-1105634 and DMS-1317118. Guan’s research was supported by the National Institute of Health grant 7R01DA029081 and the National Science Foundation grant DMS-0845368.