Semiparametric regression analysis of panel count data allowing for within-subject correlation

• Published in: Computational statistics & data analysis Vol. 97; pp. 47 - 59
• Main Authors: Yao, Bin, Wang, Lianming, He, Xin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2016
• Subjects: Algorithms; Computation; computer software; Correlation; Counting; EM algorithm; Estimates; Gamma frailty; Mathematical analysis; Mathematical models; Monotone splines; Panel count data; Panels; Poisson process; regression analysis; skin neoplasms; urinary bladder neoplasms; variance; Panel count data; EM algorithm; Monotone splines; Poisson process; Gamma frailty
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2015.11.017

In this paper, a maximum likelihood approach is proposed for analyzing panel count data under the gamma frailty non-homogeneous Poisson process model. The approach allows one to estimate the baseline mean function and the regression parameters jointly while taking the within-subject correlation into account. The within-subject correlation is quantified explicitly by Pearson’s correlation coefficient. Monotone splines are adopted to approximate the unspecified nondecreasing baseline mean function in the model. An expectation–maximization (EM) algorithm is derived to facilitate the computation by exploiting a data augmentation based on Poisson latent variables. The EM algorithm is robust to initial values, easy to implement, converges fast, and provides closed-form variance estimates. It can be also applied to the non-homogeneous Poisson model without frailty. The proposed approach is evaluated through simulations and illustrated by two real-life examples coming from a skin cancer study and a bladder tumor study. A companion R package PCDSpline has been developed and is available on R CRAN for public use.