title: Joint partially linear model for longitudinal data with informative drop-outs.
abstract: In biomedical research, a steep rise or decline in longitudinal biomarkers may indicate latent disease progression, which may subsequently cause patients to drop out of the study. Ignoring the informative drop-out can cause bias in estimation of the longitudinal model. In such cases, a full parametric specification may be insufficient to capture the complicated pattern of the longitudinal biomarkers. For these types of longitudinal data with the issue of informative drop-outs, we develop a joint partially linear model, with an aim to find the trajectory of the longitudinal biomarker. Specifically, an arbitrary function of time along with linear fixed and random covariate effects is proposed in the model for the biomarker, while a flexible semiparametric transformation model is used to describe the drop-out mechanism. Advantages of this semiparametric joint modeling approach are the following: 1) it provides an easier interpretation, compared to standard nonparametric regression models, and 2) it is a natural way to control for common (observable and unobservable) prognostic factors that may affect both the longitudinal trajectory and the drop-out process. We describe a sieve maximum likelihood estimation procedure using the EM algorithm, where the Akaike information criterion (AIC) and Bayesian information criterion (BIC) are considered to select the number of knots. We show that the proposed estimators achieve desirable asymptotic properties through empirical process theory. The proposed methods are evaluated by simulation studies and applied to prostate cancer data.
authors.affiliation: Department of Biostatistics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A.
authors.forename: Sehee
authors.initials: S
authors.lastname: Kim
authors.affiliation: Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A.
authors.forename: Donglin
authors.initials: D
authors.lastname: Zeng
authors.affiliation: Department of Biostatistics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A.
authors.forename: Jeremy M G
authors.initials: JM
authors.lastname: Taylor
mesh_terms: D001499:Bayes Theorem; D015982:Bias; D015415:Biomarkers; D001699:Biometry / Q000379:methods*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D018450:Disease Progression; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D008137:Longitudinal Studies; D008297:Male; D011379:Prognosis; D011471:Prostatic Neoplasms / Q000473:pathology
chemical_list: D015415:Biomarkers
keywords: Joint models; Longitudinal data; Nonparametric maximum likelihood; Partially linear model; Random effects; Sieve maximum likelihood; Transformation models