title: Simultaneous variable selection for joint models of longitudinal and survival outcomes.
abstract: Joint models of longitudinal and survival outcomes have been used with increasing frequency in clinical investigations. Correct specification of fixed and random effects is essential for practical data analysis. Simultaneous selection of variables in both longitudinal and survival components functions as a necessary safeguard against model misspecification. However, variable selection in such models has not been studied. No existing computational tools, to the best of our knowledge, have been made available to practitioners. In this article, we describe a penalized likelihood method with adaptive least absolute shrinkage and selection operator (ALASSO) penalty functions for simultaneous selection of fixed and random effects in joint models. To perform selection in variance components of random effects, we reparameterize the variance components using a Cholesky decomposition; in doing so, a penalty function of group shrinkage is introduced. To reduce the estimation bias resulted from penalization, we propose a two-stage selection procedure in which the magnitude of the bias is ameliorated in the second stage. The penalized likelihood is approximated by Gaussian quadrature and optimized by an EM algorithm. Simulation study showed excellent selection results in the first stage and small estimation biases in the second stage. To illustrate, we analyzed a longitudinally observed clinical marker and patient survival in a cohort of patients with heart failure.
authors.affiliation: Department of Biostatistics, Indiana University School of Medicine and Fairbanks School of Public Health, Indianapolis, Indiana, U.S.A.
authors.forename: Zangdong
authors.initials: Z
authors.lastname: He
authors.affiliation: Department of Biostatistics, Indiana University School of Medicine and Fairbanks School of Public Health, Indianapolis, Indiana, U.S.A.|Regenstrief Institute, Inc., Indianapolis, Indiana, U.S.A.
authors.forename: Wanzhu
authors.initials: W
authors.lastname: Tu
authors.affiliation: Department of Biostatistics and Medical Informatics, University of Wisconsin, Madison, Wisconsin, U.S.A.
authors.forename: Sijian
authors.initials: S
authors.lastname: Wang
authors.affiliation: Eli Lilly & Company, Indianapolis, Indiana, U.S.A.
authors.forename: Haoda
authors.initials: H
authors.lastname: Fu
authors.affiliation: Department of Biostatistics, Indiana University School of Medicine and Fairbanks School of Public Health, Indianapolis, Indiana, U.S.A.
authors.forename: Zhangsheng
authors.initials: Z
authors.lastname: Yu
mesh_terms: D000465:Algorithms; D015415:Biomarkers / Q000097:blood; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D004812:Epidemiologic Methods; D006333:Heart Failure / Q000097:blood* / Q000401:mortality*; D006801:Humans; D008137:Longitudinal Studies; D015233:Models, Statistical; D020097:Natriuretic Peptide, Brain / Q000097:blood; D009716:Numerical Analysis, Computer-Assisted; D017063:Outcome Assessment, Health Care / Q000379:methods*; D015203:Reproducibility of Results; D018570:Risk Assessment / Q000379:methods; D012680:Sensitivity and Specificity; D016019:Survival Analysis
chemical_list: D015415:Biomarkers; D020097:Natriuretic Peptide, Brain
keywords: ALASSO; Cholesky decomposition; EM algorithm; Gaussian quadrature; Joint models; Mixed effect selection