Simultaneous Variable Selection for Joint Models of Longitudinal and Survival Outcomes

Abstract

Summary 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 paper, 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.

Exploring causality mechanism in the joint analysis of longitudinal and survival data

“…Such a latent variable could be continuous, e.g., random effects 5–11 , or discrete, e.g., latent class 12,13 , or both 14 . Recently, joint models have also been incorporated in the machine learning framework through statistical boosting 15 and variable selection by adaptive LASSO 16 . In this paper we will focus on shared random effects models, though the extension to shared latent class models is straightforward in principle.…”

Linear and nonlinear variable selection in competing risks data

“…However, Wang and Tsai showed that GCV approach tended to choose the tuning parameters that lead to an overfitted model. Following Wang and Tsai, Ha et al, and He et al, we use a BIC‐type criterion based on the penalized log‐likelihood for tuning parameter selection: where are the estimators obtained by maximizing at a given tuning parameter combination, denoted as ρ =( ρ β , ρ γ ), and is the value of evaluated at the estimated . The k is the total number of nonzero estimates of .…”

Variable selection for joint models of multivariate longitudinal measurements and event time data

“…The off‐diagonal penalty on a precision matrix was considered by Zhang and Zou for graphical models. We note that He et al imposed penalties on the diagonal elements of covariances matrix since their goal is to select the random covariates. Our goal is not to select random intercepts and slopes in the submodel of longitudinal variables.…”

“…We are interested in the association between trajectories of multiple longitudinal processes and survival time. Therefore, the joint model we consider in this article is different from that in He et al…”

“…We are interested in the association between trajectories of multiple longitudinal processes and survival time. Therefore, the joint model we consider in this article is different from that in He et al 15 We aim at developing a variable selection method to choose features from multiple longitudinal processes for the survival submodel. A multivariate linear mixed effect model is used to describe the multiple longitudinal processes.…”