Joint analysis of mixed types of outcomes with latent variables

Abstract

We propose a joint modeling approach to investigating the observed and latent risk factors of mixed types of outcomes. The proposed model comprises three parts. The first part is an exploratory factor analysis model that summarizes latent factors through multiple observed variables. The second part is a proportional hazards model that examines the observed and latent risk factors of multivariate time‐to‐event outcomes. The third part is a linear regression model that investigates the determinants of a continuous outcome. We develop a Bayesian approach coupled with MCMC methods to determine the number of latent factors, the association between latent and observed variables, and the important risk factors of different types of outcomes. A modified stochastic search item selection algorithm, which introduces normal‐mixture‐inverse gamma priors to factor loadings and regression coefficients, is developed for simultaneous model selection and parameter estimation. The proposed method is subjected to simulation studies for empirical performance assessment and then applied to a study concerning the risk factors of type 2 diabetes and the associated complications.

Joint analysis of multivariate failure time data with latent variables

“…An ADF-GLS approach for the factor analysis model and a borrow-strength approach for the MAH model are combined to obtain consistent and asymptotically normal estimators. Compared with existing methods proposed by Pan et al, 19,18,20 the joint model is especially attractive and flexible in that the distributions of the latent variables and random errors are left unspecified and the failure times of interest are correlated. The proposed estimation procedure can be easily implemented.…”

“…They first summarized the effectiveness of treatment using three longitudinal outcomes and then regressed the covariates on the overall treatment effect. Pan et al 18–20 characterized the latent medical traits of diabetic patients and then investigated the latent risk factors of diabetic complications through hazards models. Nevertheless, the previous studies assumed that the latent factors and residual errors followed the normal distribution.…”

A joint model for multivariate longitudinal and survival data to discover the conversion to Alzheimer's disease

“…The baseline hazard function is unknown, and providing the evidence of a parametric hazard function shape is usually difficult in substantive studies. We follow the existing literature (eg, Ibrahim et al, 24 Yin and Ibrahim, 25 Lee et al, 16 Pan et al 26 ) to approximate through a commonly used piecewise constant distribution. One can also use B‐splines 27,28 to obtain a more flexible and smooth estimate of (eg, Zhou et al 29 ).…”

Regression analysis of logistic model with latent variables

“…Pham et al 14 analyzed the effects of biologically structured latent factors on the drug's action mechanisms with the use of a joint modeling approach, wherein the latent factors (the biological pathways) in their conditional autoregressive model was characterized by several gene expressions through a CFA model. Pan et al [15][16][17] grouped clinical variables into latent medical traits of diabetic patients and evaluated the effect of risk factors on the hazards of diabetic complications.…”