A semiparametric transition model with latent traits for longitudinal multistate data

Abstract

We propose a general multistate transition model. The model is developed for the analysis of repeated episodes of multiple states representing different health status. Transitions among multiple states are modeled jointly using multivariate latent traits with factor loadings. Different types of state transition are described by flexible transition-specific nonparametric baseline intensities. A state-specific latent trait is used to capture individual tendency of the sojourn in the state that cannot be explained by covariates and to account for correlation among repeated sojourns in the same state within an individual. Correlation among sojourns across different states within an individual is accounted for by the correlation between the different latent traits. The factor loadings for a latent trait accommodate the dependence of the transitions to different competing states from a same state. We obtain the semiparametric maximum likelihood estimates through an expectation-maximization (EM) algorithm. The method is illustrated by studying repeated transitions between independence and disability states of activities of daily living (ADL) with death as an absorbing state in a longitudinal aging study. The performance of the estimation procedure is assessed by simulation studies.

Figure 1

Plots of the baseline intensities. Circles are nonparametric estimates of the baseline intensities. Lines are the loess-smoothed estimates. Top left: transition from ADL independence to disability, the scale of the intensity is amplified by 1000 times; top right: transition from ADL independence to death, the scale of the intensity is amplified by 100,000 times; bottom left: transition from ADL disability to independence; bottom right: transition from ADL disability to death.