Semiparametric Latent Variable Models for Chronic Diseases with Responses of Multiple Types and Scales

Abstract

In chronic diseases, research often centers on discovering a latent trait trajectory that manifests itself through multiple response variables on different measurement scales. In longitudinal studies, it is common to collect multivariate response data consisting of mixtures of continuous, survival, ordinal, count and multinomial variables. Development of the methodology was motivated by situations when measuring and predicting the latent trait can provide important insights for managing the observed phenotype.

In Chapter II, we study survival models of cancer where a latent trait is responsible for the cure process. Traditional cure models assume that the cure status is determined at the beginning of the follow up. However, patients often receive treatments during the follow up time that may affect their chance of cure. We propose a dynamic joint cure model where a cure process is affected by time-dependent covariates. Therapeutic interventions and prognostic factors can follow two causal paths affecting survival directly or through the latent cure process.

Chapter III addresses the challenge of latent trait measurement through multiple outcomes of different scales, which are often collected when the construct of interest cannot be measured directly. We proposed a shared latent variable model where a logistic link is used to accommodate nonparametrically transformed continuous, ordinal, count, multinomial and survival outcomes. The proposed model avoids restrictive normality assumptions and allows for negative correlation among outcomes. The model provides a subject-specific measure of the latent trait.

Chapter IV extends the method of Chapter III to allow for longitudinal responses of mixed types. We proposed a joint modeling approach for nonparametrically transformed multivariate longitudinal responses of mixed scales. Multivariate longitudinal responses of mixed continuous, ordinal, count and multinomial outcomes and a time-to-event outcome are linked through a shared latent trait trajectory measurement. The model is used to provide a subject-specific measure of the latent trait trajectory through multiple correlated responses observed repeatedly on the subject.