Inferences for Joint Modelling of Repeated Ordinal Scores and Time to Event Data

Arindom Chakraborty,Kalyan Das

doi:10.1080/17486701003789096

Arindom Chakraborty, Kalyan Das

Open Access

https://doi.org/10.1080/17486701003789096

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Abstract

In clinical trials and other follow-up studies, it is natural that a response variable is repeatedly measured during follow-up and the occurrence of some key event is also monitored. There has been a considerable study on the joint modelling these measures together with information on covariates. But most of the studies are related to continuous outcomes. In many situations instead of observing continuous outcomes, repeated ordinal outcomes are recorded over time. The joint modelling of such serial outcomes and the time to event data then becomes a bit complicated. In this article we have attempted to analyse such models through a latent variable model. In view of the longitudinal variation on the ordinal outcome measure, it is desirable to account for the dependence between ordered categorical responses and survival time for different causes due to unobserved factors. A flexible Monte Carlo EM (MCEM) method based on exact likelihood is proposed that can simultaneously handle the longitudinal ordinal data and also the censored time to event data. A computationally more efficient MCEM method based on approximation of the likelihood is also proposed. The method is applied to a number of ordinal scores and survival data from trials of a treatment for children suffering from Duchenne Muscular Dystrophy. Finally, a simulation study is conducted to examine the finite sample properties of the proposed estimators in the joint model under two different methods.

Highlights

In recent years, researchers have shown great interest to record the values of key longitudinal covariates until the occurrence of survival time of a subject
The three methods may give different results, which is evident from Table 1
In most cases we found that the approximate estimates are closer to exact estimates than the linear mixed model estimates, and the linear mixed model method generally produces larger standard errors than the approximate estimates, possibly indicating inefficiency of the method based on a linear mixed model

Summary

Introduction

Researchers have shown great interest to record the values of key longitudinal covariates until the occurrence of survival time (or event time) of a subject. The truncation of a patient’s response can raise similar problems to those that have been considered in the event of patient dropout [12,14,18]. The primary interest in such models is in drawing inferences for the marginal distributions of the longitudinal response in the absence of dropout. Often the longitudinal model and survival model are assumed to share some unobserved variables. In this case, separate models can result in biased estimates. Separate models can result in biased estimates This necessitates the development of a joint model.

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