A multistate Markov chain model for longitudinal, categorical quality-of-life data subject to non-ignorable missingness

Abstract

Quality-of-life (QOL) is an important outcome in clinical research, particularly in cancer clinical trials. Typically, data are collected longitudinally from patients during treatment and subsequent follow-up. Missing data are a common problem, and missingness may arise in a non-ignorable fashion. In particular, the probability that a patient misses an assessment may depend on the patient's QOL at the time of the scheduled assessment. We propose a Markov chain model for the analysis of categorical outcomes derived from QOL measures. Our model assumes that transitions between QOL states depend on covariates through generalized logit models or proportional odds models. To account for non-ignorable missingness, we incorporate logistic regression models for the conditional probabilities of observing measurements, given their actual values. The model can accommodate time-dependent covariates. Estimation is by maximum likelihood, summing over all possible values of the missing measurements. We describe options for selecting parsimonious models, and we study the finite-sample properties of the estimators by simulation. We apply the techniques to data from a breast cancer clinical trial in which QOL assessments were made longitudinally, and in which missing data frequently arose.

Chemical suitability of groundwater for irrigation in Trimohoni and Sagardari union, Keshabpur Upazila, Jessore, Bangladesh

“…In a position to pick one out of two alternative inference methods that are equally efficient, the simple answer is to pick the one that is simple in theory, easy to apply and computationally less intensive. In all of these respects our proposed EM approach outperforms the likelihood approach proposed by Cole et al (2005). Therefore, one can avoid doing complex algebra and complicated programming algorithm by using our proposed EM algorithm technique accommodating both longitudinal nature of the data and non-ignorable missingness and get efficient estimates.…”

“…ML estimates proposed by Cole et al (2005) are also reported in the same table. Table 2 shows that both covariates gender and age have significant effect on transition from the state 'no depression' to 'depression'.…”

“…Fairclough (2002) described multiple imputation techniques for non-ignorable missing longitudinal quality-of-life (QOL) data. Cole et al (2005) developed a multistate Markov chain model for the analysis of longitudinal, categorical outcomes derived from QOL measures with the advantage over existing methods by allowing two or more QOL states, while accommodating both intermittent, informative missingness and covariate effects for first order dependency. For the purpose of inference, estimation of the regression parameters was carried out by a maximum likelihood method, summing over all possible values of the missing observations, which involves huge number of parameters to be estimated.…”

EM algorithm for longitudinal data with non-ignorable missing values: An application to health data

“…Accordingly a common logistic regression model is assumed for the nonresponse model. That is, the conditional probability that is observed given that is defined by (2) Following Cole et. al.…”

Estimation of average treatment effect with incompletely observed longitudinal data: Application to a smoking cessation study

“…Among them are [19], [20], [21], [22] for general models; [2], [3] for the generalized estimating equations, [23] for linear mixed models. More recently, [24],[25], [26],[27] discussed handling missing outcomes in various longitudinal data models. The missing data mechanism models proposed in the literature usually cannot accommodate complex missing data patterns that are nonmonotone and nonsaturated (not all potential missing patterns occur).…”