A Selection Model for Longitudinal Data with Non-Ignorable Non-Monotone Missing Values

Ahmed M Gad

doi:10.6339/jds.201104_09(2).0003

Abstract

Missing values are not uncommon in longitudinal data studies. Missingness could be due to withdrawal from the study (dropout) or intermittent. The missing data mechanism is termed non-ignorable if the probability of missingness depends on the unobserved (missing) observations. This paper presents a model for continuous longitudinal data with non-ignorable non-monotone missing values. Two separate models, for the response and missingness, are assumed. The response is modeled as multivariate nor mal whereas the binomial model for missingness process. Parameters in the adopted model are estimated using the stochastic EM algorithm. The proposed model (approach) is then applied to an example from the International Breast Cancer Study Group.

Highlights

Longitudinal data consist of time sequence of measurements on several subjects
The missing values is termed non-ignorable if the probability of being missing depends on the unobserved measurements
One of the relevant determinants of quality of life was the Perceived Adjustment to Chronic Illness Scale (PACIS). This is one-item scale comprising a global patient rating of the amount of effort costs to cope with illness. In this trial the PACIS assessments for patients who remained alive during the 15 months of the study are analyzed

Summary

Introduction

Longitudinal data consist of time sequence of measurements on several subjects. Longitudinal data frequently involve some missing values. The missing values is termed non-ignorable if the probability of being missing depends on the unobserved measurements In this case a model is needed for both the observed and missing data for unbiased inference. Gad (1994) propose a model that combine logistic model for the dropout process and normal linear model for the response. They formulate the log-likelihood and the parameter estimates are obtained by using Simplex method. The aim of this paper is to propose a selection model for longitudinal data with dropout and intermittent missing values. As we are aware, this is the first paper to propose a model for continuous longitudinal data with non-ignorable intermittent and dropout missing values.

Model and Notation

Estimation

Application

Findings

Conclusion