Assessing uncertainty about parameter estimates with incomplete repeated ordinal data

Abstract

Data collected in clinical trials involving follow-up of patients over a period of time will almost inevitably be incomplete. Patients will fail to turn up at some of the intended measurement times or will not complete the study, giving rise to various patterns of missingness. In these circumstances, the validity of the conclusions drawn from an analysis of available cases depends crucially on the mechanism driving the missing data process; this in turn cannot be known for certain. For incomplete categorical data, various authors have recently proposed taking into account in a systematic way the ignorance caused by incomplete data. In particular, the idea of intervals of ignorance has been introduced, whereby point estimates for parameters of interest are replaced by intervals or regions of ignorance (Vansteelandt and Goetghebeur, 2001; Kenward et al., 2001; Molenberghs et al., 2001). These are identified by the set of estimates corresponding to possible outcomes for the missing data under little or no assumptions about the missing data mechanism. Here we extend this idea to incomplete repeated ordinal data. We describe a modified version of standard algorithms used for fitting marginal models to longitudinal categorical data, which enables calculation of intervals of ignorance for the parameters of interest. The ideas are illustrated using dental pain measurements from a longitudinal clinical trial.