Diggle-Kenward Model for Dropout

In medical research, studies are often designed in which specific parameters are measured repeatedly over time in the participating subjects. This allows for modeling the process of change within each subject separately, based on both subject-specific factors (such as gender) and experiment-specific factors (such as treatment). The analysis of such longitudinal data requires statistical models that take into account the association between the measurements within subjects. During the past decade, a lot of effort has been put into the search for flexible longitudinal models.

In practice, longitudinal studies often suffer from attrition (i.e., subjects dropping out earlier than scheduled) for reasons outside the control of the investigator. The resulting data are then unbalanced with unequal numbers of measures for each participant. Nowadays, several statistical packages can handle unbalanced longitudinal data. However, they yield valid inferences only under specific assumptions for the dropout process.

Generally, valid inferences can be obtained only by modeling the response measurements and the dropout process simultaneously. Making various assumptions about the dropout mechanism, a large variety of models for continuous as well as categorical outcomes have been proposed in the statistical literature. With the volume of literature on models for incomplete data increasing, there has been growing concern about the critical dependence of many of these models on the validity of the underlying assumptions. To compound the issue, the data often have very little to say about the correctness of such assumptions.

When referring to the missing-value, or nonresponse, process we will use the terminology of Little and Rubin. A nonresponse process is said to be missing completely at random (MCAR) if the missingness is independent of both unobserved and observed data, and missing at random (MAR) if, conditional on the observed data, the missingness is independent of the unobserved measurements. A process that is neither MCAR nor MAR is termed nonrandom (MNAR). In the context of likelihood inference, and when the parameters describing the measurement process are functionally independent of the parameters describing the missingness process, MCAR and MAR are ignorable, whereas a nonrandom process is nonignorable. Ignorability implies that valid inferences about the measurement model parameters can be obtained by analyzing the observed data alone, obviating the need for formulation of a dropout model.

We will present one modeling framework that has been developed for incomplete longitudinal data of a continuous nature, proposed by Diggle and Kenward.

The model has been subject to criticism because it is rather vulnerable to the modeling assumptions made. These concerns will be discussed and a number of ways for dealing with it explored, with a prominent place given to sensitivity analysis.