Sensitivity analysis for incomplete data.

摘要

In a longitudinal study each unit is measured on several occasions. It is not unusual in practice for some sequences of measurements to terminate early for reasons outside the control of the investigator, and any unit so affected is often called a dropout. It might therefore be necessary to accommodate dropout in the modeling process.; Rubin (1976) and Little and Rubin (1987) make important distinctions between different missing values processes. A dropout process is said to be completely random if the dropout is independent of both unobserved and observed data and random if, conditional on the observed data, the dropout is independent of the unobserved measurements; otherwise the dropout process is termed non-random.; One approach is to estimate from the available data the parameters of a model representing a non-random dropout mechanism. It may be difficult to justify the particular choice of dropout model, and it does not necessarily follow that the data contain information on the parameters of the particular model chosen, but where such information exists the fitted model may provide some insight into the nature of the dropout process and of the sensitivity of the analysis to assumptions about this process. This is the route taken by Diggle and Kenward (1994) in the context of continuous data and Molenberghs, Kenward, and Lesaffre (1997) for categorical data.; With the volume of literature on non-random missing data increasing, there has been growing concern about the fact that models often rest on strong assumptions and relatively little evidence from the data themselves. This point was already raised by Glynn, Laird en Rubin (1986) who indicate that this is typical for so-called selection models, where the joint distribution of the measurement and missingness processes is factored into the marginal distribution of the measurement process and the conditional process of the missingness process given the measurements. Since the model of Diggle and Kenward (1994) fits within the class of selection models, it is fair to say that it raised, at first, too high expectations. This was made clear by many discussants of this paper. This implies that, for example, formal tests for the null hypothesis of random missingness, while technically possible, should be approached with caution.; In response, there is a growing awareness of the need for methods that investigate the sensitivity of the results with respect to the model assumptions. Molenberghs, Goetghebeur and Lipsitz (1997) illustrate the need for sensitivity analysis by reviewing some of the issues that arise with models for non-random missing data. While a general awareness of the need for sensitivity analysis has grown, only few actual proposals have been made. Moreover, many of these are to be considered as useful but ad hoc approaches.; This work proposes to investigate formal tools for sensitivity analysis. The main data settings are continuous longitudinal data with covariates. Influence of MAR models to small changes into the direction of informative dropout will be explored using the local influence approach of Cook (1986) and this will be compared with Global alternatives. The data settings are selection models, pattern-mixture models, joint log-linear models, and random-effects models.