Missing Data

The problem of dealing with missing values is common throughout statistical work and is present whenever human subjects are enrolled. Respondents may refuse participation or may be unreachable. Patients in clinical and epidemiological studies may with draw their initial consent without further explanation. Early work on missing values was largely concerned with algorithmic and computational solutions to the induced lack of balance or deviations from the intended study design (Afifi and Elashoff 1966; Hartley and Hocking 1971). More recently general algorithms such as the Expectation-Maximization (EM) (Dempster et al. 1977), and data imputation and augmentation procedures (Rubin1987;Tanner andWong1987) combined with powerful computing resources have largely provided a solution to this aspect of the problem. There remains the very difficult and important question of assessing the impact of missing data on subsequent statistical inference. Conditions can be formulated, under which an analysis that proceeds as if the missing data are missing by design, that is, ignoring the missing value process, can provide valid answers to study questions. While such an approach is attractive from a pragmatic point of view, the difficulty is that such conditions can rarely be assumed to hold with full certainty. Indeed, assumptions will be required that cannot be assessed from the data under analysis. Hence in this setting there cannot be anything that could be termed a definitive analysis, and hence any analysis of preference is ideally to be supplemented with a so-called sensitivity analysis.