chapter  19
20 Pages

Shared-parameter models

ByPaul S. Albert, Dean A. Follmann

Modeling longitudinal data subject to missingness has been an active area for biostatistical research. The missing-data mechanism is said to be missing completely at random if the probability of missing is independent of both observed and unobserved data, missing at random (MAR) if the probability of missing is independent of only the observed data, and not missing at random (NMAR) if the probability of missingness depends on the unobserved data (Rubin, 1976; Little and Rubin, 1987). It is well known that naive methods may result in biased inferences under an NMAR mechanism. The use of shared (random) parameter models has been one approach to accounting for non-random missingness. In this formulation, a model for the longitudinal response measurements is linked with a model for the missing-data mechanism through a set of random effects that are shared between the two processes. For example, in a study of repeated measurements of lung function, Wu and Carroll (1988) proposed a model whereby the response process, which was modeled with a linear mixed model with a random intercept and slope, was linked with the censoring process by including an individual’s random slope as a covariate in a probit model for the censoring process. When the probit regression coefficient for the random slope is not zero, there is dependence between the response and missing-data processes. Failure to account for this dependence can lead to biased estimation. Shared-parameter models (Follmann and Wu, 1995) induce a type of non-randomly missing-data mechanism that has been called “informative missingness” (Wu and Caroll, 1988). For review and comparison with other methods, see Little (1995), Hogan and Laird (1997b), and Vonesh, Greene, and Schlucher (2006).