Analyzing Longitudinal Data with Non-ignorable Missing

Abstract

In longitudinal studies, data are often missing despite every attempt made to collect complete data. When the missingness is informative and hence not ignorable, it is generally difficult to analyze non-ignorable missing (NIM) data since the distributional assumptions about missing data are not easily verifiable using traditional goodness of fit tests or otherwise. Selection models and pattern-mixture models are two common approaches to analyze NIM data. Each approach has its advantages and disadvantages. Methods proposed in this thesis fall into the category of pattern-mixture models. Traditionally, patterns are determined by time to occurrence of missing. This definition often results into the problem of not all parameters being identifiable. Moreover, marginalization is commonly required and can be very tricky when outcomes are discrete.

It is recognized that patterns can and need to be defined by covariates, surrogate variables and⁄or time to missing. We propose two approaches to model NIM data: (i) pseudo-imputation (PI) approach, in which we first obtain predictive means within each pattern, get transformed predictive means by using a suitable link function and then fit with covariates to obtain marginal estimates; (ii) joint-modeling (JM) approach, in which patterns considered as random effects are marginalized within a generalized linear mixed model framework. The JM approach is shown to be able to capture the dependence of missing indicators on missing outcomes in some degree as is the case with NIM data. Some of the main advantages of these proposed approaches include (i) the capability to handle both continuous and discrete responses, (ii) avoidance of the problem of under-identifiability, (iii) availability of marginal estimates, and (iv) computational efficiency. When the missingness does depend on the patterns, results based on simulated data suggest that both approaches yield accurate estimates if the underlying number of patterns is specified correctly. Otherwise the PI method leads to biased results whereas the JM approach still provides reasonably accurate estimates.

Finally, we extend our approaches to a generalized additive model (GAM) replacing the GLM framework. When the underlying relationship is highly non-linear, our extended approaches with a GAM framework provide flexibility and more accurate estimates. The JM approach along with generalized additive models can provide more flexibility than the PI approach since it uses a more robust model for the missing indicator