ANALYSIS OF LONGITUDINAL DATA WITH NON-IGNORABLE NONMONOTONE MISSING VALUES

A full likelihood method is proposed to analyse continuous longitudina l data with non-ignorable (informative) missing values and non-monoton e patterns. The problem arose in a breast cancer clinical trial where repeated assessments of quality of life were collected: patients rated their coping ability during and after treatment. We allow the missing ness probabilities to depend on unobserved responses, and we use a mul tivariate normal model for the outcomes. A first-order Markov dependen ce structure for the responses is a natural choice and facilitates the construction of the likelihood; estimates are obtained via the Nelder -Mead simplex algorithm. Computations are difficult and become intract able with more than three or four assessments. Applying the method to the quality-of-life data results in easily interpretable estimates, co nfirms the suspicion that the data are non-ignorably missing and highl ights the likely bias of standard methods. Although treatment comparis ons are not affected here. the methods are useful for obtaining unbias ed means and estimating trends over time.