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Analysis of longitudinal data with non-ignorable non-monotone missing values. (English) Zbl 0905.62113
Summary: A full likelihood method is proposed to analyse continuous longitudinal data with non-ignorable (informative) missing values and non-monotone 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 missingness probabilities to depend on unobserved responses, and we use a multivariate normal model for the outcomes.
A first-order Markov dependence structure for the responses is a natural choice and facilitates the construction of the likelihood; estimates are obtained via the Nelder-Mead simplex algorithm [J. A. Nelder and R. Mead, Computer J. 7, 308-313 (1965; Zbl 0229.65053)]. Computations are difficult and become intractable with more than three or four assessments. Applying the method to the quality-of-life data results in easily interpretable estimates, confirms the suspicion that the data are non-ignorably missing and highlights the likely bias of standard methods. Although treatment comparisons are not affected here, the methods are useful for obtaining unbiased means and estimating trends over time.

62P10 Applications of statistics to biology and medical sciences; meta analysis
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