Analysis of longitudinal data with non-ignorable non-monotone missing values

• Published in: Applied statistics 1998, Vol.47 (3), p.425-438
• Main Authors: Troxel, A. B., Harrington, D. P., Lipsitz, S. R.
• Format: Article
• Language: English
• Subjects: Confidence interval; Estimation bias; Exact sciences and technology; Health outcomes; Incomplete data; Longitudinal data; Markov correlation; Mathematics; Maximum likelihood; Maximum likelihood estimation; Missing data; Modeling; Multivariate analysis; Nonparametric inference; Parametric models; Probability and statistics; Quality of life; Repeated measurements; Sciences and techniques of general use; Standard error; Statistics
• ISSN: 0035-9254; 1467-9876
• DOI: 10.1111/1467-9876.00119

A full likelihood method is proposed to analyse continuous longitudinal data with nonignorable (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. 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.