Fitting Multivariate Linear Mixed Model for Multiple Outcomes Longitudinal Data with Non-ignorable Dropout

摘要

Measurements made on several outcomes for the same unit, implying multivariate longitudinal data, are very likely to be correlated. Therefore, fitting such a data structure can be quite challenging due to the high dimensioned correlations exist within and between outcomes over time. Moreover, an additional challenge is encountered in longitudinal studies due to premature withdrawal of the subjects from the study resulting in incomplete (missing) data. Incomplete data is more problematic when missing data mechanism is related to the unobserved outcomes implying what so-called non-ignorable missing data or missing not at random (MNAR). Obtaining valid estimation under non-ignorable assumption requires that the missing-data mechanism be modeled as a part of the estimation process. The multiple continuous outcome-based data model is introduced via the Gaussian multivariate linear mixed models while the missing-data mechanism is linked to the data model via the selection model such that the missing-data mechanism parameters are fitted using the multivariate logistic regression. This article proposes and develops the stochastic expectation-maximization (SEM) algorithm to fit MLMM in the presence of non-ignorable dropout. In the M-step maximizing likelihood function is implemented via a new proposed Quasi-Newton (QN) algorithm that is of EM type, while maximizing the multivariate logistic regression is implemented via Newton-Raphson (NR) algorithm. A simulation study is conducted to assess the performance of the proposed techniques.