Longitudinal data analysis with non-ignorable missing data

Abstract

A common problem in the longitudinal data analysis is the missing data problem. Two types of missing patterns are generally considered in statistical literature: monotone and non-monotone missing data. Nonmonotone missing data occur when study participants intermittently miss scheduled visits, while monotone missing data can be from discontinued participation, loss to follow-up, and mortality. Although many novel statistical approaches have been developed to handle missing data in recent years, few methods are available to provide inferences to handle both types of missing data simultaneously. In this article, a latent random effects model is proposed to analyze longitudinal outcomes with both monotone and non-monotone missingness in the context of missing not at random. Another significant contribution of this article is to propose a new computational algorithm for latent random effects models. To reduce the computational burden of high-dimensional integration problem in latent random effects models, we develop a new computational algorithm that uses a new adaptive quadrature approach in conjunction with the Taylor series approximation for the likelihood function to simplify the E-step computation in the expectation-maximization algorithm. Simulation study is performed and the data from the scleroderma lung study are used to demonstrate the effectiveness of this method.

Keywords: Adaptive quadrature; joint model; missing not at random; scleroderma study.

Figure 1

Longitudinal FVC in the placebo and CYC groups during the first 12 months. In the Scleroderma lung study, the forced vital capacity (FVC, expressed as a percentage of the predicted value) is measured at baseline and at three-month intervals throughout the study. In this figure, two subjects (01-ALS-013 and 04-JWW-010) in the placebo group are highlighted as examples of study dropouts at 6 and 9 months, and two subjects (08-S-L-018 and 09-NEP-005) in the CYC group are examples of missed visits at 6 and 9 months.