Α Markov model for longitudinal studies with incomplete dichotomous outcomes

Abstract

Missing outcome data constitute a serious threat to the validity and precision of inferences from randomized controlled trials. In this paper, we propose the use of a multistate Markov model for the analysis of incomplete individual patient data for a dichotomous outcome reported over a period of time. The model accounts for patients dropping out of the study and also for patients relapsing. The time of each observation is accounted for, and the model allows the estimation of time-dependent relative treatment effects. We apply our methods to data from a study comparing the effectiveness of 2 pharmacological treatments for schizophrenia. The model jointly estimates the relative efficacy and the dropout rate and also allows for a wide range of clinically interesting inferences to be made. Assumptions about the missingness mechanism and the unobserved outcomes of patients dropping out can be incorporated into the analysis. The presented method constitutes a viable candidate for analyzing longitudinal, incomplete binary data.

Keywords: Bayesian analysis; missing data; multistate models.

Figure 1

(A) A 3‐state model with transitions between states 1 and 2 allowed both ways. State 3 is an absorbing state and corresponds to a patient dropping out of the study. Each transition from state Χ to state Ψ is associated with a transition rate γ_ΧΨ. (B‐F) Four‐state models with 2 unobserved states incorporating different assumptions about the missingness mechanism

Figure 2

Model estimates from the 3‐state model (lines) and actual observations in the data (dots). The y‐axis shows the probability of a patient being found in each state as a function of time (shown on the x‐axis). Dashed lines and white dots for amisulpride, thick lines and black dots for risperidone