Modeling Pain score in clinical trials using a joint survival-longitudinal mixed model with a Beta distribution in presence of missing values not occurring at random.
Marion Bouillon-Pichault, Bruno Boulanger, Astrid Jullion, Bianca Teodorecu
Objectives: In clinical trials investigating pain drugs, the pain is usually assessed by means of a score or a Visual Analogic Scale (VAS) always bounded in [0,10]. In such trials there are potentially two major sources of bias for estimating the real effect of a new drug assumed to decrease pain. The objective is to propose a method that allows an unbiased estimation of the treatment effect.
Methods:First, given the bounded nature of the Pain score, the use of a Beta distribution is preferred instead of a normal distribution that can lead to bias in estimates. For that purpose, a longitudinal mixed effect model with a Beta-Normal distribution has been developed to model pain score over the duration of the study.
Second, in this type of study in chronic or acute pain, the rate of dropouts by requiring rescue medication is in general large - from 15% to 35% - during the four first weeks and mostly linked to a lack of perceived efficacy, i.e. the dropouts are informative. In that case the data are missing not at random (NAR). To assess the efficacy of a new drug, the focus is on both the longitudinal data and the time-to-event, time to rescue medication here, with the aim to understand the association between both processes. Indeed a new pain drug will be declared more efficacious if time to rescue medication has been significantly prolonged and if pain score decreases more than placebo.
Results: The use of a Beta distribution for the pain scores and the joint modeling of both longitudinal and time to event data lead to unbiased treatment estimates. Ignoring the dropouts mechanism provides an underestimation of the treatment effect which can go up to 30% in some situations.
Conclusions: For the later, unbiased estimates for the longitudinal model in presence of missing values NAR can only be obtained if jointly modeled with the dropout mechanism.