Simultaneous Bayesian modelling of skew-normal longitudinal measurements with non-ignorable dropout

Most often in genetic improvement studies, repeated measurements are observed on an individual animal, and these repeated measurements are often skewed. From the practical viewpoint, logarithm transformations of variables are usually adopted to reduce skewness, and this works satisfactorily in many cases. In most longitudinal datasets, however, because of the high rate of missingness, skewness often remains after transformation, the achievement of joint normality for each component of separately transformed variables, which are often difficult to interpret, is unrealistic. For this purpose, a more general form of distributions for considering skewness in the model should be used. In this paper, we used Bayesian joint modelling of longitudinal and survival data when data set presents skewness. A skew-normal mixed-effects model for longitudinal measurements and a Cox proportional hazard model for time to event variable were considered. We performed some simulation studies to investigate the performance of the proposed method to skewness in random effects, different dropout rates and sample sizes. Furthermore, we illustrated the proposed method using Nigerian indigenous chickens (NIC) dataset. The longitudinal outcomes of NIC data set were skewed, and presented left censored dropout. We assumed different model structures for the analysis of this data set and considered two versions of the deviance information criteria: namely, the conditional criteria (given the random effects) and marginal criteria (averaging over the random effects) in selecting the true model. These criteria were computed using the importance sampling method.