A Bayesian sensitivity analysis of the effect of different random effects distributions on growth curve models

Growth curve data consist of repeated measurements of a continuous growth process of human, animal, plant, microbial or bacterial genetic data over time in a population of individuals. A classical approach for analysing such data is the use of non-linear mixed effects models under normality assumption for the responses. But, sometimes the underlying population that the sample is extracted from is an abnormal population or includes some homogeneous sub-samples. So, detection of original properties of the population is an important scientific question of interest. In this paper, a sensitivity analysis of using different parametric and non-parametric distributions for the random effects on the results of applying non-linear mixed models is proposed for emphasizing the possible heterogeneity in the population. A Bayesian MCMC procedure is developed for parameter estimation and inference is performed via a hierarchical Bayesian framework. The methodology is illustrated using a real data set on study of influence of menarche on changes in body fat accretion.