Longitudinal binary response models using alternative links for medical data

Motivated for a medical data about schizophrenia symptoms where an imbalanced binary response is observed, we introduce a broad class of link functions, called power and reverse power, as an alternative to analyse longitudinal binary data, particularly when it is imbalanced as is common in medical data. Bayesian estimation using an MCMC procedure through the No-U-Turn Sampler algorithm is proposed. Posterior predictive checks, Bayesian randomized quantile residuals, and a Bayesian influence measures are considered for model diagnostics. Different models are compared using selection model criteria. A simulation study is developed to analyse the prior sensitivity of the variance of the random effect and to assess the performance of the proposed model in the presence of imbalanced data. Finally, an application of the methodology studied in a set of medical data on the presence of schizophrenia symptom "thought disorder" is considered. In this data set, the presence of symptoms is much less than the absence, thus we show, in practice, the usefulness of using alternative link functions in imbalanced data.