Fernanda Schumacher, Ph.D., Division of Biostatistics, College of Public Health, Ohio State University

"Scale Mixture of Skew-Normal Linear Mixed Models: a Bayesian approach using Hamiltonian Monte Carlo"

In clinical trials, studies often present longitudinal or clustered data. These studies are commonly analyzed using linear mixed models, and for mathematical convenience, it is usually assumed that both random effect and error term follow normal distributions. These restrictive assumptions, however, may result in a lack of robustness against departures from the normal distribution and invalid statistical inferences. An interesting extension to make these models more flexible by accounting for skewness and heavy tails is considering the scale mixture of skew-normal class of distributions. Nevertheless, a practical problem may arise when modeling distributions derived from the skew-normal: the possibility that the maximum likelihood estimate of the parameter that regulates skewness diverges. In this work, this anomaly is illustrated for a clinical trial involving schizophrenia, and a Bayesian estimation via Hamiltonian Monte Carlo is proposed and evaluated as an alternative approach. This is joint work with Larissa Avila Matos, Victor Hugo Lachos, and Francisco Louzada Neto.

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