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Abstract:
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Analysis of heterogeneous data where the conditional distributions vary differently with the covariates for the tails and the central location are often analyzed by quantile regression methods. Traditional quantile regression, based on minimizing the sum of absolute residuals, has been developed for independent data and is widely used. When repeated observations are taken on each unit, however, the assumption of independence is no longer valid and alternative methods are required. We propose a parametric Bayesian approach to model the population medians using the Markov chain Monte Carlo algorithm. The approach will be compared to maximum likelihood estimation and inference, an approach based on a transformation to log-normality, and a marginal model technique akin to GEE. Data from recent randomized clinical trials will be used to illustrate the methodology.
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