A Comparison and Integration of Quantile Regression and Finite Mixture Modeling

• Activity Number: 410
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Richard Willke and Ching-Ray Yu*+ and Birol Emir and Kelly Zou and Javier Cabrera
• Companies: Pfizer and Pfizer and Pfizer and Pfizer and Rutgers University
• Keywords: Quantile regression ; finite mixture models ; Mahalanobis distance ; nonparametric method ; parametric method ; Monte-Carlo

Abstract

Quantile regression (QR) and parametric finite mixture models (FMM) are useful methods for estimating marginal treatment effects at different points in an outcome distribution while controlling for covariate effects. However, they may not yield similar inferences at any given point in the outcome distribution; also , FMM estimation is not as robust as QR. In this research, we aim to reconcile the differences in estimates by comparing and integrating QR and FMM. First, we model the structure of covariate effects within and between distribution components in FMM. Based on this model and the resulting estimates in sample data, we compare the proximity of FMM and QR estimates using Mahalanobis distance measures. We propose new methodology for estimating FMM components by applying QR for a selection of quantiles satisfying an optimality criterion. Our method is robust and computationally fast and stable. This integrated approach incorporates nonparametric and parametric methods to help interpret estimated effects from QR and FMM, depending on the underlying distributions and the covariates. These methods are compared and illustrated using Monte-Carlo simulations and real-data examples.