Assessing the regression to the mean for non-normal populations via kernel estimators

Background : Part of the change over time of a response in longitudinal studies may be attributed to the re-gression to the mean. The component of change due to regression to the mean is more pronounced in the subjects with extreme initial values. Das and Mulder proposed a nonparametric approach to estimate the regression to the mean. Aim : In this paper, Das and Mulders method is made data-adaptive for empirical distributions via kernel estimation approaches, while retaining the orig-inal assumptions made by them. Results : We use the best approaches for kernel density and hazard function estimation in our methods. This makes our approach extremely user friendly for a practitioner via the state of the art procedures and packages available in statistical softwares such as SAS and R for kernel density and hazard function estimation. We also estimate the standard error of our estimates of regression to the mean via nonparametric bootstrap methods. Finally, our methods are illustrated by analyzing the percent predicted FEV1 measurements available from the Cystic Fibrosis Foundations National Patient Registry. Conclusion : The kernel based approach presented in this article is a user-friendly method to assess the regression to the mean in non-normal populations.