A New Approach for Nonparametric Inferences Based on Longitudinal Data Subject to Limit of Detection Applied to Evaluations of Mice Data

• Activity Number: 662
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Seongeun Kim*+ and Albert Vexler
• Companies: The State University of New York at Buffalo and New York State University at Buffalo
• Keywords: Limit of detection ; left-censored data ; Autoregressive model ; Kaplan-Meier product limit estimator ; Newton-Raphson method ; Bootstrap method

Abstract

We propose distribution-free techniques to evaluate longitudinal data subject to limit of detection (LOD). The proposed methods utilize non-parametric estimation of multivariate autoregressive (AR) models. We approximate the parametric approach developed by Vexler et al. (2011) without knowledge of the data distributions. The Kaplan-Meier product limit estimator of the distribution function is used to replace the left-censored observations caused by the LOD while deriving non-parametric approximations to the likelihood constructions from Vexler et al. (2011). The Newton-Raphson iteration method is employed in order to solve non-linear equations with respect to different longitudinal data characteristics of interest. Monte Carlo simulations and Bootstrap methods are implemented to examine the performance of the estimators for the AR models when the LOD is in effect. We apply the proposed non-parametric estimation to analyze three real mice data.