Statistics and Its Interface

Volume 7 (2014)

Number 1

We dedicate this special issue to Dr. Gang Zheng, a great colleague and dear friend to many of us.

Estimation of rank-tracking probabilities using nonparametric mixed-effects models for longitudinal data

Pages: 87 – 99

DOI: http://dx.doi.org/10.4310/SII.2014.v7.n1.a10

Authors

Xin Tian (Office of Biostatistics Research, National Heart, Lung and Blood Institute, Bethesda, Maryland, U.S.A.)

Colin O. Wu (Office of Biostatistics Research, National Heart, Lung and Blood Institute, Bethesda, Maryland, U.S.A.)

Abstract

An important scientific objective of longitudinal studies involves tracking the probability of a subject having certain health status over the course of the study. Proper definitions and estimates of disease risk tracking have important implications in the design and analysis of long-term biomedical studies and in developing guidelines for disease prevention and intervention. We study in this paper a class of “rank-tracking probabilities” (RTP) to describe a subject’s conditional probabilities of having certain health outcomes at two different time points. Structural nonparametric estimation and inferences for the RTPs and their functions are developed based on nonparametric mixed-effects models and B-spline smoothing methods. Statistical properties of our procedures are investigated through a simulation study. We apply our methods to an epidemiological study of childhood cardiovascular risk factors, and demonstrate that the RTPs and their nonparametric estimators provide useful tools to quantitatively evaluate whether the cardiovascular risks, such as obesity and hypertension, can be tracked from early childhood to adolescence.

Keywords

basis approximation, conditional distribution, longitudinal study, mixed model, timevarying coefficient model, rank-tracking probability

2010 Mathematics Subject Classification

Primary 62G08, 62H10. Secondary 62P10, 65D10.

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