Nonparametric Estimation of Conditional Distributions and Rank-Tracking Probabilities With Time-Varying Transformation Models in Longitudinal Studies

Colin O. Wu and Xin Tian

Journal of the American Statistical Association, 2013, vol. 108, issue 503, 971-982

Abstract: An objective of longitudinal analysis is to estimate the conditional distributions of an outcome variable through a regression model. The approaches based on modeling the conditional means are not appropriate for this task when the conditional distributions are skewed or cannot be approximated by a normal distribution through a known transformation. We study a class of time-varying transformation models and a two-step smoothing method for the estimation of the conditional distribution functions. Based on our models, we propose a rank-tracking probability and a rank-tracking probability ratio to measure the strength of tracking ability of an outcome variable at two different time points. Our models and estimation method can be applied to a wide range of scientific objectives that cannot be evaluated by the conditional mean-based models. We derive the asymptotic properties for the two-step local polynomial estimators of the conditional distribution functions. Finite sample properties of our procedures are investigated through a simulation study. Application of our models and estimation method is demonstrated through an epidemiological study of childhood growth and blood pressure. Supplementary materials for this article are available online.

Date: 2013
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DOI: 10.1080/01621459.2013.808949

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