Nonparametric estimation for time-varying transformation models with longitudinal data

Regression methods for longitudinal analyses have traditionally focused on conditional-mean-based models. In many situations, the relevant scientific questions could be better studied by modelling the conditional distributions of the outcome variables as a function of time and other covariates. In this paper, we propose a class of time-varying transformation models for modelling the cumulative distribution function of a response variable conditioning on a set of covariates, and develop a two-step smoothing method for estimating the time-varying parameters. Applications and finite sample properties of our models and smoothing estimators are demonstrated through a cohort study of childhood obesity and cardiovascular risk factors, and a simulation study. Theoretical properties are developed for the two-step local polynomial estimators. Our approach provides a useful statistical tool in longitudinal analysis when the conditional-mean-based methods are inappropriate.

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