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B0500
Title: P-spline estimation in varying coefficient models with right censored data Authors:  Anneleen Verhasselt - Hasselt University (Belgium) [presenting]
Paul Janssen - Hasselt University (Belgium)
Kim Hendrickx - Hasselt University (Belgium)
Abstract: Modeling the relationship between the response and one or more covariates is an important activity in statistics. Several regression models have been proposed in the literature among which the classical linear regression model is the simplest model. Varying coefficient models provide an extension of the classical linear model; they are still linear in the covariates, but the regression coefficients are smooth functions in one or more other variables. The attraction of these models is the ability of capturing complex relationships in the data. In a variety of scientific fields responses are subject to random right censoring, among others time-to-event in medicine (survival data). We estimate the varying coefficients - for random right censored data - using P-splines. To apply the P-spline method in case responses are subject to right censoring we first transform the observed response (which can be a time-to-event or a censored observation) into a 'synthetic' response, where the conditional means (conditioning is on the covariates) of the time-to-event and the synthetic response are matched. The P-spline method is then applied to the transformed data. We study the asymptotic properties of our estimators and discuss how to select the smoothing parameters and the transformation parameter in a data-driven way. In addition, we demonstrate with simulated and real data the finite sample behavior of the estimators.