Project R-13798

Developing statistical models for multivariate left-censored variables: a joint model using copula functions for the association and a conditional regression model with left-censored response and covariate variables. (Research)

Left-censored data is commonly obtained when a measuring device is not able to measure the variables of interest below certain tresholds. In this project, we introduce first a joint model for a bivariate vector of left-censored data by using a copula function for the association between the components. For the marginal distribution of each variable we assume a semi-prametric Cox's regression model. Afterwards, we develop a conditional regression model in which both the response and the covariate variable are left-censored. In this model, the distribution of the covariate variable has a strong influence on the finite dimensional parameters of the conditional regression model. To minimize this influence, we assume first a nonparametric Kaplan-Meier estimator for the left-censored covariate and afterwards a smoothed version of it through Bernstein polynomials. As results of this project, we investigate the asymptotic consistency and asymptotic normality of the finite dimensional parameters in the different models. Hereto we also show the almost sure consistency of the infinite dimensional parameters in the form of the baseline hazard function of the Cox's regression model or the non-parametric Kaplan-Meier estimator for the left-censored covariate. Furthermore these methods are illustrated through on real life data sets and userfriendly oftware will be provided.

01 October 2023 - 30 September 2027