A0319
Title: Estimating the linear relation between variables that are never jointly observed: An application to in vivo experiments
Authors: Polina Arsenteva - Institut de Mathematiques de Bourgogne (France) [presenting]
Mohamed Amine Benadjaoud - IRSN (France)
Herve Cardot - Universite de Bourgogne (France)
Abstract: The motivation comes from in vivo experiments in which different measurements are performed on different animals. Thus, the variables of interest can never be observed simultaneously, making the task of estimating the linear regression coefficients challenging. Assuming that the global experiment can be decomposed into subpopulations (corresponding, for example, to different doses of a treatment substance) with distinct first moments, we propose different estimators of the linear regression, which take into account this additional information. We consider a method of moments approach as well as an approach based on optimal transport theory. These estimators are proved to be consistent as well as asymptotically Gaussian under weak hypotheses. Bootstrap techniques are shown to give consistent confidence intervals for the estimated parameter. A Monte Carlo study is conducted to assess and compare the finite sample performances. Finally, the proposed approaches are illustrated in the context of radiobiology, namely a preclinical study on mice investigating the multiscale correlation between the inflammation process (gene expression) and lung injury (septal thickening) appearing after irradiation, with a further comparison of the results across several irradiation configurations.
