Improving the Estimation of the Odds Ratio in Sampling Surveys using Auxiliary Information

Résumé

The odds-ratio measure is widely used in Health and Social surveys where the aim is to compare the odds of a certain event between a population at risk and a population not at risk. It can be defined using logistic regression through an estimating equation that allows a generalization to continuous risk variable. Data from surveys need to be analyzed in a proper way by taking into account the survey weights. Because the odds-ratio is a complex parameter, the analyst has to circumvent some difficulties when estimating confidence intervals. The present paper suggests a nonparametric approach that can take advantage of some auxiliary information in order to improve on the precision of the odds-ratio estimator. The approach consists in B-spline modelling which can handle the nonlinear structure of the parameter in a flexible way and is easy to implement. The variance estimation issue is solved through a linearization approach and confidence intervals are derived. Two small illustrations are discussed.