Improving the estimation of the odds-ratio using auxiliary information

TL;DR

This paper introduces a nonparametric B-spline calibration method that incorporates survey weights and auxiliary information to improve the precision of odds ratio estimation in health and social surveys.

Contribution

It proposes a novel B-spline calibration approach for odds ratio estimation that handles nonlinear structures and can be implemented with standard survey software.

Findings

Improved precision of odds ratio estimates demonstrated on two examples.

Method effectively incorporates auxiliary information and survey weights.

Variance estimation via linearization enhances reliability.

Abstract

The odds ratio measure is used in health and social surveys where the odds of a certain event is to be compared between two populations. It is defined using logistic regression, and requires that data from surveys are accompanied by their weights. A nonparametric estimation method that incorporates survey weights and auxiliary information may improve the precision of the odds ratio estimator. It consists in $B$-spline calibration which can handle the nonlinear structure of the parameter. The variance is estimated through linearization. Implementation is possible through standard survey softwares. The gain in precision depends on the data as shown on two examples.