On Modeling and Estimation for the Relative Risk and Risk Difference

TL;DR

This paper introduces a new nuisance model, the conditional log odds-product, to improve estimation of relative risk and risk difference by addressing variation dependence issues, enabling robust statistical inference.

Contribution

It proposes the conditional log odds-product as a novel nuisance model that simplifies estimation and allows for doubly-robust methods in risk modeling.

Findings

The proposed model facilitates maximum-likelihood estimation.

Simulation studies demonstrate improved estimation accuracy.

Application to real data shows practical utility.

Abstract

A common problem in formulating models for the relative risk and risk difference is the variation dependence between these parameters and the baseline risk, which is a nuisance model. We address this problem by proposing the conditional log odds-product as a preferred nuisance model. This novel nuisance model facilitates maximum-likelihood estimation, but also permits doubly-robust estimation for the parameters of interest. Our approach is illustrated via simulations and a data analysis.