On Modeling and Estimation for the Relative Risk and Risk Difference

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. An R package implementing the proposed methods is available on CRAN. Supplementary materials for this article are available online.

KEYWORDS:

• Bivariate mapping
• Estimating equation
• Semiparametric model
• Variation independence

Supplementary Materials

The online supplement contains the R code and additional proofs for the article.

Acknowledgment

The authors thank Sander Greenland for helpful conversations, encouragement and the data from Neutra, Greenland, and Friedman (1980). The authors also thank Dick Kronmal, Eric Tchetgen Tchetgen, and Ken Rice for valuable comments.

Funding

This research was supported by U.S. National Institutes of Health grant R01 AI032475, AI113251, and ONR grant N00014-15-1-2672.