Ratio estimation via Poisson regression and Generalized Estimating Equations

In this article, we show that ratio estimates, and their asymptotic variances can be correctly obtained from a Poisson regression with appropriately chosen link function and Generalized Estimating Equation techniques. The sandwich estimator of variance is shown to be algebraically equal to the usual asymptotic variance obtained by considering a Taylor series expansion. The result is similar in spirit to the widely known fact that the odds ratio can be obtained from the estimated coefficients of a logistic regression with appropriately coded explanatory variables. The result is particularly useful as GEE methods are now available in many software packages. Some examples are given to illustrate our proposal. The result is also applicable to clustered data.