Efficient estimation of relative risk, odds ratio and their logarithms for rare events

TL;DR

This paper introduces sequential estimators for relative risk and odds ratio that efficiently achieve a specified mean-square error, especially effective for rare or moderately rare attributes.

Contribution

It proposes new sequential estimators that guarantee targeted accuracy with high efficiency for rare event analysis.

Findings

Estimators achieve the desired mean-square error with fewer observations.

High efficiency of estimators when attribute prevalence is low or moderate.

Method guarantees consistent estimation across different sample sizes.

Abstract

Sequential estimators are proposed for the relative risk, odds ratio, log relative risk or log odds ratio of a dichotomous attribute in two populations. The estimators take the same number of observations from each population, and guarantee that the relative mean-square error for the relative risk or odds ratio, or the mean-square error for their logarithmic versions, is less than a given target. The efficiency of the estimators, defined in terms of the Cram\'er-Rao bound, is high when the considered attribute is rare or moderately rare.