Method to estimate relative risk using exposed proportion and case group data

Abstract

A change in risk of an event occurring, which is affected with a factor, is a common issue in many research fields, and relative risk is widely used because of intuitive interpretation. Estimating relative risk has required data from two follow-up groups and can thus be cost and time consuming. Subjects for whom an event occurred (case group) are often observed but generally analyzed in comparison to those for whom an event did not (control group); however, estimating relative risk using case group data without approximation is hindered. In this study, an obstacle to estimate relative risk using case control data is clarified as a mathematical expression and a new equation to estimate relative risk using the exposed proportion and case group data is proposed. The proposed equation is derived without using the Bayesian methods. A method to estimate the confidence interval for the proposed estimator is also provided. The usefulness of the proposed equation, which requires neither control nor follow-up groups, is demonstrated for both theoretical and real-life examples.