Estimating Relative Risk When Observing Zero Events-Frequentist Inference and Bayesian Credibility Intervals.

Sören Möller,Linda Juel Ahrenfeldt

doi:10.3390/ijerph18115527

Abstract

Relative risk (RR) is a preferred measure for investigating associations in clinical and epidemiological studies with dichotomous outcomes. However, if the outcome of interest is rare, it frequently occurs that no events are observed in one of the comparison groups. In this case, many of the standard methods used to obtain confidence intervals (CIs) for the RRs are not feasible, even in studies with strong statistical evidence of an association. Different strategies for solving this challenge have been suggested in the literature. This paper, which uses both mathematical arguments and statistical simulations, aims to present, compare, and discuss the different statistical approaches to obtain CIs for RRs in the case of no events in one of the comparison groups. Moreover, we compare these frequentist methods with Bayesian approaches to determine credibility intervals (CrIs) for the RRs. Our results indicate that most of the suggested approaches can be used to obtain CIs (or CrIs) for RRs in the case of no events, although one-sided intervals obtained by methods based on deliberate, probabilistic considerations should be preferred over ad hoc methods. In addition, we demonstrate that Bayesian approaches can be used to obtain CrIs in these situations. Thus, it is possible to obtain statistical inference for the RR, even in studies with no events in one of the comparison groups, and CIs for the RRs should always be provided. However, it is important to note that the obtained intervals are sensitive to the method chosen in the case of small sample sizes.

Highlights

Published: 21 May 2021In both observational and experimental studies, the relative risk (RR) is one of the preferred measures for reporting associations between dichotomous exposures/risk factors and a dichotomous outcome
When comparing the approaches of moving and adding one observation, respectively, we find that adding one observation generally results in narrower confidence intervals (CIs) than moving one, especially in Example A, which has the smallest sample size
The proportion-based Bayesian approaches result in credibility intervals (CrIs), which are similar in magnitude to the CIs obtained by frequentist approaches

Summary

Introduction

Published: 21 May 2021In both observational and experimental studies, the relative risk (RR) is one of the preferred measures for reporting associations between dichotomous exposures/risk factors and a dichotomous outcome. When estimating an RR, researchers may encounter a challenge if one of the comparison groups does not experience any event (or if everyone in a group experiences an event), as this would result in an RR of zero or ∞, respectively. In these cases, confidence intervals (CIs) for the RR cannot be reported, and in the resulting research papers, it is often concluded that the sample was not large enough to obtain sufficient inference about the RR. As the RR is a measure of an association, this is not reasonable

Objectives

Methods

Results

Discussion

Conclusion