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

Area of Science:

• Biostatistics
• Epidemiology
• Clinical Research

Background:

• Relative risk (RR) is crucial for dichotomous outcomes in clinical and epidemiological studies.
• Rare outcomes can lead to zero events in a comparison group, rendering standard confidence interval (CI) methods for RR infeasible.
• Existing literature offers various strategies to address this common challenge.

Purpose of the Study:

• To present, compare, and discuss statistical approaches for obtaining confidence intervals (CIs) for relative risk (RR) when no events are observed in one group.
• To compare frequentist methods with Bayesian approaches for credibility intervals (CrIs) in such scenarios.
• To evaluate the suitability of different methods for statistical inference with rare outcomes.

Main Methods:

• Mathematical arguments and statistical simulations were employed.
• Frequentist methods for confidence intervals (CIs) were analyzed.
• Bayesian approaches for credibility intervals (CrIs) were compared with frequentist methods.

Main Results:

• Most suggested approaches can yield CIs (or CrIs) for RRs even with no events in a group.
• One-sided intervals derived from probabilistic considerations are preferable to ad hoc methods.
• Bayesian approaches effectively provide CrIs in these challenging situations.
• Obtained intervals are sensitive to the chosen method with small sample sizes.

Conclusions:

• Statistical inference for RR is possible even with zero events in a comparison group.
• Confidence intervals (CIs) for RRs should always be reported in such studies.
• The choice of method significantly impacts results, particularly with small sample sizes.
• Probabilistic and Bayesian methods offer robust solutions for rare outcome analysis.