# Bayesian estimation of the measurement of interactions in epidemiological studies

## TL;DR

This paper introduces a Bayesian method for estimating additive interactions in epidemiological studies, offering a new approach that performs well compared to traditional methods.

## Contribution

The study proposes a Bayesian framework for estimating and calculating credible intervals for additive interaction measures.

## Key findings

- Bayesian estimates were close to true values in simulations.
- Bayesian credible intervals were more balanced than frequentist confidence intervals.
- The Bayesian method outperformed bootstrap and delta methods in small samples.

## Abstract

Interaction identification is important in epidemiological studies and can be detected by including a product term in the model. However, as Rothman noted, a product term in exponential models may be regarded as multiplicative rather than additive to better reflect biological interactions. Currently, the additive interaction is largely measured by the relative excess risk due to interaction (RERI), the attributable proportion due to interaction (AP), and the synergy index (S), and confidence intervals are developed via frequentist approaches. However, few studies have focused on the same issue from a Bayesian perspective. The present study aims to provide a Bayesian view of the estimation and credible intervals of the additive interaction measures.

Bayesian logistic regression was employed, and estimates and credible intervals were calculated from posterior samples of the RERI, AP and S. Since Bayesian inference depends only on posterior samples, it is very easy to apply this method to preventive factors. The validity of the proposed method was verified by comparing the Bayesian method with the delta and bootstrap approaches in simulation studies with example data.

In all the simulation studies, the Bayesian estimates were very close to the corresponding true values. Due to the skewness of the interaction measures, compared with the confidence intervals of the delta method, the credible intervals of the Bayesian approach were more balanced and matched the nominal 95% level. Compared with the bootstrap method, the Bayesian method appeared to be a competitive alternative and fared better when small sample sizes were used.

The proposed Bayesian method is a competitive alternative to other methods. This approach can assist epidemiologists in detecting additive-scale interactions.