# Likelihood-Based Confidence Intervals for ratio of risk ratios

Ratio of Risk Ratio (RRR), along with Relative Excess Risk Due to Interaction (RERI), has been used to quantify the joint effects of 2 exposures in epidemiology.

Quoting Joshua N. Pritikin

CIs based on standard errors (SEs) are common in practice, but likelihood-based CIs are worth consideration. In comparison to SEs, likelihood-based CIs are typically more difficult to estimate, but are more robust to model (re)parameterization.

This shows how confidence intervals for the ratio of ratios can be calculated using standard error "when the data can be considered at least approximately normally distributed."

Given the example dataset from Nie et al, 2010:

The ratio of RR for A in strata of B can be calculated using:

$$RRR(A) = RR(B=1)/RR(B=0)$$

My questions are:

1. How can I implement in practice in R the estimation of likelihood-based confidence intervals for the RRR above?
2. Is there a simpler alternative (e.g., bootstrap approaches, delta method) that is robust even when the data cannot " be considered ...approximately normally distributed" and could be easy to implement in R to derive CI for RRR above?
• R code questions are off-topic here strictly speaking but for your Q1, does it not work to fit a log-binomial model and then use confint() on the fitted model? – mdewey Dec 7 '18 at 17:22