Relative Risk P - Value

Question

Several sources indicate to use Z = lnRR/((SE)(lnRR)) to determine the P value for testing measurements of Relative Risk. I have been unable to find the origin of this approach. Is this an appropriate technique?

Answer 1

I interpret the parentheses in what you wrote to mean:

$$Z=\frac{\ln RR}{\text{SE}(\ln RR)}, $$

where $\text{SE}$ is the standard error. This is a type of Wald test, on a single coefficient.* Models of relative risk are typically fit in a log scale via maximum-likelihood methods, for which theory indicates an asymptotic normal distribution of coefficient estimates. Testing that z value against a standard normal distribution provides the p value.

This is one of 3 types of test typically used with maximum-likelihood models. With small sample sizes a likelihood-ratio test for $\ln RR$ might be preferable, but that requires fitting two models, one with the predictor and one without. Wald tests on all coefficients are easily obtained from a single model fit, so those are what are usually reported in initial summaries of model results.

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*Technically, a Wald test is based on a chi-square statistics and can evaluate multiple coefficients at once. With a single coefficient, the Wald test is equivalent to this z-test.