Estimating risk ratio from any standard epidemiological design by doubling the cases

Despite the ease of interpretation and communication of a risk ratio (RR), and several other advantages in specific settings, the odds ratio (OR) is more commonly reported in epidemiological and clinical research. This is due to the familiarity of the logistic regression model for estimating adjusted ORs from data gathered in a cross-sectional, cohort or case-control design. The preservation of the OR (but not RR) in case-control samples has contributed to the perception that it is the only valid measure of relative risk from case-control samples. For cohort or cross-sectional data, a method known as ‘doubling-the-cases’ provides valid estimates of RR and an expression for a robust standard error has been derived, but is not available in statistical software packages.

In this paper, we first describe the doubling-of-cases approach in the cohort setting and then extend its application to case-control studies by incorporating sampling weights and deriving an expression for a robust standard error. The performance of the estimator is evaluated using simulated data, and its application illustrated in a study of neonatal jaundice. We provide an R package that implements the method for any standard design.

Our work illustrates that the doubling-of-cases approach for estimating an adjusted RR from cross-sectional or cohort data can also yield valid RR estimates from case-control data. The approach is straightforward to apply, involving simple modification of the data followed by logistic regression analysis. The method performed well for case-control data from simulated cohorts with a range of prevalence rates. In the application to neonatal jaundice, the RR estimates were similar to those from relative risk regression, whereas the OR from naive logistic regression overestimated the RR despite the low prevalence of the outcome.

By providing an R package that estimates an adjusted RR from cohort, cross-sectional or case-control studies, we have enabled the method to be easily implemented with familiar software, so that investigators are not limited to reporting an OR and can examine the RR when it is of interest.