Odds ratio (OR) and relative risk (RR) are the most commonly used statistical indicators for the estimation of the association between exposure and outcome. In the cohort study with rare outcomes, the estimated OR approximately equals RR, but RR seems more interpretable. The study aims to explore the difference between OR and RR estimated by different multivariate analyses to provide reference for the selection of more appropriate multivariate regression methods and reporting indicators for estimating the association between exposure and rare outcome in cohort studies. This case study used the data from China birth cohort study. Modes of conception and congenital disabilities were regarded as exposure and outcome, respectively. Maternal age, family history of congenital disabilities with clear evidence were included as covariates. Logistic regression, log-binomial regression, and Poisson regression were used to estimate the OR and RR, respectively. Then, OR, RR, and their 95%CI estimated by three regression models were compared. The OR estimated by logistic regression was approximately equal to the RR estimated by log-binomial regression or Poisson regression. However, the RR estimated by log-binomial regression or Poisson regression was closer to 1.00, with a narrower 95%CI. Log-binomial regression or Poisson regression might have non convergence or over dispersion problems. It is recommended to report the RR obtained by log-binomial regression or Poisson regression in the cohort study with rare outcomes if applicable.

Cohort study; Rare outcome; Odds ratio; Relative risk; Multivariate analysis