Table 3:

Eight methods to estimate adjusted risk ratios that have been described in the literature

 Mantel–Haenszel method to estimate a risk ratio (14), (15) A Mantel–Haenszel risk ratio is calculated by taking a weighted average of risk ratios in strata of covariables, where the weight depends on the size of the strata. Log–binomial regression (8) Log–binomial regression is a generalized linear model with a log link and a binomial distribution. It is similar to logistic regression, except that the link function is a log link instead of a logit link, hence providing risk ratios instead of odds ratios. Ordinary Poisson regression (7) The data are fitted with a generalized linear model with a log link and a Poisson distribution. This approach yields correct estimates of the risk ratio, but the obtained standard errors are in general too large. Poisson regression with robust standard errors (9) Robust standard errors are estimated with a procedure known as sandwich estimation (16) to account for the incorrect assumption of Poisson distributed outcomes in the Poisson regression approach. Method proposed by Zhang and Yu (5) A risk ratio is calculated based on the odds ratio and the incidence of the outcome in the unexposed group. Doubling-of-cases method, proposed by Miettinen (17) Miettinen proposed to include those with the outcome twice in the data set, i.e., once with the outcome and once without the outcome. Then the odds ratio that is estimated by logistic regression analysis in the “new” cohort is in fact the risk ratio of the “original” cohort: the odds ratio is an exact estimation of the risk ratio. This solution is akin to the case–cohort study with a sampling at baseline of 100%. However, the obtained standard errors are too large. Doubling-of-cases method with robust standard errors (18) Robust standard errors are estimated with a procedure known as sandwich estimation (16) to adjust for the too-large standard errors obtained by the doubling-of-cases method proposed by Miettinen. Method proposed by Austin (19) This method uses logistic regression analysis to estimate individual probabilities of having the outcome if a subject would have been either exposed or unexposed. A risk ratio is then calculated by taking the ratio of the means of these probabilities.