Measuring and estimating treatment effect on dichotomous outcome of a population

In different studies for treatment effect on dichotomous outcome of a certain population, one uses different regression models, leading to different measures of the treatment effect. In observational studies, the common measures of the treatment effect are: the conditional risk difference based on a linear model, the conditional risk ratio based on a log-linear model, and the conditional odds ratio based on a logistic model; in randomized trials, the common measures are: the marginal risk difference based on a linear model, the marginal risk ratio based on a log-linear model, and the marginal odds ratio based on a logistic model. In this article, we instead express these measures in terms of the risk of a dichotomous outcome conditional on covariates and treatment, where the risk is then described by a regression model. These expressions of the measures do not explicitly depend on the regression model. As a result, we are able to use one regression model in one study to estimate all these measures by maximum likelihood. We show that these measures have causal interpretations and reflect different aspects of the same underlying treatment effect under the assumption of no unmeasured confounding covariate given observed covariates. We get confidence intervals for these measures by finding approximate distributions of the maximum likelihood estimates of these measures. As an illustration, we estimate these measures for the effect of a triple therapy on eradication of Helicobacter pylori among Vietnamese children and are able to compare the treatment effect in this study with those in other studies.