The risk ratio effect measure is often the main parameter of interest in epidemiologic studies with a binary outcome. In this paper, the author presents a simple and efficient two-stage approach to estimate the risk ratios directly, which does not directly rely on consistency for an estimate of the baseline risk. This latter property is a key advantage of the approach over existing methods, because, unlike these other methods, the proposed approach obviates the need to restrict the predicted risk probabilities to fall below one, in order to recover efficient inferences about risk ratios. An additional appeal of the approach is that it is easy to implement. Finally, when the primary interest is in the effect of a specific binary exposure, a simple doubly robust closed-form estimator is derived, for the multiplicative effect of the exposure. Specifically, we show how one can adjust for confounding by incorporating a working regression model for the propensity score so that the correct inferences about the multiplicative effect of the exposure are recovered if either this model is correct or a working model for the association between confounders and outcome risk is correct, but both do not necessarily hold.