Revisiting the relationship between baseline risk and risk under treatment

In medical practice, it is generally accepted that the 'effect model' describing the relationship between baseline risk and risk under treatment is linear, i.e. 'relative risk' is constant. Absolute benefit is then proportional to a patient's baseline risk and the treatment is most effective among high-risk patients. Alternatively, the 'effect model' becomes curvilinear when 'odds ratio' is considered to be constant. However these two models are based on purely empirical considerations, and there is still no theoretical approach to support either the linear or the non-linear relation.

From logistic and sigmoidal Emax (Hill) models, we derived a phenomenological model which includes the possibility of integrating both beneficial and harmful effects. Instead of a linear relation, our model suggests that the relationship is curvilinear i.e. the moderate-risk patients gain most from the treatment in opposition to those with low or high risk.

Two approaches can be proposed to investigate in practice such a model. The retrospective one is to perform a meta-analysis of clinical trials with subgroups of patients including a great range of baseline risks. The prospective one is to perform a large clinical trial in which patients are recruited according to several prestratified diverse and high risk groups.

For the quantification of the treatment effect and considering such a model, the discrepancy between odds ratio and relative risk may be related not only to the level of risk under control conditions, but also to the characteristics of the dose-effect relation and the amount of dose administered. In the proposed approach, OR may be considered as constant in the whole range of Rc, and depending only on the intrinsic characteristics of the treatment. Therefore, OR should be preferred rather than RR to summarize information on treatment efficacy.