Revisiting the relationship between baseline risk and risk under treatment

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.The questions about whether and how the treatment benefit varies according to a patient's certain characteristics have deserved several works recently. [1-4] Available evidence as well as theoretical considerations support such links. Baseline risk (i.e. the risk of outcome for a patient under no treatment conditions) is used as a convenient summary of numerous characteristics which may be potential risk factors. The relation found between baseline risk and risk under treatment (quoted as the 'effect model' of the treatment [5]) indicates that some patients respond better, i.e. with a greater absolute risk reduction, to a given treatment than others do. L'Abbé plot [6] is a convenient graphical representation of the