Derivative ratio as a measure of effect: Sex over age of occurrence of myocardial infarction in Brazil

The concept of relative risk (RR) as an incidence rate ratio is extended to a ratio of derivatives of cumulative occurrences of events with respect to any continuous variable whose domain is partitioned in sub-domains of study and referent groups to be contrasted. RR, thus expressed as a function, allows the identification of key values of the independent variable through which effect, as a relation between sub-domains, is modulated. The effect of sex over age of occurrence of myocardial infarction in a sample of Brazilian patients is analysed. Male sex, as contrasted to female, is acknowledged as a risk factor for the disease but it is known that this risk wanes with aging. Derivatives of cumulative occurrences with respect to age are calculated for men and women. Given the normal distribution of these occurrences, derivatives are found to be very similar to the corresponding normal density functions, with difference not greater than 0.005. This provides an easy way of identifying the derivatives whose ratio is likewise easily calculated. Results suggest that, in the Brazilian sample of patients studied, the greatest men to women RR is 1.9 at the age of 23.5 years and that at the age of 61.2 years risks become evens.21426326