ESTIMATING RELATIVE RISK OF DISEASE FROM OUTPUTS OF LOGISTIC-REGRESSION WHEN THE DISEASE IS NOT RARE

Many epidemiologic studies in the veterinary field aim to quantify the relationships between risk factors and the occurrence of diseases. Th e strength of the association between a factor and a disease can be me asured by (i) a relative risk (RR), or (ii) an odds ratio (OR) which i s widely used because it is directly derived from the estimates of log istic regression. RR directly provides the relative increase in the pr obability of disease occurrence in case of exposure. OR is often inter pretated as a multiplicative factor of the risk of disease occurrence when exposed, although it is not a good approximation of RR when the d isease is not rare. The objective of this paper is to propose a method to estimate RR of disease from adjusted odds ratios derived from logi stic regression when the disease is not rare. The method of estimation is developed for three different cases: (i) the factor and the outcom e are dichotomous; (ii) the factor has more than two classes, and the outcome is dichotomous; and (iii) the factor and the outcome both have mon than two classes. In all cases, the principles of estimation are the same: in a subpopulation including individuals diseased at level j (D-j) and not diseased (D-0). when exposed to level i (F-i) or not ex posed to the factor (F-0), (R) over cap R-ij can be calculated with ad justed (O) over cap R-ij, and the frequencies of individuals exposed t o level i (n(i&j)), of those not exposed (n(0&j)) and of those disease d (n(i&j)) among the individuals exposed to level i and not exposed, ( R) over cap R-ij is the positive solution of the formula: n(i&j)(R) ov er cap R-ij(2) + [n(0&j) - (n(&ij) (1 - (O) over cap R-&ij)) - (ni(&j) (O) over cap R-ij)](R) over cap R-ij - (n(0&j)(O) over cap R-ij) = 0 S imulations were done to assess the relative weight of the exposure rat e, disease risk and Value of (O) over cap R-ij in the difference betwe en (R) over cap R-ij and (O) over cap R-ij. The difference between (O) over cap R-ij and (R) over cap R-ij depends upon (i), first of all, t he disease risk in the population, but also (ii) the value of ORij, an d to a less extent (iii) the exposure rate. Simulations also showed th at ranking of the risk-factor levels according to their effect cannot always rely on OR. (C) 1998 Elsevier Science B.V. All rights reserved.