  In linear regression modelling the distortion of effects after marginalizing
over variables of the conditioning set has been widely studied in several
contexts. For Gaussian variables, the relationship between marginal and partial
regression coefficients is well-established and the issue is often addressed as
a result of W. G. Cochran. Possible generalizations beyond the linear Gaussian
case have been developed, nevertheless the case of discrete variables is still
challenging, in particular in medical and social science settings. A
multivariate regression framework is proposed for binary data with regression
coefficients given by the logarithm of relative risks and a multivariate
Relative Risk formula is derived to define the relationship between marginal
and conditional relative risks. The method is illustrated through the analysis
of the morphine data in order to assess the effect of preoperative oral
morphine administration on the postoperative pain relief.
