INTERRELATIONSHIPS OF RELATIVE RISKS OF BIRTH-DEFECTS IN EMBRYONIC AND FETAL DEATHS, IN LIVEBIRTHS, AND IN ALL CONCEPTUSES

Most studies of associations with birth defects are undertaken in livebirths. An observed association in livebirths different from unity may be compatible with no association in conceptuses if "balanced" by a particular relative risk in embryonic and fetal deaths. We derived formulae to address the following queries: (1) If one observes in livebirths a relative risk of birth defect, r(def,lb,) then, with what combinations of relative risk of defect in embryonic and fetal deaths, r(def,efd,) and in all conceptuses, r(def,) is this value compatible? (2) What balancing relative risk in embryonic and fetal deaths is predicted if there is no causal association in all conceptuses? (3) Under what circumstances is there no relative risk in embryonic and fetal deaths that can balance an observed relative risk in livebirths? We present an expression for r(def,efd) in terms of five other variables: r(def,lb,) r(def,) and r(efd) (the relative risk of embryonic or fetal death), and the lethalities of the average (unexposed) conceptus and of the (unexposed) defective conceptus. This equation enables one to derive the balancing relative risk in embryonic and fetal deaths, bal r(def,efd,) which is the value of r(def,efd) when r(def) = 1.0. If bal r(def,efd) is negative, no such balancing relative risk exists, and any observed association in livebirths is incompatible with a null association in all conceptuses, that is, the association cannot be explained completely by differential selection of conceptuses with defect.