Some possible effects of birth control on the incidence of disorders and on the influence of birth order

SUMMARY Selective limitation of family size will reduce the relative incidence R of a disorder if for different values of i there are differences in the probability pi that a child born to the ith set of parents is affected, and if the size si of the ith sibship (in the absence of affected offspring) is independent of pi. When si=s for all i, R will be reduced more when the criterion of termination is A= 1 (i.e. when the presence of one affected offspring terminates the sibship) than when the value of A is greater than one, and this reduction in R for any value of A (A< s) will increase with increasing values of s. To facilitate the measurement of R under various general conditions, and to assess the magnitude of the effect of selective limitation on R, various formulae are given herein. The relation between birth rank and the relative incidence of a disorder will be affected by the selective limitation of family size regardless of whether the relation is determined by the control group method, by the Greenwood‐Yule method, or by the Penrose (1934) modification of the Greenwood‐Yule method. With the control group method (where the affected cases are compared with a control group representative of all births) the ‘effect of being first‐born’ will be exaggerated in a positive direction when A= 1 if there is a negative correlation (for each j) between the probability pij‐ that the jth offspring of the ith set of parents is affected and the probability Qoij‐that there are no affected offspring among the first (j ‐ 1) offspring of the ith set of parents. With the Greenwood‐Yule method or the Penrose modification, the ‘effect of being first‐born’ will be exaggerated in a negative direction when A = I; even if this effect is positive when there is no selective limitation, it will appear to be negative when the Greenwood‐Yule method is used with A= 1. To facilitate the measurement of the effect of selective limitation on the ‘birth rank effect’, various formulae are given herein.