By design, twins in the ES unscreened and screened samples had different probabilities of selection into the study. This violates the assumption of equal probability of selection for all observations that is fundamental to simple random samples. Unequal selection probabilities, however, can be accommodated by means of sampling weights, which commonly represent the inverse of the probability of selection into the sample (Kalton, 1983). The ES design effectively oversampled for high-risk pairs, which therefore make up a greater percentage of the total sample than they would in the population. If we assume that the unscreened sample is representative of the population, it is possible to derive weights that adjust the screened male and female samples relative to the unscreened ones, and thus effectively equate them. More specifically, it is possible to assign weights that mathematically adjust for differences between unscreened and screened samples in the number of twin pairs above the screening threshold. This results in assigning greater weight to the unscreened pairs and less weight to the screened ones. Because selection in the ES sampling frame occurred at the level of twin pairs, each twin within the same pair is assigned the same weight.
