An Algorithm to Construct All 2**n Sequences of Sibling Pairs with Application to Families with Two Monozygotic and One Dizygotic Triplets

• Activity Number: 233
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 12:00 PM to 1:50 PM
• Sponsor: General Methodology
• Author(s): Nina Kohn*+ and Gene S. Fisch and Catherine Derom and Martin L. Lesser
• Companies: North Shore LIJ Research Institute and North Shore LIJ Research Institute and Catholic University, Leuven and North Shore LIJ Research Institute
• Keywords: intraclass correlation ; twins ; triplets ; Cartesian product ; algorithm

Abstract

The intraclass correlation (ICC) is commonly used to compute the correlation between k>=2 unordered measures such as IQ. In monozygotic (MZ) triplets, there are three indistinguishable persons and the ICC for k=3 is easily applied. However, in the case of triplets where there are two MZs and one dizygotic twin (DZ), the MZs are distinguishable from the DZ, but not from one another, rendering the usual ICC calculation invalid. For n families of such triplets, we propose a measure of ICC, whereby all 2**n within-family pairwise combinations of one of the two MZs with the single DZ are constructed (a "restricted" Cartesian product) and the standard ICC for k=2 is computed. The mean of those 2**n ICCs is then used to measure correlation between the MZs and the DZ. Construction of datasets consisting of all of these possible combinations is nontrivial. We developed an efficient algorithm using SAS to enumerate all 2n samples. The algorithm is general: it can be used with any number of triplet sets. It can also be used to enumerate all samples constructed by selecting 1 of k siblings or k-1 of k siblings.