Differences in recurrence risk by birth order of the first affected child provide evidence of genetic heterogeneity

Genetic heterogeneity has adverse implications for detecting linkage, determining mode of transmission, and estimating segregation ratios. This paper describes a new method for detecting genetic heterogeneity by mode of inheritance. The expected birth order of the first affected child within a sibship is related to segregation ratio "p." The probability of a first affected child having a given ordinal position decreases through the birth order by a factor of 1-p for each prior unaffected child. When p is high, an exponential decline through the birth order is observed, and first affected children tend to be early-born. When p is low, 1-p is nearly 1, so first affected children are distributed more evenly through the birth order. If families belonging to subgroups 1 and 2 have differing segregation ratios p1 and p², then the expected birth order distribution of first affected children for these two sets of families will differ. If ascertainment is complete, there will be a higher concentration of families with the greater of p1 and p2 among the pooled group whose first born is affected, than among those whose first affected child is later born. Defining E(Rk) as the expected recurrence rate within families whose first affected child is k^th born, it can be demonstrated that E(Rk) is a decreasing function in k if and only if p1 ≠ p2. Empiric recurrence risks for families stratified by birth order of the first affected child can be assessed for stepwise decreases using isotonic regression. A positive test provides direct evidence of genetic heterogeneity by mode of inheritance, with potential relevance to linkage study and genetic counselling. This approach will be illustrated using population-based studies of autism.