Exact elods and exact power for affected sib pairs analyzed for linkage under simple right and wrong models

In the struggle to understand the inheritance of complex psychiatric diseases, investigators frequently turn to affected sib pair (ASP) methods of linkage analysis. This paper examines the quantity of "information" (as indicated by the expected maximum lod score [ELOD] and/or power), when ASP data originating from simple dominant or recessive inheritance are analyzed for linkage, both as simple dominant and as simple recessive. That is, these data are analyzed under both right and wrong models. Results are exact (i.e., not based on asymptotic approximations) and thus hold for small sample sizes (e.g., n = 20 sib pairs), as well as for large samples. It is shown that analyzing dominant ASPs (that is, sib pairs suffering from a dominantly inherited disease) as recessive (i.e., under the wrong model) can reduce the ELOD by 20-24% when recombination fraction (theta) is small. In situations where theta is large or gene frequency high, the information loss is less, because in those situations dominant ASPs contain very little information to begin with. For recessive ASPs, the information loss when analyzed under the wrong model is even more pronounced. The fact that a decision to sample ASP data discards more potential linkage information for dominant diseases than for recessive ones is also discussed, as are implications for more complex models. These findings are also of interest because it has been shown that the nonparametric Mean Test of ASPs is statistically identical to recessive lod score analysis [Knapp et al., Hum Hered 44:44-51, 1994]. Hence, the power results for the recessive analyses are also valid for the Mean Test, and thus are valuable for comparing how dominant and recessive ASP data fare in this particular nonparametric analysis.