Relationship uncertainty linkage statistics (RULS): affected relative pair statistics that model relationship uncertainty

Abstract

Linkage analysis programs invariably assume that the stated familial relationships are correct. Thus, it is common practice to resolve relationship errors by either discarding individuals with erroneous relationships or using an inferred alternative pedigree structure. These approaches are less than ideal because discarding data is wasteful and using inferred data can be statistically unsound. We have developed two linkage statistics that model relationship uncertainty by weighting over the possible true relationships. Simulations of data containing relationship errors were used to assess our statistics and compare them to the maximum-likelihood statistic (MLS) and the Sall non-parametric LOD score using true and discarded (where problematic individuals with erroneous relationships are discarded from the pedigree) structures. We simulated both small pedigree (SP) and large pedigree (LP) data sets typed genome-wide. Both data sets have several underlying true relationships; SP has one apparent relationship--full sibling--and LP has several different apparent relationship types. The results show that for both SP and LP, our relationship uncertainty linkage statistics (RULS) have power nearly as high as the MLS and Sall using the true structure. Also, the RULS have greater power to detect linkage than the MLS and Sall using the discarded structure. For example, for the SP data set and a dominant disease model, both the RULS had power of about 93%, while Sall and MLS have 90% and 83% power on the discarded structure. Thus, our RULS provide a statistically sound and powerful approach to the commonly encountered problem of relationship errors.