Comparison of 'model-free' and 'model-based' linkage statistics in the presence of locus heterogeneity: Single data set and multiple data set applications

Earlier work [Knapp et al.: Hum Hered 1994;44:44-51] focusing on affected sib pair (ASP) data established the equivalence between the mean test and a test based on a simple recessive lod score, as well as equivalences between certain forms of the maximum likelihood score (MLS) statistic [Risch: Am J Hum Genet 1990;46:242-253] and particular forms of the lod score. Here we extend the results of Knapp et al. [1994] by reconsidering these equivalences for ASP data, but in the presence of locus heterogeneity. We show that Risch's MLS statistic under the possible triangle constraints [Holmans: Am J Hum Genet 1993;52:362-374] is locally equivalent to the ordinary heterogeneity lod score assuming a simple recessive model (HLOD/R); while the one-parameter MLS assuming no dominance variance is locally equivalent to the (homogeneity) recessive lod. The companion paper (this issue, pp 199-208) showed that when considering multiple data sets in the presence of locus heterogeneity, the HLOD can suffer appreciable losses in power. We show here that in ASP data, these equivalences ensure that this same loss in power is incurred by both forms of the MLS statistic as well. The companion paper also introduced an adaptation of the lod, the compound lod score (HLOD/C). We confirm that the HLOD/C maintains higher power than these 'model-free' methods when applied to multiple heterogeneous data sets, even when it is calculated assuming the wrong genetic model.