Extension of conditional model-free likelihood-based linkage analysis to additive and other models

We have previously described extending our method of 'model-free' linkage analysis, implemented in the MFLINK program, in order to deal with liability classes. This allows a new form of conditional two-locus linkage analysis, meaning that the genotypes of a known risk locus can be used to define liability classes so that their effects can be incorporated in tests for linkage at additional loci. In this method, relationships between transmission models for different liability classes were constrained so that there was a constant multiplicative effect on penetrance values. Here we present further extensions to the method to allow for different relationships. In particular, rather than only having a multiplicative effect on risk of affection we now allow specification of a multiplicative effect on risk of non-affection, or a combination of both relationships, across liability classes. We now also allow specification of an additive effect on penetrance. By way of example, we apply these methods to genome scan data for Alzheimer's disease using apolipoprotein E genotype to define liability classes. We show that, although in general the different methods produce results which tend to be quite highly correlated, certain markers can produce quite different results according to the method applied and that these could well lead to differences of interpretation. Without knowing a priori which relationship is likely to be most appropriate to describe the overall combined effect of the two loci one might be obliged to apply a number of different methods. This in turn may lead to the familiar difficulties associated with multiple testing. Nevertheless, the new method allows researchers greater flexibility in analysing linkage data for diseases in which one or more risk polymorphisms have already been identified.