Association statistics under the PPL framework

In this paper, we extend the PPL framework to the analysis of case-control (CC) data and introduce three new linkage disequilibrium (LD) statistics. These statistics measure the evidence for or against LD, rather than testing the null hypothesis of no LD, and they therefore avoid the need for multiple testing corrections. They are suitable not only for CC designs but also can be used in application to family data, ranging from trios to complex pedigrees, all under the same statistical framework, allowing for the seamless analysis of disparate data structures. They also provide other core advantages of the PPL framework, including the use of sequential updating to accumulate LD evidence across potentially heterogeneous sets or subsets of data; parameterization in terms of a very general trait likelihood, which simultaneously considers dominant, recessive, and additive models; and a straightforward mechanism for modeling two-locus epistasis. Finally, by implementing the new statistics within the PPL framework, we have a ready mechanism for incorporating linkage information, obtained from distinct data, into LD analyses in the form of a prior distribution. Here we examine the performance of the proposed LD statistics using simulated data, as well as assessing the effects of key modeling violations on this performance.