Volume measures for linkage disequilibrium

Background: Defining measures of linkage disequilibrium (LD) that have good small sample properties and are applicable to multiallelic markers poses some challenges. The potential of volume measures in this context has been noted before, but their use has been hampered by computational challenges. Results: We design a sequential importance sampling algorithm to evaluate volume measures on I x J tables. The algorithm is implemented in a C routine at a complement to exhaustive enumeration. We make the C code available as open source. We achieve fast and accurate evaluation of volume measures in two dimensional tables. Conclusion: Applying our code to simulated and real datasets reinforces the belief that volume measures are a very useful tool for LD evaluation: they are not inflated in small samples, their definition encompasses multiallelic markers, and they can be computed with appreciable speed.