Percentiles of the Null Distribution of 2 Maximum Lod Score Tests

We here consider the null distribution of the maximum lod score (LOD-M) obtained upon maximizing over transmission model parameters (penetrance values, dominance, and allele frequency) as well as the recombination fraction. Also considered is the lod score maximized over a fixed choice of genetic model parameters and recombination-fraction values set prior to the analysis (MMLS) as proposed by Hodge et al. [1]. The objective is to fit parametric distributions to MMLS and LOD-M. Our results are based on 3,600 simulations of samples of n = 100 nuclear families ascertained for having one affected member and at least one other sibling available for linkage analysis. Each null distribution is approximately a mixture p²₀ + (1 – p)²v. The values of MMLS appear to fit the mixture 0.20²₀ + 0.80χ²1.6. The mixture distribution 0.13²₀ + 0.87χ²2.8. appears to describe the null distribution of LOD-M. From these results we derive a simple method for obtaining critical values of LOD-M and MMLS.