One traditional method for evaluating the significance of a lod score score peak obtained from a genome scan relies on gene-dropping to simulate hundreds or thousands of replicate genomes under the null hypothesis. These replicates can then be used to reproduce the underlying null distribution for any statistic of interest. For a Kong and Cox lod score, evaluation of a hypothesis H involves repetition of the following steps several thousand times:

1. Simulate pedigree data similar to the original with respect to family relationships, marker placement and allele frequencies, but assuming no linkage and no association by gene-dropping



2. Perform linkage analysis on the simulated data to generate a lod score profile (L₁,L₂ , ... L_p) consisting of one Kong and Cox lod score for each analysis position. The algorithm for calculating the i^th lod score, L_i is
   
   
   1. Let F = {F₁, F₂, ... F_N } be the set of all families in the data set. Let G be the set of simulated genotypes.
      
      
   2. For each family F_f in F, calculate a family-specific z-score at position i as where is the expected sharing score for family f at position i given genotypes G, and is sharing expected under the null hypothesis of no linkage.
      
      
   3. Calculate the lod score at the i^th position as where delta-hat is the maximum likelihood estimate of delta.
   
   
   
   
   4. Count the simulation as "positive" if the profile of simulated lod scores (L₁, L₂ , ... L_p) satisfies H.
      
      
      
3. For a total of M data sets, estimate a p-value for H as where P is the number of positive simulations.

References for Kong and Cox tests of linkage

Kong and Cox (1997) Allele-sharing models: LOD scores and accurate linkage tests. American Journal of Human Genetics 61:1179-1188

Whittemore and Halpern (1994) A class of tests for linkage using affected pedigree members. Biometrics 50118-127