Power study of likelihood based linkage statistics

The likelihood ratio statistics LOD and HLOD have been developed to detect the linkage between trait and marker using pedigree data. However, when the assumed genetic model parameter values are incorrect, significant power loss can occur in the analysis. To avoid the risk of assuming the wrong parameter values, the method of maximizing the statistics over the parameter values has been suggested. In this study, the power of LOD and HLOD scores maximized over finite number of models (LOD2, HLOD2, LOD20, HLOD20) and the power of MLOD and MHLOD scores maximized over the entire parameter range are investigated.; The distributions of these statistics under the null and alternative hypotheses are studied. We first derive the asymptotic null distributions and compare them to our simulated values. The inflation of Type I error using a fixed critical value and critical values corresponding to a fixed Type I error for these MLOD and MHLOD statistics are obtained from the derived asymptotic null distributions. The null distributions of MLOD and MHLOD are mixtures of chi-square distributions of 1--6 degrees of freedom depending on the boundary condition.; For the maximization of MLOD and MHLOD in the multidimensional parameter space, an algorithm using Powell's modified direction set method is developed. The MLOD and MHLOD scores have been calculated from the simulated data using this algorithm. From the data generated under the assumption of no linkage, an empirical null distribution is obtained and compared with the theoretically derived distribution. Also power of these statistics is calculated from the result of simulation. MLOD and MHLOD showed greater power than maximized LOD and HLOD over 2 or 20 models (LODk, HLODk for k = 2, or 20) for the generating models with phenocopies, even upon using the increased critical values needed to maintain a fixed Type I error. MLOD and MHLOD always have greater power than LOD and HLOD over 2 or 20 models if we fix the critical value across the statistics.