POLY provides accurate and efficient algorithms to analytically compute the power of the variance component linkage analysis in GENERAL pedigrees. The algorithms in this power analysis involve the approximation of the noncentrality parameter for the likelihood-ratio test by its Taylor expansions, and details are given in publication by Chen and Abecasis (2006).

For a data set with pedigree structures and phenotypes, the format of input files for POLY are described in the manual. The power analysis command is through option "--a". e.g.,

prompt> poly -d ex.dat -p ex.ped --tr 1 --a 

The above command first estimates the heritability of the first trait using variance components polygenic analysis. An analytical power analysis is then followed.

For a real data set, the heritability of a QTL can be estimated automatically from the data by the polygenic analysis in POLY. There are several options for power analysis, simply through "--a n" option. Different values of n correspond to different algorithms of analytical power calculation:

• --a 2: approximation based on the second-order Talor expansion of the LRT statistic
• --a 3: approximation based on the third-order Talor expansion of the LRT statisitc
• --a 4: another version of approximation based on the third-order Talor expansion
• --a or --a 1: the default analytical power calculation. Currently it is set to be the same as --a 4

For a data set with simulated phenotypes, the heritability of a QTL can be specified by users through option "--herit value" where the value specifies the value of the heritability. i.e., the power analysis command may look like:

prompt> poly -d ex.dat -p ex.ped --a 4 --herit 0.7

This command assume the trait value has overall heritibility 0.7 and analytical power calculation option 4 is performed.

For a data set with only pedigree structures and without phenotypes, one can creat a .dat file with one line "T trait", and add the sixth column in the .ped file with 0 (or anything else). Then the power analysis command may look like:

prompt> poly -d ex.dat -p ex.ped --a 4 --herit 0.7

In addition to the unique feature that arbitrarily large pedigrees can be handled by POLY, Chen and Abecasis (2006) also developed super efficient efficient algorithms for a special type of pedigrees -- tree-like pedigrees. Most simulated pedigrees in simulation studies fall into this category. POLY can recognize these tree-like pedigrees and performs optimal algorithms automatically. The new algorithm can be hundreds times more efficient than regular algorithms. So simulated pedigrees, usually all pedigrees in the data set have the same pedigree structure. In order to save the computing time, one can specify "--a 12", "--a 13", or "--a 14" to replace the regular options. e.g., If there are 20 pedigrees in the data set, then the optimal analytical power calculation will be approximately 20 times faster.

 We use POLY to analyze all 98 quantitative traits Sardinia data where 6,148 individuals participated. We predict the statistical powers in terms of LOD scores in a future linkage study. The LOD scores at a QTL that accounts for 10% of the phenotypic variance is shown in this link.