The ALLELE Procedure

Example 3.2 Computing Linkage Disequilibrium Measures for SNP Data

The following data set contains 44 individuals’ genotypes at five SNPs.

data snps;
   input s1-s10;
   datalines;
2 2 2 1 2 1 1 1 2 2
2 2 2 2 2 1 1 1 2 2
2 2 2 2 2 1 2 1 2 2
2 2 2 2 . . 1 1 2 2
2 2 2 2 1 2 1 2 2 2
2 2 2 2 . . 2 1 2 2
2 2 2 2 2 1 2 1 2 2
2 2 2 2 . . 2 1 2 2
2 2 2 2 1 1 1 1 2 2
2 2 1 1 2 2 2 1 2 2
2 2 2 1 2 2 2 1 2 2
2 2 2 2 1 1 1 1 2 2

   ... more lines ...   

2 2 2 1 2 2 2 1 2 2
2 2 2 2 2 2 2 1 2 2
2 2 2 2 2 1 1 1 2 2
2 2 2 2 2 2 1 1 2 2
2 2 2 2 2 1 2 1 2 2
2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 1 2 2
2 2 2 2 2 2 2 1 2 2
;

Now an analysis using PROC ALLELE can be performed as follows:

proc allele data=snps prefix=SNP nofreq haplo=est 
      corrcoeff dprime;
   var s1-s10;
run;

This analysis produces summary statistics of the five SNPs as well as the "Linkage Disequilibrium Measures" table, which contains estimated two-locus haplotype frequencies and disequilibrium coefficients, and the linkage disequilibrium measures $\text{[math]}$ and $\text{[math]}$ . The allele and genotype frequency output tables are suppressed with the NOFREQ option.

The results from the analysis are shown in Output 3.2.1 and Output 3.2.2. Note the names of the markers that are used.

Output 3.2.1 Summary of SNPs for the ALLELE Procedure

The ALLELE Procedure

Marker Summary
Locus	Number of Indiv	Number of Alleles	Polymorph Info Content	Heterozygosity	Allelic Diversity	Test for HWE
Locus	Number of Indiv	Number of Alleles	Polymorph Info Content	Heterozygosity	Allelic Diversity	Chi- Square	DF	Pr > ChiSq
SNP1	44	1	0.0000	0.0000	0.0000	0.0000	0	.
SNP2	44	2	0.1190	0.0909	0.1271	3.5627	1	0.0591
SNP3	41	2	0.3283	0.4390	0.4140	0.1493	1	0.6992
SNP4	43	2	0.3728	0.4884	0.4957	0.0093	1	0.9231
SNP5	44	1	0.0000	0.0000	0.0000	0.0000	0	.

There are two SNPs that have only one allele appearing in the data.

Output 3.2.2 Linkage Disequilibrium Measures for SNPs Using the ALLELE Procedure

Linkage Disequilibrium Measures
Locus1	Locus2	Number of Indiv	Haplotype	Frequency	LD Coeff	Corr Coeff	Lewontin's D'
SNP1	SNP2	44	2-1	0.0682	0.0000	.	.
SNP1	SNP2	44	2-2	0.9318	0.0000	.	.
SNP1	SNP3	41	2-1	0.2927	0.0000	.	.
SNP1	SNP3	41	2-2	0.7073	0.0000	.	.
SNP1	SNP4	43	2-1	0.5465	0.0000	.	.
SNP1	SNP4	43	2-2	0.4535	0.0000	.	.
SNP1	SNP5	44	2-2	1.0000	0.0000	.	.
SNP2	SNP3	41	1-2	0.0732	0.0214	0.1807	1.0000
SNP2	SNP3	41	2-1	0.2927	0.0214	0.1807	1.0000
SNP2	SNP3	41	2-2	0.6341	-0.0214	-0.1807	-1.0000
SNP2	SNP4	43	1-1	0.0331	-0.0050	-0.0398	-0.1322
SNP2	SNP4	43	1-2	0.0367	0.0050	0.0398	0.1322
SNP2	SNP4	43	2-1	0.5134	0.0050	0.0398	0.1322
SNP2	SNP4	43	2-2	0.4168	-0.0050	-0.0398	-0.1322
SNP2	SNP5	44	1-2	0.0682	0.0000	.	.
SNP2	SNP5	44	2-2	0.9318	0.0000	.	.
SNP3	SNP4	40	1-1	0.2221	0.0608	0.2661	0.4382
SNP3	SNP4	40	1-2	0.0779	-0.0608	-0.2661	-0.4382
SNP3	SNP4	40	2-1	0.3154	-0.0608	-0.2661	-0.4382
SNP3	SNP4	40	2-2	0.3846	0.0608	0.2661	0.4382
SNP3	SNP5	41	1-2	0.2927	0.0000	.	.
SNP3	SNP5	41	2-2	0.7073	0.0000	.	.
SNP4	SNP5	43	1-2	0.5465	0.0000	.	.
SNP4	SNP5	43	2-2	0.4535	0.0000	.	.

In Output 3.2.2, the values for the linkage disequilibrium measures are missing for several haplotypes; this occurs when there is only one allele at one of the markers contained in the haplotype, and thus the denominators for these measures are zero. Also note that when the markers are biallelic, the gametic disequilibria have the same absolute values for all four possible haplotypes.