PROC HAPLOTYPE: Testing for Linkage Disequilibrium

The HAPLOTYPE Procedure

Example 8.3 Testing for Linkage Disequilibrium

Again looking at the data from the Lab of Statistical Genetics at Rockefeller University (2001), if you request the test for linkage disequilibrium by specifying the LD option in the PROC HAPLOTYPE statement as follows, the "Test for Allelic Associations" table containing the test statistics is included in the output.

   proc haplotype data=ehdata ld;
      var m1-m6;
   run;

The "Haplotype Frequencies" table (Output 8.3.1) now contains an extra column of the haplotype frequencies under the null hypothesis.

Output 8.3.1 Haplotype Frequencies under the Null and Alternative Hypotheses

The HAPLOTYPE Procedure

Haplotype Frequencies
Number	Haplotype	H0 Freq	H1 Freq	Standard Error	95% Confidence Limits
1	1-1-1	0.08172	0.09124	0.01353	0.06472	0.11775
2	1-1-2	0.05605	0.02124	0.00677	0.00796	0.03452
3	1-1-3	0.10006	0.11501	0.01499	0.08563	0.14439
4	1-2-1	0.09084	0.07952	0.01271	0.05461	0.10443
5	1-2-2	0.06231	0.06726	0.01177	0.04419	0.09032
6	1-2-3	0.11122	0.12794	0.01569	0.09718	0.15870
7	2-1-1	0.08100	0.05540	0.01075	0.03433	0.07647
8	2-1-2	0.05556	0.11690	0.01510	0.08732	0.14649
9	2-1-3	0.09918	0.07378	0.01228	0.04971	0.09785
10	2-2-1	0.09005	0.11746	0.01513	0.08781	0.14711
11	2-2-2	0.06176	0.03028	0.00805	0.01450	0.04606
12	2-2-3	0.11025	0.10398	0.01434	0.07587	0.13209

Note that since the INIT= option was omitted from the PROC HAPLOTYPE statement, the initial haplotype frequencies used in the EM algorithm are identical to the frequencies that appear in the H0 FREQ column in Output 8.3.1. The frequencies in the H1 FREQ column are those calculated from the final iteration of the EM algorithm, and these frequencies’ standard errors and confidence limits are included in the table as well.

Output 8.3.2 displays the log likelihood under the null hypothesis assuming independence among all the loci and the alternative, which allows for associations between markers. The empirical chi-square test statistic of the likelihood ratio test is calculated as $\text{[math]}$ with degrees of freedom $\text{[math]}$ that gives a $\text{[math]}$ -value $\text{[math]}$ . The test indicates significant linkage disequilibrium among the three loci, as shown in the online documentation from the Lab of Statistical Genetics at Rockefeller University (2001).

Output 8.3.2 Testing for Linkage Disequilibrium Using the LD Option

Test for Allelic Associations
Hypothesis	DF	LogLike	Chi-Square	Pr > ChiSq
H0: No Association	4	-953.89697
H1: Allelic Associations	11	-934.98180	37.8303	<.0001

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