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
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 with degrees of freedom that gives a -value . 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 |