Stata Technical Bulletin
As there are four possible haplotypes, there are three odds ratios per stratum, which gives three degrees of freedom for the
effect modification test.
Grouping haplotypes
For two biallelic loci there are four possible haplotypes. If there is some a priori reason that the association is due to
only one of the haplotypes, then the effect modification test discussed previously will have lower power than one which groups
the other three haplotypes as the comparison group. The grouping allows only one odds ratio per stratum and hence a one
degree-of-freedom test. When phase is unknown, the grouping must be performed within the EM algorithm using a constrained
log-linear model because the haplotypes are not observed. If the phase was known, this grouping is performed before running
hapipf.
The relationship between the two odds ratios can be specified by using a constrained log-linear model. The constrained
log-linear model uses constraint files and are explained in Mander (2000).
The one degree of freedom test of effect modification is the likelihood-ratio test comparing the common odds ratio model
and the model where the odds ratios differ. The base model is L_1*L_2*S+S*D and the L_1*L_2*D margin is fit using the
constraint files. The file (stratal.dta) below is the constraint file for the common-odds model. Note that only one odds ratio
is freely estimated and all the cells in the L_1*L_2*D margin are specified.
|
11 |
12 |
D |
Ifreq | |
|
1. |
1 |
1 |
0 |
1 |
|
2. |
1 |
1 |
1 |
1 |
|
3. |
1 |
2 |
0 |
1 |
|
4. |
1 |
2 |
1 |
1 |
|
ε. |
2 |
1 |
0 |
1 |
|
6. |
2 |
1 |
1 |
1 |
|
7. |
2 |
2 |
0 |
1 |
|
S. |
2 |
2 |
1 |
The file (strata2.dta) below is the constraint file for the effect modification for one specific haplotype 2.2. All the cells
in the L_1*L_2*D*S margin are specified and two odds ratios are allowed, the base model is exactly the same.
|
11 |
12 |
D |
Ifreq |
S | |
|
1. |
1 |
1 |
0 |
1 |
0 |
|
2. |
1 |
1 |
0 |
1 |
1 |
|
3. |
1 |
1 |
1 |
1 |
0 |
|
4. |
1 |
1 |
1 |
1 |
1 |
|
ε. |
1 |
2 |
0 |
1 |
0 |
|
6. |
1 |
2 |
0 |
1 |
1 |
|
7. |
1 |
2 |
1 |
1 |
0 |
|
8. |
1 |
2 |
1 |
1 |
1 |
|
9. |
2 |
1 |
0 |
1 |
0 |
|
10. |
2 |
1 |
0 |
1 |
1 |
|
11. |
2 |
1 |
1 |
1 |
0 |
|
12. |
2 |
1 |
1 |
1 |
1 |
|
13. |
2 |
2 |
0 |
1 |
0 |
|
14. |
2 |
2 |
0 |
1 |
1 |
|
ιε. |
2 |
2 |
1 |
0 | |
|
16. |
2 |
2 |
1 |
1 |
The following commands obtain the likelihood for both models.
. hapipf al a2 bl b2, ipf(S*D+11*12*S) confile(stratal) convars(ll 12 D)
. hapipf al a2 bl b2, ipf(S*D+11*12*S) confile(strata2) convars(ll 12 D S)
From the output, the likelihood-ratio test statistic is .82741365 on one degree of freedom which is not significant at the 5% level.
Additional information
There are numerous models that the log-linear model can specify, and a detailed description of these can be found in Mander
and Clayton (2000).
References
Mander, A. P. 2000. sbe34: Log-linear modeling using iterative proportional fitting. Stata Technical Bulletin 55: 10-12.
Mander, A. P. and D. G. Clayton. 2000. Haplotype analysis in population-based association studies using Stata. In preparation.
Sham, P. 1998. Statistics in Human Genetics. London: Arnold.
Wilkinson, G. N. and C. E. Rogers. 1973. Symbolic description of factorial models for analysis of variance. Applied Statistics 22: 392-399.