I tried repeating Paul Pharoah's analysis & got
essentially the same answers
However, the problem only arises when fitting both alleles at once.
If I use
xtlogit case allele2 if allele0| allele2, or
I get
------------------------------------------------------------------------------
case | OR Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
allele2 | 1.011836 .0798964 0.15 0.882 .8667581 1.181198
-------------+----------------------------------------------------------------
/lnsig2u | -4.015044 .701948 -5.390836 -2.639251
-------------+----------------------------------------------------------------
sigma_u | .1343211 .0471432 .0675141 .2672354
rho | .0054542 .0038077 .0013836 .0212463
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) = 4557.62 Prob >= chibar2 = 0.000
This is very similar to -metan- & to -cc-
cc case allele2 if allele0| allele2, by(st)
study | OR [95% Conf. Interval] M-H Weight
-----------------+-------------------------------------------------
1 | 1.543568 .8175427 2.976996 8.822736 (exact)
2 | 1.965573 1.073019 3.67396 8.657382 (exact)
3 | .7776123 .5184206 1.163567 29.46082 (exact)
4 | 1.244903 .8505777 1.824859 25.93921 (exact)
5 | .9165455 .6630693 1.263553 41.88866 (exact)
6 | .8405524 .6093421 1.159476 43.69371 (exact)
7 | .9585875 .7257767 1.269623 53.53306 (exact)
8 | 1.038503 .8535848 1.263426 102.7595 (exact)
9 | .9407818 .7907902 1.119215 137.0404 (exact)
-----------------+-------------------------------------------------
Crude | .9884827 .9012316 1.084181 (exact)
M-H combined | .9914067 .9038977 1.087388
-------------------------------------------------------------------
Test of homogeneity (M-H) chi2(8) = 12.59 Pr>chi2 = 0.1268
Test that combined OR = 1:
Mantel-Haenszel chi2(1) = 0.03
Pr>chi2 = 0.8548
Date: Fri, 1 Dec 2006 09:50:44 -0000
From: "Paul Pharoah" <[email protected]>
Subject: st: Random effects logistic regression: -metan- v -xtlogit-
multiple case-control studies differ (substantially) between metan-
and �xtlogit- ?
Data are from nine unmatched cases control studies of SNP genotype
study � study variable
gene00 RR genotype frequency in controls
gene01 RQ genotype frequency in controls
gene02 QQ genotype frequency in controls
gene10 RR genotype frequency in cases
gene11 RQ genotype frequency in cases
gene12 QQ genotype frequency in cases
study gene00 gene01 gene02 gene10 gene11 gene12
1 228 141 19 241 188 31
2 149 144 21 148 119 41
3 252 299 74 254 290 58
4 256 274 68 251 251 83
5 425 499 127 314 307 86
6 309 353 108 354 350 104
7 328 391 109 609 669 194
8 947 1030 313 740 875 254
9 1054 1173 360 1083 1268 348
The following command generates the random effects pooled OR for QQ vs RR
genotype
. metan gene00 gene02 gene10 gene12, random or
Study | OR [95% Conf. Interval] % Weight
- -----------------+-------------------------------------------------------
1 | 1.54357 .847914 2.80996 3.92373
2 | 1.96557 1.10822 3.48619 4.2419
3 | .777612 .52893 1.14322 8.12115
4 | 1.2449 .864373 1.79296 8.81242
5 | .916545 .672142 1.24982 11.0651
6 | .840552 .61681 1.14546 11.0958
7 | .958588 .731544 1.2561 13.1761
8 | 1.0385 .857574 1.2576 18.8354
9 | .940782 .793702 1.11512 20.7284
- -----------------+-------------------------------------------------------
D+L pooled OR | 1.00456 .885302 1.13988
- -----------------+-------------------------------------------------------
Heterogeneity chi-squared = 12.59 (d.f. = 8) p = 0.127
Estimate of between-study variance Tau-squared = 0.0125
Test of OR=1 : z= 0.07 p = 0.944
And, the RQ vs RR random effects pooled OR
. metan gene00 gene01 gene10 gene11, random or
Study | OR [95% Conf. Interval] % Weight
- -----------------+-------------------------------------------------------
1 | 1.26141 .949866 1.67514 6.51369
2 | .831973 .596507 1.16039 4.98645
3 | .962263 .758749 1.22036 8.60693
4 | .934307 .731869 1.19274 8.25621
5 | .832716 .679269 1.02083 10.7657
6 | .865463 .699804 1.07034 10.1444
7 | .921522 .767211 1.10687 12.4064
8 | 1.08715 .952918 1.24029 18.0585
9 | 1.05204 .936656 1.18164 20.2618
- -----------------+-------------------------------------------------------
D+L pooled OR | .978139 .902773 1.0598
- -----------------+-------------------------------------------------------
Heterogeneity chi-squared = 12.01 (d.f. = 8) p = 0.151
Estimate of between-study variance Tau-squared = 0.0047
Test of OR=1 : z= 0.54 p = 0.589
If the data are reshaped from wide into long using the following series of
commands
. reshape long gene0 gene1 gene2, i(study) j(case)
. reshape long weight , i(study case) j(alleles)
. expand weight
The fixed effects pooled genotype specific effects obtained by logistic
regression are the same as the fixed effects from �metan-. I.e.
. xi: logistic case i.alleles, nolog
i.alleles _Ialleles_0-2 (naturally coded; _Ialleles_0 omitted)
Logistic regression Number of obs =
18961
LR chi2(2) =
0.10
Prob > chi2 =
0.9501
Log likelihood = -13142.621 Pseudo R2 =
0.0000
- ----------------------------------------------------------------------------
- --
case | Odds Ratio Std. Err. z P>|z| [95% Conf.
Interval]
- -------------+--------------------------------------------------------------
- --
_Ialleles_1 | .9914684 .0308417 -0.28 0.783 .9328256
1.053798
_Ialleles_2 | .9884827 .046065 -0.25 0.804 .9021974
1.08302
- ----------------------------------------------------------------------------
- --
But, the random effects estimates using xtlogit and study as the panel
variable are very different and clearly wrong.
. xi: xtlogit case i.alleles , i(study) re or
i.alleles _Ialleles_0-2 (naturally coded; _Ialleles_0 omitted)
Fitting comparison model:
Iteration 0: log likelihood = -13142.672
Iteration 1: log likelihood = -13142.621
Fitting full model:
tau = 0.0 log likelihood = -5971.0991
tau = 0.1 log likelihood = -5971.4368
Random-effects logistic regression Number of obs =
18961
Group variable (i): study Number of groups =
9
Random effects u_i ~ Gaussian Obs per group: min =
622
avg =
2106.8
max =
5286
Wald chi2(2) =
7.45
Log likelihood = -5965.7258 Prob > chi2 =
0.0242
- ----------------------------------------------------------------------------
- --
case | OR Std. Err. z P>|z| [95% Conf.
Interval]
- -------------+--------------------------------------------------------------
- --
_Ialleles_1 | 1.050559 .1153838 0.45 0.653 .8470957
1.302893
_Ialleles_2 | 1.778091 .3759296 2.72 0.006 1.174871
2.691025
- -------------+--------------------------------------------------------------
- --
/lnsig2u | -5.132952
1.966205 -8.986643 -1.279262
- -------------+--------------------------------------------------------------
- --
sigma_u | .0768057 .0755079 .0111834
.527487
rho | .0017899 .003513 .000038
.0779804
- ----------------------------------------------------------------------------
- --
Likelihood-ratio test of rho=0: chibar2(01) = 1.4e+04 Prob >= chibar2 =
0.000
The QQ vs RR OR is bigger than all but one of the study specific ORs, so is
clearly wrong.
So
Metan xtlogit
Pooled OR RQ vs RR 0.98 1.05
Pooled OR QQ vs RR 1.00 1.74
Any ideas?
Many thanks
Paul Pharoah
Cancer Research UK Senior Clinical research Fellow
Strangeways Research Raboratory
Dept of Oncology
University of Canbridge
========================
Paul T Seed, MSc CStat
Lecturer in Medical Statistics
King's College London,
Division of Reproduction and Endocrinology
St Thomas' Hospital,
Lambeth Palace Road,
London SE1 7EH
Funded by the Wellcome Trust & Tommy's the Baby Charity
http://www.mfru.info/lecturenotes.html
([email protected])
tel (+44) (0) 20 7188 3642
fax (+44) (0) 20 7620 1227
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