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RE: st: Random effects logistic regression: -metan- v -xtlogit-
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From |
"Paul Pharoah" <[email protected]> |
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To |
<[email protected]> |
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Subject |
RE: st: Random effects logistic regression: -metan- v -xtlogit- |
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Date |
Wed, 6 Dec 2006 14:20:01 -0000 |
Thanks Roger. A single between study variance for both comparisons cannot
be right.
I have been playing around with this command a bit and get some very odd
results.
Using the same data set (9 studies) the output from the following series of
command
-xtlogit caco allele1 allele2 if study>1, i(study) re or
-xtlogit caco allele1 allele2 if study>2, i(study) re or
-xtlogit caco allele1 allele2 if study>3, i(study) re or
-xtlogit caco allele1 allele2 if study>4, i(study) re or
which eliminates one of the study sets at a time is:
.xtlogit caco allele1 allele2 if study>1, i(study) re or
Fitting comparison model:
Iteration 0: log likelihood = -11538.253
Iteration 1: log likelihood = -11538.213
Iteration 2: log likelihood = -11538.213
Fitting full model:
tau = 0.0 log likelihood = -5267.0828
tau = 0.1 log likelihood = -5264.6107
tau = 0.2 log likelihood = -5265.389
Iteration 0: log likelihood = -5264.6107 (not concave)
Iteration 1: log likelihood = -5259.6619 (not concave)
Iteration 2: log likelihood = -5259.5018 (not concave)
Iteration 3: log likelihood = -5258.9279
Iteration 4: log likelihood = -5258.3001
Iteration 5: log likelihood = -5258.2601
Iteration 6: log likelihood = -5258.2598
Random-effects logistic regression Number of obs =
16661
Group variable (i): study Number of groups =
8
Random effects u_i ~ Gaussian Obs per group: min =
622
avg =
2082.6
max =
5286
Wald chi2(2) =
7.45
Log likelihood = -5258.2598 Prob > chi2 =
0.0242
----------------------------------------------------------------------------
--
caco | OR Std. Err. z P>|z| [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
allele1 | 1.050561 .1153839 0.45 0.653 .8470966
1.302894
allele2 | 1.778096 .3759308 2.72 0.006 1.174875
2.691033
-------------+--------------------------------------------------------------
--
/lnsig2u | -5.132587
1.965858 -8.985597 -1.279576
-------------+--------------------------------------------------------------
--
sigma_u | .0768198 .0755084 .0111893
.5274041
rho | .0017906 .0035137 .0000381
.0779578
----------------------------------------------------------------------------
--
Likelihood-ratio test of rho=0: chibar2(01) = 1.3e+04 Prob >= chibar2 =
0.000
. xtlogit caco allele1 allele2 if study>2, i(study) re or
Fitting comparison model:
Iteration 0: log likelihood = -10687.799
Iteration 1: log likelihood = -10687.797
Fitting full model:
tau = 0.0 log likelihood = -4559.6058
tau = 0.1 log likelihood = -4556.9484
tau = 0.2 log likelihood = -4557.6271
Iteration 0: log likelihood = -4556.9484 (not concave)
Iteration 1: log likelihood = -4551.3385
Iteration 2: log likelihood = -4550.8101
Iteration 3: log likelihood = -4550.7939
Iteration 4: log likelihood = -4550.7938
Random-effects logistic regression Number of obs =
15434
Group variable (i): study Number of groups =
7
Random effects u_i ~ Gaussian Obs per group: min =
622
avg =
2204.9
max =
5286
Wald chi2(2) =
7.45
Log likelihood = -4550.7938 Prob > chi2 =
0.0242
----------------------------------------------------------------------------
--
caco | OR Std. Err. z P>|z| [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
allele1 | 1.050561 .1153839 0.45 0.653 .8470968
1.302895
allele2 | 1.778098 .3759306 2.72 0.006 1.174876
2.691034
-------------+--------------------------------------------------------------
--
/lnsig2u | -5.132558
1.965825 -8.985504 -1.279611
-------------+--------------------------------------------------------------
--
sigma_u | .0768209 .0755082 .0111898
.5273949
rho | .0017906 .0035137 .0000381
.0779552
----------------------------------------------------------------------------
--
Likelihood-ratio test of rho=0: chibar2(01) = 1.2e+04 Prob >= chibar2 =
0.000
. xtlogit caco allele1 allele2 if study>3, i(study) re or
Fitting comparison model:
Iteration 0: log likelihood = -10096.462
Iteration 1: log likelihood = -10096.433
Fitting full model:
tau = 0.0 log likelihood = -3968.7172
tau = 0.1 log likelihood = -3969.9616
Iteration 0: log likelihood = -3968.7172
Iteration 1: log likelihood = -3963.9951
Iteration 2: log likelihood = -3963.9916
Iteration 3: log likelihood = -3963.9916
Random-effects logistic regression Number of obs =
14586
Group variable (i): study Number of groups =
6
Random effects u_i ~ Gaussian Obs per group: min =
622
avg =
2431.0
max =
5286
Wald chi2(2) =
8.50
Log likelihood = -3963.9916 Prob > chi2 =
0.0142
----------------------------------------------------------------------------
--
caco | OR Std. Err. z P>|z| [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
allele1 | .8319726 .1412296 -1.08 0.279 .5965066
1.160387
allele2 | 1.965592 .5746718 2.31 0.021 1.108234
3.486226
-------------+--------------------------------------------------------------
--
/lnsig2u | -21.93577 6622.872 -13002.53
12958.65
-------------+--------------------------------------------------------------
--
sigma_u | .0000172 .0571117 0
.
rho | 9.04e-11 5.99e-07 0
.
----------------------------------------------------------------------------
--
Likelihood-ratio test of rho=0: chibar2(01) = 0.00 Prob >= chibar2 =
1.000
. xtlogit caco allele1 allele2 if study>4, i(study) re or
Fitting comparison model:
Iteration 0: log likelihood = -9275.8601
Iteration 1: log likelihood = -9275.7897
Iteration 2: log likelihood = -9275.7897
Fitting full model:
tau = 0.0 log likelihood = -3261.5633
tau = 0.1 log likelihood = -3262.6943
Iteration 0: log likelihood = -3261.5633
Iteration 1: log likelihood = -3256.5289
Iteration 2: log likelihood = -3256.5256
Iteration 3: log likelihood = -3256.5256
Random-effects logistic regression Number of obs =
13403
Group variable (i): study Number of groups =
5
Random effects u_i ~ Gaussian Obs per group: min =
622
avg =
2680.6
max =
5286
Wald chi2(2) =
8.50
Log likelihood = -3256.5256 Prob > chi2 =
0.0142
----------------------------------------------------------------------------
--
caco | OR Std. Err. z P>|z| [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
allele1 | .8319726 .1412296 -1.08 0.279 .5965066
1.160387
allele2 | 1.965573 .5746652 2.31 0.021 1.108223
3.486189
-------------+--------------------------------------------------------------
--
/lnsig2u | -26.26776 57773.18 -113259.6
113207.1
-------------+--------------------------------------------------------------
--
sigma_u | 1.98e-06 .0571117 0
.
rho | 1.19e-12 6.86e-08 0
.
----------------------------------------------------------------------------
--
Likelihood-ratio test of rho=0: chibar2(01) = 0.00 Prob >= chibar2 =
1.000
As you can see the first two results have the same estimates and variances
(despite different sample sizes), but the estiamtes then change for the
third and fourth (which are again the same. This is not correct.
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]]On Behalf Of Roger Harbord
> Sent: 06 December 2006 07:24
> To: [email protected]
> Subject: Re: st: Random effects logistic regression: -metan- v -xtlogit-
>
>
> This suggests the discrepancy is due to different between-study
> variances for the two comparisons. In -metan- you're fitting each
> comparison separately with its own between-study variance. In -xtlogit-
> Paul Pharoah was fitting it all in a single model with a single
> between-study variance for both comparisons.
>
> Roger.
>
> Paul Seed wrote:
> > 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=3D0: chibar2(01) =3D 4557.62 Prob
> >=3D chib=
> ar2
> > =3D 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) =3D 12.59 Pr>chi2 =3D 0.1268
> >
> > Test that combined OR =3D 1:
> > Mantel-Haenszel chi2(1) =3D 0.03
> > Pr>chi2 =3D 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 =ADxtlogit- ?
> >>
> >> Data are from nine unmatched cases control studies of SNP genotype
> >>
> >> study =AD 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 =3D 12.59 (d.f. =3D 8) p =3D 0.127
> >> Estimate of between-study variance Tau-squared =3D 0.0125
> >> Test of OR=3D1 : z=3D 0.07 p =3D 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 =3D 12.01 (d.f. =3D 8) p =3D 0.151
> >> Estimate of between-study variance Tau-squared =3D 0.0047
> >> Test of OR=3D1 : z=3D 0.54 p =3D 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 =ADmetan-. I.e.
> >>
> >> . xi: logistic case i.alleles, nolog
> >>
> >> i.alleles _Ialleles_0-2 (naturally coded; _Ialleles_0
> >> omitted)
> >>
> >> Logistic regression Number of obs =3D
> >> 18961
> >> LR chi2(2) =3D
> >> 0.10
> >> Prob > chi2 =3D
> >> 0.9501
> >> Log likelihood =3D -13142.621 Pseudo R2 =3D
> >> 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 =3D -13142.672
> >> Iteration 1: log likelihood =3D -13142.621
> >>
> >> Fitting full model:
> >>
> >> tau =3D 0.0 log likelihood =3D -5971.0991
> >> tau =3D 0.1 log likelihood =3D -5971.4368
> >>
> >> Random-effects logistic regression Number of obs =3D
> >> 18961
> >> Group variable (i): study Number of groups =3D
> >> 9
> >>
> >> Random effects u_i ~ Gaussian Obs per group: min =3D
> >> 622
> >> avg =3D
> >> 2106.8
> >> max =3D
> >> 5286
> >>
> >> Wald chi2(2) =3D
> >> 7.45
> >> Log likelihood =3D -5965.7258 Prob > chi2
> =3D
> >> 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=3D0: chibar2(01) =3D 1.4e+04
> Prob >=3D chi=
> bar2 =3D
> >> 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
>
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>
*
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