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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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