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Re: st: Random effects logistic regression: -metan- v -xtlogit-


From   Paul Seed <[email protected]>
To   [email protected]
Subject   Re: st: Random effects logistic regression: -metan- v -xtlogit-
Date   Tue, 05 Dec 2006 13:39:08 +0000

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


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