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st: Questions on a meta-regression problem


From   "G Livesey" <glivesey@inlogic.co.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Questions on a meta-regression problem
Date   Thu, 23 Apr 2009 21:38:22 +0100

Dear Statalisters

I am meta-analysing prospective studies relating health outcomes to nutrient
dose, and would gladly welcome comments and help with solutions where
possible.

Rather than meta-analyse the slopes from each study to obtain a mean, tau
and se for the slopes (such as with the GLST module) , I would like the
primary unit of study to be the quantile (irater than the study level) and
use dose values (as continuous) rather than quantile levels for dose
(categories). To achieve this involves some prior calculations to bring a
common metric to the dose and a common referent dose, which otherwise differ
between studies. The  broader range of nutrient dose than found in
individual studies (>2 fold)  would help with fitting an overall slope and
viewing the wider picture. Such advantage seems not to be without other,
possible disadvantage - unless statlisters have a solution:

The problem is that quantiles within studies may not be truly independent
(e.g.  Studies might not have identical conditions or may be biased). The
question is. therefore, is  there (or can there be) a solution to this
problem?  No ready made solution is obvious (to me) in a search of
meta-analysis commands or net searches.  If not, what post-analyses might be
done to limit any error incurred? For example, metareg P-values for the
coefficients might be recalculated to a lower number of degrees of freedom,
likewise for tau, but how should one define the degrees of freedom for the
coefficients and for tau, and  how should one  perform an appropriate
recalculation of Tau  (the estimate of Tau within studies is close to zero,
possibly averaging near zero, though may not always be so)? 

The problem does not seems extensive with this dataset, however, I would
appreciate viewpoints or potential solutions on this issue .  An example
dataset with meta-regression commands is described below. But does anyone
know of another module that could offer a better approach to this problem.


With thanks, and in admiration of the many solutions statalisters release
each day on the statalist.

Geoff. Livesey.


----------------------------------------------------------------------------
-----------------------------------------------------------------------
In the example here 8 prospective studies relate nutrient intake to health
in males and females. Information available is

source_n , the id for the published source of the study.
Qn , the id for the quintile in each source_n.
m_y, the median natural log of rate ratio, adjusted so that all studies have
a common referent rate ratio at nutrient dose predefined as zero. 
se_y the standard error of m_y.
x1, dose above a predefined dose.
fr_male, the fraction of participants that are male.



 source_n   Qn      m_y    se_y    x1   fr_male .


1    1    0.052   0.050    13         0
1    2    0.052   0.061    32         0
1    3    0.138   0.073    44         0
1    4    0.148   0.083    56         0
1    5    0.251   0.092    81         0
2    1    0.043   0.066    -7         0
2    2    0.002   0.067     5         0
2    3   -0.108   0.070    13         0
2    4   -0.040   0.072    20         0
2    5   -0.008   0.074    32         0
3    1   -0.116   0.250    23       .52
3    2    0.289   0.256    34      .588
3    3   -0.116   0.262    76       .55
3    4    0.289   0.267    87      .585
3    5    0.146   0.273    98      .457
4    1    0.012   0.078     7         0
4    2    0.227   0.081    23         0
4    3    0.211   0.083    34         0
4    4    0.235   0.086    44         0
4    5    0.397   0.088    60         0
5    1    0.022   0.088     5         1
5    2    0.089   0.100    20         1
5    3    0.061   0.112    31         1
5    4    0.144   0.122    42         1
5    5    0.245   0.133    64         1
6    1    0.025   0.060    17         0
6    2    0.295   0.090    31         0
6    3    0.207   0.116    40         0
6    4    0.156   0.140    51         0
6    5    0.310   0.163    68         0
7    1    0.068   0.134   -18       .63
7    2   -0.186   0.169    20      .559
7    3    0.037   0.137    46      .516
7    4    0.228   0.115    73      .472
7    5    0.263   0.111   110      .493
8    1    0.418   0.068    84         0 
8    2    0.476   0.063   101         0 
8    3    0.387   0.059   110         0 
8    4    0.625   0.055   120         0 
8    5    0.710   0.050   155         0 


/*generate interaction  with sex (code: male=1, female=0, mixedsex!=0|1)*/
gen x1_X_fr_male =x1 * fr_male

/*For theoretical reasons, constant fixed at zero for males and females*/

/*model 1 without interaction,  I-squared_res  =  58.08%*/
metareg  m_y  x1   ///
    ,wsse(se_y) knapphartung  reml lrtau2 noconstant 

/*model 2 with interaction,  I-squared_res  =  29.35% and model F has
P=0.0000*/
 metareg  m_y  x1  x1_X_fr_male ///
  ,wsse(se_y) knapphartung  reml lrtau2 noconstant



. 


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