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.
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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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