I usually find the answer to these questions in the PDF documentation, but here I was unable to.
What is the mathematical formula that Stata uses (using default options) to estimate a confidence interval for a total effect in a meta analysis?
Example:
How did Stata use studies 1 to 10 CIs to get at [0.857,1.418]?
What is the mathematical formula that Stata uses (using default options) to estimate a confidence interval for a total effect in a meta analysis?
Example:
Code:
. webuse metaset
(Generic effect sizes; fictional data)
. meta set es cil ciu
Meta-analysis setting information
Study information
No. of studies: 10
Study label: Generic
Study size: N/A
Effect size
Type: <generic>
Label: Effect size
Variable: es
Precision
Std. err.: _meta_se
CI: [_meta_cil, _meta_ciu]
CI level: 95%, controlled by level()
User CI: [cil, ciu]
User CI level: 95%, controlled by civarlevel()
Model and method
Model: Random effects
Method: REML
. meta summ
Effect-size label: Effect size
Effect size: es
Std. err.: _meta_se
Meta-analysis summary Number of studies = 10
Random-effects model Heterogeneity:
Method: REML tau2 = 0.0157
I2 (%) = 5.30
H2 = 1.06
--------------------------------------------------------------------
Study | Effect size [95% conf. interval] % weight
------------------+-------------------------------------------------
Study 1 | 1.480 -0.352 3.311 2.30
Study 2 | 0.999 -0.933 2.931 2.07
Study 3 | 1.272 0.427 2.117 10.15
Study 4 | 1.001 0.750 1.252 63.77
Study 5 | 1.179 -0.527 2.884 2.65
Study 6 | 1.939 0.427 3.452 3.35
Study 7 | 2.377 1.005 3.750 4.05
Study 8 | 0.694 -0.569 1.956 4.75
Study 9 | 1.099 -0.147 2.345 4.88
Study 10 | 1.805 -0.151 3.761 2.02
------------------+-------------------------------------------------
theta | 1.138 0.857 1.418
--------------------------------------------------------------------
Test of theta = 0: z = 7.95 Prob > |z| = 0.0000
Test of homogeneity: Q = chi2(9) = 6.34 Prob > Q = 0.7054
