Generic meta
GENERIC DATA
Learning outcomes:
You will have knowledge about and be able:
- Conduct fixed and random effects meta-analysis
- Measure effect size
- Explore heterogeneity using sub-group and meta-regression analyses
- Explore and address small study effects using funnel plot and trim and fill
STEPS in conducting Generic Data meta-analysis
- STEP 1 - LOAD DATA
- STEP 2 - DECLARE, UPDATE & DESCRIBE meta data
- STEP 3 - SUMMARIZE meta data by using a TABLE or a FOREST PLOT
- STEP 4- EXPLORE HETEROGENEITY - SUB-GROUP and META-REGRESSION analysis
- STEP 5- EXPLORE and ADDRESS SMALL-STUDY EFFECTS
Materials and setup
Laptop users: you will need a copy of Stata installed on your machine.
- You can install a licensed version from https://warwick.ac.uk/services/its/servicessupport/software/list/stata
- Find class materials at Click to Download
- Download and extract to your desktop or any folder of your choice!
Link to YouTube Video Lecture
Click the image below:
STEP 1 - LOAD DATA
The meta command accepts effect sizes and confidence intervals, not just count data. By specifying two variables after commands, you indicate to Stata that the variables represent effect sizes and standard error.
Below are results from trials that examined effect of exercise on depression.
Contains data from Exercise for depression
- Id: ID no. of study
- study: First author of study
- smd: Standardised mean difference
- varsmd: Var(smd)
- sesmd: SE(smd)
- abstract: Published as abstract?
- duration: Duration of follow-up (weeks)
- itt: Intention-to-treat analysis?
- alloc: Allocation concealment adequate?
- Phd: Published as PhD thesis?
Option 1 Copy and paste from Excel (see attached exercise4deprsn.xlsx below)
edit
Option 2
Input raw directly into Stata (using ‘do file editor’ type doedit)
clear all input id str20 study smd varsmd sesmd abstract duration itt alloc phd 1 Mutrie -2.53 0.16 0.4 1 4 0 0 0 2 McNeil -1.07 0.1681 0.41 0 6 0 0 0 3 Reuter -2.1 0.16 0.4 1 10 0 0 0 4 Doyne -1.2 0.1849 0.43 0 8 0 0 0 5 Hess-Homeier -0.82 0.3249 0.57 0 8 0 0 1 6 Epstein -0.84 0.2116 0.46 0 8 0 0 1 7 Martinsen -1.16 0.0784 0.28 0 9 0 1 0 8 Singh -0.45 0.1156 0.34 0 10 1 1 0 9 Klein 0.25 0.2601 0.51 0 12 0 0 0 10 Veale -0.53 0.0576 0.24 0 12 0 1 0 end
Option 3 Load Stata data file directly from Excel file
import excel using data/exercise4deprsn.xlsx, firstrow clear
describe
(10 vars, 10 obs)
Contains data
obs: 10
vars: 10
--------------------------------------------------------------------------------
storage display value
variable name type format label variable label
--------------------------------------------------------------------------------
id byte %10.0g id
study str12 %12s study
smd double %10.0g smd
varsmd double %10.0g varsmd
sesmd double %10.0g sesmd
abstract byte %10.0g abstract
duration byte %10.0g duration
itt byte %10.0g itt
alloc byte %10.0g alloc
phd byte %10.0g phd
--------------------------------------------------------------------------------
Sorted by:
Note: Dataset has changed since last saved.
Option 4 Load Stata data file directly (if already saved)
use data/exercise4deprsn.dta, clear
describe
(Excercise for depression)
Contains data from data/exercise4deprsn.dta
obs: 10 Excercise for depression
vars: 10 11 Oct 2015 21:16
(_dta has notes)
--------------------------------------------------------------------------------
storage display value
variable name type format label variable label
--------------------------------------------------------------------------------
id byte %3.0f * ID no. of study
study str12 %-12s First author of study
smd float %6.2f Standardised mean difference
varsmd float %7.4f Var(smd)
sesmd float %9.0g SE(smd)
abstract byte %-8.0g noyes Published as abstract?
duration byte %8.0g Duration of follow-up (weeks)
itt byte %-8.0g noyes Intention-to-treat analysis?
alloc byte %-8.0g noyes Allocation concealment adequate?
phd byte %-8.0g noyes Published as PhD thesis?
* indicated variables have notes
--------------------------------------------------------------------------------
Sorted by: id
STEP 2- DECLARE, UPDATE & DESCRIBE meta data
meta set smd sesmd, studylabel(study) eslabel(Std. Mean Diff.)
Meta-analysis setting information
Study information
No. of studies: 10
Study label: study
Study size: N/A
Effect size
Type: Generic
Label: Std. Mean Diff.
Variable: smd
Precision
Std. Err.: sesmd
CI: [_meta_cil, _meta_ciu]
CI level: 95%
Model and method
Model: Random-effects
Method: REML
STEP 3- SUMMARIZE meta data by using a TABLE or a FOREST PLOT
Now, combine the results of trials, using the fixed- and random effects model
Q2.1 - What are the summary estimates and 95% CI for both fixed and random-effects
Click For Answer
- Fixed: -1.01 (95% CI -1.24 to -0.79); - Random -1.06 (95% CI -1.53 to -0.59)
Q2.2 - Are the results homogenous?
Click For Answer
No, there is evidence of statistically significant substantial heterogeneity (I2 = 75%)meta forestplot, nullrefline fixed
graph display
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Study label: study
meta forestplot, nullrefline random
graph display
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Study label: study
STEP 4- EXPLORE HETEROGENEITY - SUB-GROUP and META-REGRESSION analysis
Examine the pooled estimates differ according to following study characteristics:
- Publication type
- Intention to treat analysis
- Allocation concealment
- Published as PhD thesis or not
meta forestplot, nullrefline random subgroup(abstract)
graph display
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Study label: study
meta forestplot, nullrefline random subgroup(itt)
graph display
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Study label: study
meta forestplot, nullrefline random subgroup(alloc)
graph display
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Study label: study
meta forestplot, nullrefline random subgroup(phd)
graph display
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Study label: study
Univariable meta-regression
Fit a meta-regression model that explains the heterogeneity in terms of study-level covariates.
Q2.3 - Which study level covariates are significant?
Click For Answer
- Unadjusted (Abstract & duration) - Adjusted (Abstract)
Q2.4 - What percentage of heterogeneity is explained for these covariates?
Click For Answer
Abstract & duration jointly explained 100% of the between study variance
meta regress abstract
meta regress duration
estat bubbleplot
graph display
meta regress itt
meta regress alloc
meta regress phd
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Random-effects meta-regression Number of obs = 10
Method: REML Residual heterogeneity:
tau2 = .03269
I2 (%) = 19.02
H2 = 1.23
R-squared (%) = 92.74
Wald chi2(1) = 20.78
Prob > chi2 = 0.0000
------------------------------------------------------------------------------
_meta_es | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
abstract | -1.564109 .3431559 -4.56 0.000 -2.236682 -.8915357
_cons | -.750891 .1463283 -5.13 0.000 -1.037689 -.4640929
------------------------------------------------------------------------------
Test of residual homogeneity: Q_res = chi2(8) = 9.94 Prob > Q_res = 0.2690
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Random-effects meta-regression Number of obs = 10
Method: REML Residual heterogeneity:
tau2 = .2019
I2 (%) = 58.10
H2 = 2.39
R-squared (%) = 55.16
Wald chi2(1) = 7.02
Prob > chi2 = 0.0081
------------------------------------------------------------------------------
_meta_es | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
duration | .2097633 .079171 2.65 0.008 .0545909 .3649357
_cons | -2.907511 .7239578 -4.02 0.000 -4.326442 -1.48858
------------------------------------------------------------------------------
Test of residual homogeneity: Q_res = chi2(8) = 18.11 Prob > Q_res = 0.0204
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Random-effects meta-regression Number of obs = 10
Method: REML Residual heterogeneity:
tau2 = .4719
I2 (%) = 76.66
H2 = 4.28
R-squared (%) = 0.00
Wald chi2(1) = 0.70
Prob > chi2 = 0.4028
------------------------------------------------------------------------------
_meta_es | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
itt | .6790167 .8116419 0.84 0.403 -.9117722 2.269806
_cons | -1.129017 .2668869 -4.23 0.000 -1.652105 -.605928
------------------------------------------------------------------------------
Test of residual homogeneity: Q_res = chi2(8) = 32.33 Prob > Q_res = 0.0001
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Random-effects meta-regression Number of obs = 10
Method: REML Residual heterogeneity:
tau2 = .4383
I2 (%) = 75.10
H2 = 4.02
R-squared (%) = 2.64
Wald chi2(1) = 1.01
Prob > chi2 = 0.3142
------------------------------------------------------------------------------
_meta_es | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
alloc | .5186852 .5153992 1.01 0.314 -.4914787 1.528849
_cons | -1.235379 .3032112 -4.07 0.000 -1.829662 -.6410955
------------------------------------------------------------------------------
Test of residual homogeneity: Q_res = chi2(8) = 28.46 Prob > Q_res = 0.0004
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Random-effects meta-regression Number of obs = 10
Method: REML Residual heterogeneity:
tau2 = .5089
I2 (%) = 79.16
H2 = 4.80
R-squared (%) = 0.00
Wald chi2(1) = 0.16
Prob > chi2 = 0.6910
------------------------------------------------------------------------------
_meta_es | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
phd | .2718996 .6840508 0.40 0.691 -1.068815 1.612615
_cons | -1.102629 .2853771 -3.86 0.000 -1.661957 -.5432998
------------------------------------------------------------------------------
Test of residual homogeneity: Q_res = chi2(8) = 35.15 Prob > Q_res = 0.0000
foreach factor of varlist abstract duration itt alloc phd {
meta regress `factor'
}
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Random-effects meta-regression Number of obs = 10
Method: REML Residual heterogeneity:
tau2 = .03269
I2 (%) = 19.02
H2 = 1.23
R-squared (%) = 92.74
Wald chi2(1) = 20.78
Prob > chi2 = 0.0000
------------------------------------------------------------------------------
_meta_es | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
abstract | -1.564109 .3431559 -4.56 0.000 -2.236682 -.8915357
_cons | -.750891 .1463283 -5.13 0.000 -1.037689 -.4640929
------------------------------------------------------------------------------
Test of residual homogeneity: Q_res = chi2(8) = 9.94 Prob > Q_res = 0.2690
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Random-effects meta-regression Number of obs = 10
Method: REML Residual heterogeneity:
tau2 = .2019
I2 (%) = 58.10
H2 = 2.39
R-squared (%) = 55.16
Wald chi2(1) = 7.02
Prob > chi2 = 0.0081
------------------------------------------------------------------------------
_meta_es | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
duration | .2097633 .079171 2.65 0.008 .0545909 .3649357
_cons | -2.907511 .7239578 -4.02 0.000 -4.326442 -1.48858
------------------------------------------------------------------------------
Test of residual homogeneity: Q_res = chi2(8) = 18.11 Prob > Q_res = 0.0204
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Random-effects meta-regression Number of obs = 10
Method: REML Residual heterogeneity:
tau2 = .4719
I2 (%) = 76.66
H2 = 4.28
R-squared (%) = 0.00
Wald chi2(1) = 0.70
Prob > chi2 = 0.4028
------------------------------------------------------------------------------
_meta_es | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
itt | .6790167 .8116419 0.84 0.403 -.9117722 2.269806
_cons | -1.129017 .2668869 -4.23 0.000 -1.652105 -.605928
------------------------------------------------------------------------------
Test of residual homogeneity: Q_res = chi2(8) = 32.33 Prob > Q_res = 0.0001
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Random-effects meta-regression Number of obs = 10
Method: REML Residual heterogeneity:
tau2 = .4383
I2 (%) = 75.10
H2 = 4.02
R-squared (%) = 2.64
Wald chi2(1) = 1.01
Prob > chi2 = 0.3142
------------------------------------------------------------------------------
_meta_es | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
alloc | .5186852 .5153992 1.01 0.314 -.4914787 1.528849
_cons | -1.235379 .3032112 -4.07 0.000 -1.829662 -.6410955
------------------------------------------------------------------------------
Test of residual homogeneity: Q_res = chi2(8) = 28.46 Prob > Q_res = 0.0004
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Random-effects meta-regression Number of obs = 10
Method: REML Residual heterogeneity:
tau2 = .5089
I2 (%) = 79.16
H2 = 4.80
R-squared (%) = 0.00
Wald chi2(1) = 0.16
Prob > chi2 = 0.6910
------------------------------------------------------------------------------
_meta_es | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
phd | .2718996 .6840508 0.40 0.691 -1.068815 1.612615
_cons | -1.102629 .2853771 -3.86 0.000 -1.661957 -.5432998
------------------------------------------------------------------------------
Test of residual homogeneity: Q_res = chi2(8) = 35.15 Prob > Q_res = 0.0000
Multivariale meta-regression
meta regress abstract duration
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Random-effects meta-regression Number of obs = 10
Method: REML Residual heterogeneity:
tau2 = 5.3e-08
I2 (%) = 0.00
H2 = 1.00
R-squared (%) = 100.00
Wald chi2(2) = 30.61
Prob > chi2 = 0.0000
------------------------------------------------------------------------------
_meta_es | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
abstract | -1.243886 .3412327 -3.65 0.000 -1.91269 -.575082
duration | .1207103 .0533561 2.26 0.024 .0161343 .2252863
_cons | -1.916086 .5312603 -3.61 0.000 -2.957337 -.8748354
------------------------------------------------------------------------------
Test of residual homogeneity: Q_res = chi2(7) = 4.82 Prob > Q_res = 0.6813
STEP 5- EXPLORE and ADDRESS SMALL-STUDY EFFECTS
Q2.5 - Examine whether there is evidence of publication bias?
Click For Answer
No evidence of publication bias
meta funnelplot, metric(invse)
graph display
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Model: Common-effect
Method: Inverse-variance
meta bias, egger
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Regression-based Egger test for small-study effects
Random-effects model
Method: REML
H0: beta1 = 0; no small-study effects
beta1 = 0.48
SE of beta1 = 2.804
z = 0.17
Prob > |z| = 0.8641
meta trimfill
Effect-size label: Std. Mean Diff.
Effect size: smd
Std. Err.: sesmd
Nonparametric trim-and-fill analysis of publication bias
Linear estimator, imputing on the right
Iteration Number of studies = 10
Model: Random-effects observed = 10
Method: REML imputed = 0
Pooling
Model: Random-effects
Method: REML
---------------------------------------------------------------
Studies | Std. Mean Diff. [95% Conf. Interval]
---------------------+-----------------------------------------
Observed | -1.056 -1.541 -0.570
Observed + Imputed | -1.056 -1.541 -0.570
---------------------------------------------------------------
GENERIC DATA
STEPS in conducting Generic Data meta-analysis
- STEP 1 - LOAD DATA
- STEP 2 - DECLARE, UPDATE & DESCRIBE meta data
- STEP 3 - SUMMARIZE meta data by using a TABLE or a FOREST PLOT
- STEP 4- EXPLORE HETEROGENEITY - SUB-GROUP and META-REGRESSION analysis
- STEP 5- EXPLORE and ADDRESS SMALL-STUDY EFFECTS