Prevalence meta
PREVALENCE OR PROPORTION DATA
Learning outcomes:
You will have knowledge about and be able:
- Conduct fixed and random effects meta-analysis
- Measure effect size HETEROGENEITY
- 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 Prevalence Data
- 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 data is from a meta-analysis that estimated the prevalence of underlying disorders in hospitalized COVID-19 patients
use data/covid-premorb.dta, clear
describe
Contains data from data/covid-premorb.dta
obs: 40
vars: 5 10 May 2020 11:34
--------------------------------------------------------------------------------
storage display value
variable name type format label variable label
--------------------------------------------------------------------------------
study str26 %-9s
morb long %12.0g morb
r double %10.0g
n double %10.0g
male double %10.0g
--------------------------------------------------------------------------------
Sorted by:
tab morb
morb | Freq. Percent Cum.
------------+-----------------------------------
CKD | 7 17.50 17.50
HTN | 7 17.50 35.00
DM | 6 15.00 50.00
Mal | 7 17.50 67.50
COPD | 5 12.50 80.00
CVD | 8 20.00 100.00
------------+-----------------------------------
Total | 40 100.00
STEP 2- DECLARE, UPDATE & DESCRIBE meta data
Not applicable initially
STEP 3- SUMMARIZE meta data by using a TABLE or a FOREST PLOT
metaprop r n, ftt random notable
graph display
metaprop r n, ftt random label(namevar=study) notable
graph display
metaprop r n, ftt random notable label(namevar=study) power(2)
graph display
STEP 4- EXPLORE HETEROGENEITY - SUB-GROUP and META-REGRESSION analysis
Q4.1 - What is the commonest pre-morb condition?
Click For Answer
Hypertension `(16.37%, 95% CI 10.15 to 23.65)` followed by cardiovascular disease `(12.11%, 95% CI 4.4 to 22.7)`
Q4.2 - What is the least common pre-mord condition?
Click For Answer
COPD `(0.95%, 95% CI 0.43 to 1.61)` followed by malignancy `(1.50%, 95% CI 0.58 to 2.73)`.
metaprop r n, ftt random label(namevar=study) power(2) by(morb)
graph di
Study | ES [95% Conf. Interval] % Weight
---------------------+---------------------------------------------------
CKD
Chaolin Huang, et al | 7.32 2.52 19.43 2.20
Nanshan Chen, et al. | 3.03 1.04 8.53 2.53
Dawei Wang, et al. ( | 2.90 1.13 7.22 2.61
Jie.Li, et al. (36) | 47.06 26.17 69.04 1.68
Wei-Jie Guan, et al. | 0.09 0.02 0.51 2.81
Jin-jin Zhang, et al | 1.43 0.39 5.06 2.62
Jian Wu, et al. (39) | 1.25 0.22 6.75 2.47
Sub-total |
Random pooled ES | 3.61 0.44 8.90 16.93
---------------------+---------------------------------------------------
HTN
Chaolin Huang, et al | 14.63 6.88 28.44 2.20
Dawei Wang, et al. ( | 31.16 24.03 39.31 2.61
Jie.Li, et al. (36) | 5.88 1.05 26.98 1.68
Wei-Jie Guan, et al. | 14.92 12.94 17.15 2.81
Xiao-Wei Xu, et al. | 8.06 3.49 17.53 2.38
Jin-jin Zhang, et al | 30.00 23.03 38.04 2.62
Kui L, et al. (40) | 9.49 5.63 15.56 2.61
Sub-total |
Random pooled ES | 16.37 10.15 23.65 16.92
---------------------+---------------------------------------------------
DM
Chaolin Huang, et al | 19.51 10.23 34.01 2.20
Dawei Wang, et al. ( | 10.14 6.14 16.31 2.61
Wei-Jie Guan, et al. | 7.37 5.97 9.07 2.81
Xiao-Wei Xu, et al. | 1.61 0.29 8.59 2.38
Jin-jin Zhang, et al | 12.14 7.72 18.59 2.62
Kui L, et al. (40) | 10.22 6.19 16.42 2.61
Sub-total |
Random pooled ES | 9.03 5.92 12.67 15.23
---------------------+---------------------------------------------------
Mal
Chaolin Huang, et al | 2.44 0.43 12.60 2.20
Nanshan Chen, et al. | 1.01 0.18 5.50 2.53
Dawei Wang, et al. ( | 7.25 3.98 12.83 2.61
Wei-Jie Guan, et al. | 0.91 0.49 1.67 2.81
Wenhua Liang,et al. | 1.13 0.72 1.78 2.82
Jian Wu, et al. (39) | 1.25 0.22 6.75 2.47
Kui L, et al. (40) | 1.46 0.40 5.17 2.61
Sub-total |
Random pooled ES | 1.50 0.58 2.73 18.06
---------------------+---------------------------------------------------
COPD
Chaolin Huang, et al | 2.44 0.43 12.60 2.20
Dawei Wang, et al. ( | 2.90 1.13 7.22 2.61
Wei-Jie Guan, et al. | 1.09 0.63 1.90 2.81
Xiao-Wei Xu, et al. | 1.61 0.29 8.59 2.38
Jin-jin Zhang, et al | 1.43 0.39 5.06 2.62
Sub-total |
Random pooled ES | 0.95 0.43 1.61 12.62
---------------------+---------------------------------------------------
CVD
Chaolin Huang, et al | 14.63 6.88 28.44 2.20
Nanshan Chen, et al. | 40.40 31.27 50.25 2.53
Dawei Wang, et al. ( | 14.49 9.58 21.33 2.61
Wei-Jie Guan, et al. | 2.46 1.69 3.55 2.81
Xiao-Wei Xu, et al. | 1.61 0.29 8.59 2.38
Jin-jin Zhang, et al | 5.00 2.44 9.96 2.62
Jian Wu, et al. (39) | 31.25 22.15 42.07 2.47
Kui L, et al. (40) | 7.30 4.01 12.92 2.61
Sub-total |
Random pooled ES | 12.11 4.40 22.75 20.24
---------------------+---------------------------------------------------
Overall |
Random pooled ES | 6.83 4.52 9.54 100.00
---------------------+---------------------------------------------------
Test(s) of heterogeneity:
Heterogeneity degrees of
statistic freedom P I^2**
CKD 60.52 6 0.00 90.09%
HTN 44.18 6 0.00 86.42%
DM 15.22 5 0.01 67.15%
Mal 17.60 6 0.01 65.91%
COPD 3.92 4 0.42 0.00%
CVD 170.42 7 0.00 95.89%
Overall 908.00 39 0.00 95.70%
** I^2: the variation in ES attributable to heterogeneity)
Random: Test for heterogeneity between sub-groups:
79.93 5 0.00
Significance test(s) of ES=0
CKD z= 2.72 p = 0.01
HTN z= 7.89 p = 0.00
DM z= 8.95 p = 0.00
Mal z= 4.49 p = 0.00
COPD z= 5.21 p = 0.00
CVD z= 4.37 p = 0.00
Overall z= 8.99 p = 0.00
-------------------------------------------------------------------------
Q4.3 - Is there is correlation between the prevalence estimates and % males
Click For Answer
No, not statistically significant
Q4.4 - Are smaller studies tended to have reported over reported the prevalence estimates
Click For Answer
Yes, smaller studies tended to report higher prevalence estimates.
d
Contains data from data/covid-premorb.dta
obs: 40
vars: 10 10 May 2020 11:34
--------------------------------------------------------------------------------
storage display value
variable name type format label variable label
--------------------------------------------------------------------------------
study str26 %-9s
morb long %12.0g morb
r double %10.0g
n double %10.0g
male double %10.0g
_ES float %9.0g ES
_seES float %9.0g se(ES)
_LCI float %9.0g Lower CI (ES)
_UCI float %9.0g Upper CI (ES)
_WT float %9.0g Random weight
--------------------------------------------------------------------------------
Sorted by:
* STEP 2- DECLARE, UPDATE & DESCRIBE meta data
meta set _ES _seES, studylabel(study) eslabel(Premorb. Prevalence.)
Meta-analysis setting information
Study information
No. of studies: 40
Study label: study
Study size: N/A
Effect size
Type: Generic
Label: Premorb. Prevalence.
Variable: _ES
Precision
Std. Err.: _seES
CI: [_meta_cil, _meta_ciu]
CI level: 95%
Model and method
Model: Random-effects
Method: REML
meta regress male
estat bubbleplot
graph di
Effect-size label: Premorb. Prevalence.
Effect size: _ES
Std. Err.: _seES
Random-effects meta-regression Number of obs = 39
Method: REML Residual heterogeneity:
tau2 = .003317
I2 (%) = 44.21
H2 = 1.79
R-squared (%) = 0.00
Wald chi2(1) = 0.04
Prob > chi2 = 0.8488
------------------------------------------------------------------------------
_meta_es | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
male | .000455 .002387 0.19 0.849 -.0042234 .0051334
_cons | .0539036 .1356548 0.40 0.691 -.211975 .3197822
------------------------------------------------------------------------------
Test of residual homogeneity: Q_res = chi2(37) = 62.24 Prob > Q_res = 0.0058
meta regress n
estat bubbleplot
graph di
Effect-size label: Premorb. Prevalence.
Effect size: _ES
Std. Err.: _seES
Random-effects meta-regression Number of obs = 40
Method: REML Residual heterogeneity:
tau2 = .002014
I2 (%) = 34.33
H2 = 1.52
R-squared (%) = 34.55
Wald chi2(1) = 5.07
Prob > chi2 = 0.0243
------------------------------------------------------------------------------
_meta_es | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
n | -.0000583 .0000259 -2.25 0.024 -.0001091 -7.57e-06
_cons | .1078519 .0215803 5.00 0.000 .0655554 .1501484
------------------------------------------------------------------------------
Test of residual homogeneity: Q_res = chi2(38) = 55.54 Prob > Q_res = 0.0329
STEP 5- EXPLORE and ADDRESS SMALL-STUDY EFFECTS
meta funnelplot, metric(invse)
graph display
Effect-size label: Premorb. Prevalence.
Effect size: _ES
Std. Err.: _seES
Model: Common-effect
Method: Inverse-variance
meta bias, egger
Effect-size label: Premorb. Prevalence.
Effect size: _ES
Std. Err.: _seES
Regression-based Egger test for small-study effects
Random-effects model
Method: REML
H0: beta1 = 0; no small-study effects
beta1 = 0.72
SE of beta1 = 0.353
z = 2.05
Prob > |z| = 0.0403
meta trimfill
Effect-size label: Premorb. Prevalence.
Effect size: _ES
Std. Err.: _seES
Nonparametric trim-and-fill analysis of publication bias
Linear estimator, imputing on the left
Iteration Number of studies = 40
Model: Random-effects observed = 40
Method: REML imputed = 0
Pooling
Model: Random-effects
Method: REML
theta: Overall Premorb. Prevalence.
---------------------------------------------------------------
Studies | theta [95% Conf. Interval]
---------------------+-----------------------------------------
Observed | 0.075 0.044 0.105
Observed + Imputed | 0.075 0.044 0.105
---------------------------------------------------------------
PREVALENCE OR PROPORTION DATA
STEPS in conducting Prevalence Data
- 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