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

  1. STEP 1 - LOAD DATA
  2. STEP 2 - DECLARE, UPDATE & DESCRIBE meta data
  3. STEP 3 - SUMMARIZE meta data by using a TABLE or a FOREST PLOT
  4. STEP 4- EXPLORE HETEROGENEITY - SUB-GROUP and META-REGRESSION analysis
  5. 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

  1. STEP 1 - LOAD DATA
  2. STEP 2 - DECLARE, UPDATE & DESCRIBE meta data
  3. STEP 3 - SUMMARIZE meta data by using a TABLE or a FOREST PLOT
  4. STEP 4- EXPLORE HETEROGENEITY - SUB-GROUP and META-REGRESSION analysis
  5. STEP 5- EXPLORE and ADDRESS SMALL-STUDY EFFECTS

Sections

  1. Overview meta-analysis data types
  2. Introduction to Stata
  3. Meta-analysis of binary data
  4. Meta-analysis of generic data
  5. Meta-analysis of continuous data
  6. Meta-analysis of prevalence data