08 September 2020
This page is a supplementary material for the lecture Statistical Methods for Meta-Analysis, in the course Systematic Review and Meta-Analysis.
It contains the Stata code for exemplifying the theoretical aspects presented in the slides using real worked example. The code has been kindly written by Nicola Orsini.
To reproduce the results you need to load the following packages
ssc install metan
ssc install metareg
ssc install metaan
ssc install metafunnel
ssc install metabias
ssc install metatrim
ssc install metacum
The example from Hine et al. (1989) contains the results from 6 studies on the mortality risk due to prophylactic use of lidocaine after a heart attack.
. set scheme s1mono, permanently
(set scheme preference recorded)
.
. clear
. use dat.hine1989.dta
.
. gen cases_1 = ai
. gen controls_1 = n1i-ai
. gen cases_0 = ci
. gen controls_0 = n2i-ci
.
. list
┌────────────────────────────────────────────────────────────────────────────────────────┐
│ study source n1i n2i ai ci cases_1 contro~1 cases_0 contro~0 │
├────────────────────────────────────────────────────────────────────────────────────────┤
1. │ 1 Chopra et al. 39 43 2 1 2 37 1 42 │
2. │ 2 Mogensen 44 44 4 4 4 40 4 40 │
3. │ 3 Pitt et al. 107 110 6 4 6 101 4 106 │
4. │ 4 Darby et al. 103 100 7 5 7 96 5 95 │
5. │ 5 Bennett et al. 110 106 7 3 7 103 3 103 │
├────────────────────────────────────────────────────────────────────────────────────────┤
6. │ 6 O'Brien et al. 154 146 11 4 11 143 4 142 │
└────────────────────────────────────────────────────────────────────────────────────────┘
Among different possibilities, we choose to compute risk differences as preferable effect size.
. metan cases_1 controls_1 cases_0 controls_0, classic textsize(200) rd lcols(source) fixed label(namevar=source) counts
Study | RD [95% Conf. Interval] % Weight
─────────────────────+───────────────────────────────────────────────────
Chopra et al. | 0.028 -0.055 0.111 7.40
Mogensen | 0.000 -0.120 0.120 7.96
Pitt et al. | 0.020 -0.036 0.076 19.63
Darby et al. | 0.018 -0.047 0.083 18.36
Bennett et al. | 0.035 -0.020 0.091 19.53
O'Brien et al. | 0.044 -0.005 0.093 27.12
─────────────────────+───────────────────────────────────────────────────
M-H pooled RD | 0.028 0.002 0.054 100.00
─────────────────────+───────────────────────────────────────────────────
Heterogeneity chi-squared = 0.87 (d.f. = 5) p = 0.972
I-squared (variation in RD attributable to heterogeneity) = 0.0%
Test of RD=0 : z= 2.11 p = 0.035
. graph export forrest_1.png, replace
(file forrest_1.png written in PNG format)
The example from Berkey et al. (1995) contains the results with the BCG vaccine dataset (Colditz et al., 1994).
. clear
. use dat.bcg.dta
. list
┌────────────────────────────────────────────────────────────────────────────────────────┐
│ trial author year tpos tneg cpos cneg ablat alloc │
├────────────────────────────────────────────────────────────────────────────────────────┤
1. │ 1 Aronson 1948 4 119 11 128 44 random │
2. │ 2 Ferguson & Simes 1949 6 300 29 274 55 random │
3. │ 3 Rosenthal et al 1960 3 228 11 209 42 random │
4. │ 4 Hart & Sutherland 1977 62 13536 248 12619 52 random │
5. │ 5 Frimodt-Moller et al 1973 33 5036 47 5761 13 alternate │
├────────────────────────────────────────────────────────────────────────────────────────┤
6. │ 6 Stein & Aronson 1953 180 1361 372 1079 44 alternate │
7. │ 7 Vandiviere et al 1973 8 2537 10 619 19 random │
8. │ 8 TPT Madras 1980 505 87886 499 87892 13 random │
9. │ 9 Coetzee & Berjak 1968 29 7470 45 7232 27 random │
10. │ 10 Rosenthal et al 1961 17 1699 65 1600 42 systematic │
├────────────────────────────────────────────────────────────────────────────────────────┤
11. │ 11 Comstock et al 1974 186 50448 141 27197 18 systematic │
12. │ 12 Comstock & Webster 1969 5 2493 3 2338 33 systematic │
13. │ 13 Comstock et al 1976 27 16886 29 17825 33 systematic │
└────────────────────────────────────────────────────────────────────────────────────────┘
. metan tpos tneg cpos cneg, classic textsize(200) rr lcols(author year) random counts
Study | RR [95% Conf. Interval] % Weight
─────────────────────+───────────────────────────────────────────────────
Aronson | 0.411 0.134 1.257 5.04
Ferguson & Simes | 0.205 0.086 0.486 6.35
Rosenthal et al | 0.260 0.073 0.919 4.42
Hart & Sutherland | 0.237 0.179 0.312 9.71
Frimodt-Moller et al | 0.804 0.516 1.254 8.87
Stein & Aronson | 0.456 0.387 0.536 10.12
Vandiviere et al | 0.198 0.078 0.499 6.01
TPT Madras | 1.012 0.895 1.145 10.21
Coetzee & Berjak | 0.625 0.393 0.996 8.75
Rosenthal et al | 0.254 0.149 0.431 8.37
Comstock et al | 0.712 0.573 0.886 9.94
Comstock & Webster | 1.562 0.374 6.528 3.80
Comstock et al | 0.983 0.582 1.659 8.40
─────────────────────+───────────────────────────────────────────────────
D+L pooled RR | 0.490 0.345 0.695 100.00
─────────────────────+───────────────────────────────────────────────────
Heterogeneity chi-squared = 152.57 (d.f. = 12) p = 0.000
I-squared (variation in RR attributable to heterogeneity) = 92.1%
Estimate of between-study variance Tau-squared = 0.3095
Test of RR=1 : z= 3.99 p = 0.000
. graph export forrest_2.png, replace
(file forrest_2.png written in PNG format)
. gen y_i = ln(_ES)
. gen se_i = _selogES
. metareg y_i ablat, wsse(se_i) reml graph
Meta-regression Number of obs = 13
REML estimate of between-study variance tau2 = .07635
% residual variation due to heterogeneity I-squared_res = 64.21%
Proportion of between-study variance explained Adj R-squared = 75.63%
With Knapp-Hartung modification
─────────────┬────────────────────────────────────────────────────────────────
y_i │ Coef. Std. Err. t P>|t| [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
ablat │ -.0291017 .0082014 -3.55 0.005 -.0471529 -.0110505
_cons │ .2514682 .2839253 0.89 0.395 -.3734471 .8763835
─────────────┴────────────────────────────────────────────────────────────────
. graph export metareg.png, replace
(file metareg.png written in PNG format)
. predict fitted, xb
. predict se_fitted, stdp
.
. gen lo = fitted-1.96*se_fitted
. gen hi = fitted+1.96*se_fitted
.
. gen o_rr = exp(y_i)
. gen f_rr = exp(fitted)
. gen f_lb = exp(lo)
. gen f_ub = exp(hi)
.
. twoway (rarea f_lb f_ub ablat, sort color(gs10%20) ) ///
> (scatter o_rr ablat [aw=1/se_i^2], msymbol(o) mc(black%50)) ///
> (scatter o_rr ablat , msymbol(i) mlabel(trial) mlabpos(3)) ///
> , yscale(log) ytitle("Relative Risk") legend(off) ///
> xscale(range(0 60)) xtitle("Absolute Latitude") ///
> ylabel(.5 1 1.5 2, angle(horiz) format(%3.2f)) plotregion(style(none)) ///
> yline(1, lp(dash))
. graph export metareg_customized.png, replace
(file metareg_customized.png written in PNG format)
The example from Viechtbauer et al. (2007) contains the results from 9 studies on the effectiveness of diuretics in pregnancy for preventing pre-eclampsia (Collins et al. (1985)).
. use dat.collins1985b.dta , clear
. list
┌─────────────────────────────────────────────────────────────────────────────┐
│ id author year pre_nti pre_nci pre_xti pre_xci │
├─────────────────────────────────────────────────────────────────────────────┤
1. │ 1 Weseley & Douglas 1962 131 136 14 14 │
2. │ 2 Flowers et al. 1962 385 134 21 17 │
3. │ 3 Menzies 1964 57 48 14 24 │
4. │ 4 Fallis et al. 1964 38 40 6 18 │
5. │ 5 Cuadros & Tatum 1964 1011 760 12 35 │
├─────────────────────────────────────────────────────────────────────────────┤
6. │ 6 Landesman et al. 1965 1370 1336 138 175 │
7. │ 7 Kraus et al. 1966 506 524 15 20 │
8. │ 8 Tervila & Vartiainen 1971 108 103 6 2 │
9. │ 9 Campbell & MacGillivray 1975 153 102 65 40 │
└─────────────────────────────────────────────────────────────────────────────┘
. gen t_c = pre_nt- pre_xti
. gen c_c = pre_nci-pre_xci
. metan pre_xti t_c pre_xci c_c, classic textsize(200) or lcols(author) random counts
Study | OR [95% Conf. Interval] % Weight
─────────────────────+───────────────────────────────────────────────────
Weseley & Douglas | 1.043 0.477 2.282 10.66
Flowers et al. | 0.397 0.203 0.778 11.94
Menzies | 0.326 0.142 0.744 10.18
Fallis et al. | 0.229 0.078 0.669 7.85
Cuadros & Tatum | 0.249 0.128 0.483 12.06
Landesman et al. | 0.743 0.586 0.942 16.98
Kraus et al. | 0.770 0.390 1.521 11.84
Tervila & Vartiainen | 2.971 0.586 15.068 4.53
Campbell & MacGilliv | 1.145 0.687 1.908 13.95
─────────────────────+───────────────────────────────────────────────────
D+L pooled OR | 0.596 0.400 0.889 100.00
─────────────────────+───────────────────────────────────────────────────
Heterogeneity chi-squared = 27.27 (d.f. = 8) p = 0.001
I-squared (variation in OR attributable to heterogeneity) = 70.7%
Estimate of between-study variance Tau-squared = 0.2298
Test of OR=1 : z= 2.54 p = 0.011
. gen y_i = ln(_ES)
. gen se_i = _selogES
.
. metaan y_i se_i , dl
DerSimonian-Laird random-effects method selected
─────────────────────┬─────────────────────────────────────────────
Study │ Effect [95% Conf. Interval] % Weight
─────────────────────┼─────────────────────────────────────────────
1 │ 0.042 -0.741 0.825 10.66
2 │ -0.924 -1.596 -0.251 11.94
3 │ -1.122 -1.949 -0.295 10.18
4 │ -1.473 -2.545 -0.402 7.85
5 │ -1.391 -2.054 -0.728 12.06
6 │ -0.297 -0.534 -0.060 16.98
7 │ -0.262 -0.942 0.419 11.84
8 │ 1.089 -0.535 2.713 4.53
9 │ 0.135 -0.375 0.646 13.95
─────────────────────┼─────────────────────────────────────────────
Overall effect (dl) │ -0.517 -0.916 -0.117 100.00
─────────────────────┴─────────────────────────────────────────────
Heterogeneity Measures
───────────────┬───────────────────────────────────
│ value df p-value
───────────────┼───────────────────────────────────
Cochrane Q │ 27.26 8 0.001
───────────────┴───────────────────────────────────
───────────────┬───────────────────────────────────
│ value [95% Conf. Interval]
───────────────┼───────────────────────────────────
I^2(%) │ 70.66 41.83 85.20
H^2 │ 3.41 1.72 6.76
tau^2(dl) │ 0.230
───────────────┴───────────────────────────────────
. metaan y_i se_i , ml
Maximum Likelihood method selected
─────────────────────┬─────────────────────────────────────────────
Study │ Effect [95% Conf. Interval] % Weight
─────────────────────┼─────────────────────────────────────────────
1 │ 0.042 -0.741 0.825 10.69
2 │ -0.924 -1.596 -0.251 11.95
3 │ -1.122 -1.949 -0.295 10.22
4 │ -1.473 -2.545 -0.402 7.92
5 │ -1.391 -2.054 -0.728 12.06
6 │ -0.297 -0.534 -0.060 16.81
7 │ -0.262 -0.942 0.419 11.85
8 │ 1.089 -0.535 2.713 4.60
9 │ 0.135 -0.375 0.646 13.89
─────────────────────┼─────────────────────────────────────────────
Overall effect (ml) │ -0.517 -0.921 -0.113 100.00
─────────────────────┴─────────────────────────────────────────────
ML method succesfully converged
Heterogeneity Measures
───────────────┬───────────────────────────────────
│ value df p-value
───────────────┼───────────────────────────────────
Cochrane Q │ 27.26 8 0.001
───────────────┴───────────────────────────────────
───────────────┬───────────────────────────────────
│ value [95% Conf. Interval]
───────────────┼───────────────────────────────────
I^2(%) │ 71.44 43.62 85.53
H^2 │ 3.50 1.77 6.91
tau^2(ml) │ 0.239
───────────────┴───────────────────────────────────
. metaan y_i se_i , reml
Restricted Maximum Likelihood (REML) method selected
─────────────────────┬─────────────────────────────────────────────
Study │ Effect [95% Conf. Interval] % Weight
─────────────────────┼─────────────────────────────────────────────
1 │ 0.042 -0.741 0.825 10.86
2 │ -0.924 -1.596 -0.251 11.95
3 │ -1.122 -1.949 -0.295 10.45
4 │ -1.473 -2.545 -0.402 8.34
5 │ -1.391 -2.054 -0.728 12.05
6 │ -0.297 -0.534 -0.060 15.86
7 │ -0.262 -0.942 0.419 11.87
8 │ 1.089 -0.535 2.713 5.07
9 │ 0.135 -0.375 0.646 13.57
─────────────────────┼─────────────────────────────────────────────
Overall effect (reml)│ -0.518 -0.956 -0.080 100.00
─────────────────────┴─────────────────────────────────────────────
REML method succesfully converged
Heterogeneity Measures
───────────────┬───────────────────────────────────
│ value df p-value
───────────────┼───────────────────────────────────
Cochrane Q │ 27.26 8 0.001
───────────────┴───────────────────────────────────
───────────────┬───────────────────────────────────
│ value [95% Conf. Interval]
───────────────┼───────────────────────────────────
I^2(%) │ 75.92 53.78 87.46
H^2 │ 4.15 2.16 7.97
tau^2(reml) │ 0.301
───────────────┴───────────────────────────────────
. use dat.hackshaw1998.dta , clear
. list
┌────────────────────────────────────────────────────────────────────────────────┐
│ study author year country design cases yi vi │
├────────────────────────────────────────────────────────────────────────────────┤
1. │ 1 Garfinkel 1981 USA cohort 153 .166 .0188 │
2. │ 2 Hirayama 1984 Japan cohort 200 .372 .033 │
3. │ 3 Butler 1988 USA cohort 8 .703 .5402 │
4. │ 4 Cardenas 1997 USA cohort 150 .182 .0313 │
5. │ 5 Chan 1982 Hong Kong case-control 84 -.288 .0797 │
├────────────────────────────────────────────────────────────────────────────────┤
6. │ 6 Correa 1983 USA case-control 22 .728 .2273 │
7. │ 7 Trichopolous 1983 Greece case-control 62 .756 .0889 │
8. │ 8 Buffler 1984 USA case-control 41 -.223 .1927 │
9. │ 9 Kabat 1984 USA case-control 24 -.236 .339 │
10. │ 10 Lam 1985 Hong Kong case-control 60 .698 .0981 │
├────────────────────────────────────────────────────────────────────────────────┤
11. │ 11 Garfinkel 1985 USA case-control 134 .207 .0456 │
12. │ 12 Wu 1985 USA case-control 29 .182 .2317 │
13. │ 13 Akiba 1986 Japan case-control 94 .419 .0796 │
14. │ 14 Lee 1986 UK case-control 32 .03 .2174 │
15. │ 15 Koo 1987 Hong Kong case-control 86 .438 .077 │
├────────────────────────────────────────────────────────────────────────────────┤
16. │ 16 Pershagen 1987 Sweden case-control 70 .03 .0715 │
17. │ 17 Humble 1987 USA case-control 20 .85 .2926 │
18. │ 18 Lam 1987 Hong Kong case-control 199 .501 .0324 │
19. │ 19 Gao 1987 China case-control 246 .174 .0363 │
20. │ 20 Brownson 1987 USA case-control 19 .419 .4838 │
├────────────────────────────────────────────────────────────────────────────────┤
21. │ 21 Geng 1988 China case-control 54 .77 .1238 │
22. │ 22 Shimizu 1988 Japan case-control 90 .077 .0711 │
23. │ 23 Inoue 1988 Japan case-control 22 .936 .3982 │
24. │ 24 Kalandidi 1990 Greece case-control 90 .482 .0896 │
25. │ 25 Sobue 1990 Japan case-control 144 .058 .0337 │
├────────────────────────────────────────────────────────────────────────────────┤
26. │ 26 Wu-Williams 1990 China case-control 417 -.236 .0161 │
27. │ 27 Liu 1991 China case-control 54 -.301 .1802 │
28. │ 28 Jockel 1991 Germany case-control 23 .82 .3171 │
29. │ 29 Brownson 1992 USA case-control 431 -.03 .0125 │
30. │ 30 Stockwell 1992 USA case-control 210 .47 .1137 │
├────────────────────────────────────────────────────────────────────────────────┤
31. │ 31 Du 1993 China case-control 75 .174 .0893 │
32. │ 32 Liu 1993 China case-control 38 .507 .176 │
33. │ 33 Fontham 1994 USA case-control 651 .231 .01 │
34. │ 34 Kabat 1995 USA case-control 67 .095 .0862 │
35. │ 35 Zaridze 1995 Russia case-control 162 .507 .0399 │
├────────────────────────────────────────────────────────────────────────────────┤
36. │ 36 Sun 1996 China case-control 230 .148 .0364 │
37. │ 37 Wang 1996 China case-control 135 .104 .0664 │
└────────────────────────────────────────────────────────────────────────────────┘
. gen si = sqrt(vi)
. metan yi si, classic textsize(200) fixed
Study | ES [95% Conf. Interval] % Weight
─────────────────────+───────────────────────────────────────────────────
1 | 0.166 -0.103 0.435 7.40
2 | 0.372 0.016 0.728 4.21
3 | 0.703 -0.738 2.144 0.26
4 | 0.182 -0.165 0.529 4.44
5 | -0.288 -0.841 0.265 1.74
6 | 0.728 -0.206 1.662 0.61
7 | 0.756 0.172 1.340 1.56
8 | -0.223 -1.083 0.637 0.72
9 | -0.236 -1.377 0.905 0.41
10 | 0.698 0.084 1.312 1.42
11 | 0.207 -0.212 0.626 3.05
12 | 0.182 -0.761 1.125 0.60
13 | 0.419 -0.134 0.972 1.75
14 | 0.030 -0.884 0.944 0.64
15 | 0.438 -0.106 0.982 1.81
16 | 0.030 -0.494 0.554 1.94
17 | 0.850 -0.210 1.910 0.48
18 | 0.501 0.148 0.854 4.29
19 | 0.174 -0.199 0.547 3.83
20 | 0.419 -0.944 1.782 0.29
21 | 0.770 0.080 1.460 1.12
22 | 0.077 -0.446 0.600 1.96
23 | 0.936 -0.301 2.173 0.35
24 | 0.482 -0.105 1.069 1.55
25 | 0.058 -0.302 0.418 4.13
26 | -0.236 -0.485 0.013 8.64
27 | -0.301 -1.133 0.531 0.77
28 | 0.820 -0.284 1.924 0.44
29 | -0.030 -0.249 0.189 11.12
30 | 0.470 -0.191 1.131 1.22
31 | 0.174 -0.412 0.760 1.56
32 | 0.507 -0.315 1.329 0.79
33 | 0.231 0.035 0.427 13.90
34 | 0.095 -0.480 0.670 1.61
35 | 0.507 0.115 0.899 3.48
36 | 0.148 -0.226 0.522 3.82
37 | 0.104 -0.401 0.609 2.09
─────────────────────+───────────────────────────────────────────────────
I-V pooled ES | 0.186 0.113 0.259 100.00
─────────────────────+───────────────────────────────────────────────────
Heterogeneity chi-squared = 47.55 (d.f. = 36) p = 0.094
I-squared (variation in ES attributable to heterogeneity) = 24.3%
Test of ES=0 : z= 4.98 p = 0.000
. metafunnel yi si, xtitle(Log odds ratio) ytitle(Standard error of log OR) Note: default data input format (theta, se_theta) assumed. . graph export funnel.png, replace (file funnel.png written in PNG format)
. metabias yi si, egger
Note: data input format theta se_theta assumed.
Egger's test for small-study effects:
Regress standard normal deviate of intervention
effect estimate against its standard error
Number of studies = 37 Root MSE = 1.081
─────────────┬────────────────────────────────────────────────────────────────
Std_Eff │ Coef. Std. Err. t P>|t| [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
slope │ .0050997 .0858426 0.06 0.953 -.1691701 .1793695
bias │ .9017812 .3784859 2.38 0.023 .133414 1.670148
─────────────┴────────────────────────────────────────────────────────────────
Test of H0: no small-study effects P = 0.023
. metatrim yi si, funnel print
Note: default data input format (theta, se_theta) assumed.
Meta-analysis
| Pooled 95% CI Asymptotic No. of
Method | Est Lower Upper z_value p_value studies
───────+────────────────────────────────────────────────────
Fixed | 0.186 0.113 0.259 4.980 0.000 37
Random | 0.214 0.122 0.306 4.538 0.000
Test for heterogeneity: Q= 47.545 on 36 degrees of freedom (p= 0.094)
Moment-based estimate of between studies variance = 0.017
Trimming estimator: Linear
Meta-analysis type: Fixed-effects model
iteration | estimate Tn # to trim diff
──────────+──────────────────────────────────────
1 | 0.186 461 6 703
2 | 0.157 484 7 46
3 | 0.156 485 7 2
4 | 0.156 485 7 0
Filled
Meta-analysis
| Pooled 95% CI Asymptotic No. of
Method | Est Lower Upper z_value p_value studies
───────+────────────────────────────────────────────────────
Fixed | 0.156 0.084 0.227 4.271 0.000 44
Random | 0.173 0.076 0.269 3.515 0.000
Test for heterogeneity: Q= 61.871 on 43 degrees of freedom (p= 0.031)
Moment-based estimate of between studies variance = 0.027
| Weights Study 95% CI
Study | Fixed Random Est Lower Upper
──────────+────────────────────────────────────────
fill 1 | 2.51 2.35 -0.62 -1.86 0.61
fill 2 | 3.42 3.13 -0.54 -1.60 0.52
fill 3 | 3.15 2.91 -0.51 -1.61 0.59
fill 4 | 8.08 6.65 -0.46 -1.15 0.23
fill 5 | 11.25 8.66 -0.44 -1.03 0.14
fill 6 | 4.40 3.94 -0.42 -1.35 0.52
fill 7 | 1.85 1.76 -0.39 -1.83 1.05
study 1 | 5.55 4.84 -0.30 -1.13 0.53
study 2 | 12.55 9.42 -0.29 -0.84 0.27
study 3 | 62.11 23.47 -0.24 -0.48 0.01
study 4 | 2.95 2.74 -0.24 -1.38 0.91
study 5 | 5.19 4.56 -0.22 -1.08 0.64
study 6 | 80.00 25.63 -0.03 -0.25 0.19
study 7 | 13.99 10.20 0.03 -0.49 0.55
study 8 | 4.60 4.10 0.03 -0.88 0.94
study 9 | 29.67 16.61 0.06 -0.30 0.42
study 10 | 14.06 10.24 0.08 -0.45 0.60
study 11 | 11.60 8.87 0.09 -0.48 0.67
study 12 | 15.06 10.76 0.10 -0.40 0.61
study 13 | 27.47 15.90 0.15 -0.23 0.52
study 14 | 53.19 22.07 0.17 -0.10 0.43
study 15 | 27.55 15.92 0.17 -0.20 0.55
study 16 | 11.20 8.63 0.17 -0.41 0.76
study 17 | 31.95 17.30 0.18 -0.16 0.53
study 18 | 4.32 3.87 0.18 -0.76 1.13
study 19 | 21.93 13.87 0.21 -0.21 0.63
study 20 | 100.00 27.39 0.23 0.04 0.43
study 21 | 30.30 16.80 0.37 0.02 0.73
study 22 | 12.56 9.42 0.42 -0.13 0.97
study 23 | 2.07 1.96 0.42 -0.94 1.78
study 24 | 12.99 9.66 0.44 -0.11 0.98
study 25 | 8.80 7.13 0.47 -0.19 1.13
study 26 | 11.16 8.61 0.48 -0.10 1.07
study 27 | 30.86 16.97 0.50 0.15 0.85
study 28 | 25.06 15.06 0.51 0.12 0.90
study 29 | 5.68 4.94 0.51 -0.32 1.33
study 30 | 10.19 8.02 0.70 0.08 1.31
study 31 | 1.85 1.76 0.70 -0.74 2.14
study 32 | 4.40 3.94 0.73 -0.21 1.66
study 33 | 11.25 8.66 0.76 0.17 1.34
study 34 | 8.08 6.65 0.77 0.08 1.46
study 35 | 3.15 2.91 0.82 -0.28 1.92
study 36 | 3.42 3.13 0.85 -0.21 1.91
study 37 | 2.51 2.35 0.94 -0.30 2.17
. graph export metatrim.png, replace
(file metatrim.png written in PNG format)
. metacum yi si, fixed graph eform lcols(study year) effect(Odds ratio)
Study | ES [95% Conf. Interval]
─────────────────────+───────────────────────────────────────────────────
1 | 1.181 0.902 1.545
2 | 1.272 1.027 1.577
3 | 1.285 1.039 1.589
4 | 1.261 1.052 1.511
5 | 1.199 1.010 1.424
6 | 1.221 1.031 1.446
7 | 1.275 1.084 1.500
8 | 1.254 1.069 1.472
9 | 1.243 1.061 1.456
10 | 1.281 1.099 1.493
11 | 1.275 1.104 1.472
12 | 1.273 1.104 1.468
13 | 1.287 1.122 1.477
14 | 1.281 1.118 1.468
15 | 1.295 1.135 1.478
16 | 1.278 1.124 1.452
17 | 1.289 1.135 1.464
18 | 1.326 1.177 1.495
19 | 1.313 1.171 1.471
20 | 1.314 1.173 1.472
21 | 1.331 1.190 1.489
22 | 1.319 1.182 1.472
23 | 1.326 1.189 1.479
24 | 1.335 1.199 1.486
25 | 1.310 1.182 1.452
26 | 1.217 1.107 1.338
27 | 1.209 1.100 1.329
28 | 1.215 1.106 1.334
29 | 1.173 1.076 1.279
30 | 1.179 1.082 1.285
31 | 1.179 1.083 1.284
32 | 1.184 1.088 1.288
33 | 1.195 1.106 1.291
34 | 1.193 1.105 1.289
35 | 1.208 1.120 1.303
36 | 1.206 1.120 1.299
37 | 1.204 1.119 1.295
─────────────────────+───────────────────────────────────────────────────
. graph export cummeta.png, replace
(file cummeta.png written in PNG format)
markstat.