6.8.5. Examples
Example 1: Meta Analysis with Inverse Variance Weights
Data on the efficacy of BCG vaccine against tuberculosis is given for eleven studies in the form of 2 x 2 tables in Colditz et al. (1994), p. 699.
Open the data file META and select the first six columns as variables. In Excel Add-In Mode, if the program asks if there are case labels in column 1, select No. On the second dialogue, assign the following tasks to the selected variables.
On the next dialogue, select Risk Ratio as the summary effect size type. Click [Finish] to display results with the default options.
Meta Analysis
Results
|
|
Risk Ratio |
Lower 95% |
Upper 95% |
-2.5465 1.8762 |
|
Canada 1933 |
0.2049 |
0.0863 |
0.4864 |
—–+—— | |
|
Northern USA 1935 |
0.4109 |
0.1343 |
1.2574 |
——-+—–|- |
|
Chicago 1941 |
0.2538 |
0.1494 |
0.4310 |
—-+— | |
|
Georgia (Sch) 1947 |
1.5619 |
0.3737 |
6.5284 |
——-|–+——— |
|
Puerto Rico 1949 |
0.7122 |
0.5725 |
0.8860 |
-+–| |
|
Georgia (Com) 1950 |
0.9828 |
0.5821 |
1.6593 |
—-|— |
|
Madanapalle 1950 |
0.8045 |
0.5163 |
1.2536 |
—+-|- |
|
UK 1950 |
0.2366 |
0.1793 |
0.3121 |
–+– | |
|
South Africa 1965 |
0.6254 |
0.3926 |
0.9962 |
—+–| |
|
Haiti 1965 |
0.1977 |
0.0784 |
0.4989 |
——+—— | |
|
Madras 1968 |
1.0120 |
0.8946 |
1.1449 |
-|- |
|
Fixed Effect |
0.7305 |
0.6668 |
0.8002 |
-+ | |
|
Random Effects |
0.5080 |
0.3361 |
0.7679 |
–+— | |
Cochran’s Q
|
|
Cochran’s Q |
Degrees of Freedom |
Probability |
Tau-square |
|
Total |
125.6261 |
10 |
0.0000 |
0.3818 |
I-Square
|
|
I-square % |
Lower 95% |
Upper 95% |
|
Total |
92.0399 |
87.7435 |
94.8302 |
|
* |
|
88.2994 |
94.1658 |
* CI using inverse noncentral chi-square function.
Begg-Mazumdar Rank Correlation
|
|
Correlation Coefficient |
Z-Statistic |
1-Tail Probability |
2-Tail Probability |
|
Kendall Rank |
-0.0909 |
-0.3892 |
0.3485 |
0.6971 |
|
Kendall Rank with CC |
-0.0727 |
-0.3114 |
0.3777 |
0.7555 |
|
|
Lower 95% |
Upper 95% |
|
Kendall Rank |
-0.6551 |
0.5383 |
|
Kendall Rank with CC |
-0.6445 |
0.5512 |
Egger Regression
|
|
Coefficient |
Standard Error |
t-Statistic |
Degrees of Freedom |
|
Intercept |
-2.6889 |
1.5541 |
-1.7303 |
9 |
|
|
1-Tail Probability |
2-Tail Probability |
Lower 95% |
Upper 95% |
|
Intercept |
0.0588 |
0.1176 |
-6.2045 |
0.8266 |
Example 2: Meta Analysis with Subgroups
Continuing from the last example, go back to the Variable Selection Dialogue, add Group (S6) to the variable list. On the second dialogue, assign the task 2 x 2 Tables / Group to this variable. In Output Options Dialogue (Step 5), uncheck the Funnel and Precision plot boxes and click the [Opt] button to the left of Results. Check Group and 2-Tail Probability and uncheck Forest Diagram.
Meta Analysis
Results
Selected by Group
|
|
Group |
Risk Ratio |
Lower 95% |
Upper 95% |
2-Tail Probability |
|
Georgia (Sch) 1947 |
Central |
1.5619 |
0.3737 |
6.5284 |
0.5412 |
|
Georgia (Comm) 1950 |
Central |
0.9828 |
0.5821 |
1.6593 |
0.9483 |
|
South Africa 1965 |
Central |
0.6254 |
0.3926 |
0.9962 |
0.0482 |
|
Fixed Effect |
Central |
0.7947 |
0.5667 |
1.1144 |
0.1828 |
|
Random Effects |
Central |
0.8117 |
0.5430 |
1.2134 |
0.3090 |
|
Canada 1933 |
Northern |
0.2049 |
0.0863 |
0.4864 |
0.0003 |
|
Northern USA 1935 |
Northern |
0.4109 |
0.1343 |
1.2574 |
0.1191 |
|
Chicago 1941 |
Northern |
0.2538 |
0.1494 |
0.4310 |
0.0000 |
|
UK 1950 |
Northern |
0.2366 |
0.1793 |
0.3121 |
0.0000 |
|
Fixed Effect |
Northern |
0.2430 |
0.1928 |
0.3061 |
0.0000 |
|
Random Effects |
Northern |
0.2430 |
0.1928 |
0.3061 |
0.0000 |
|
Puerto Rico 1949 |
Tropical |
0.7122 |
0.5725 |
0.8860 |
0.0023 |
|
Madanapalle 1950 |
Tropical |
0.8045 |
0.5163 |
1.2536 |
0.3364 |
|
Haiti 1965 |
Tropical |
0.1977 |
0.0784 |
0.4989 |
0.0006 |
|
Madras 1968 |
Tropical |
1.0120 |
0.8946 |
1.1449 |
0.8494 |
|
Fixed Effect |
Tropical |
0.9045 |
0.8154 |
1.0033 |
0.0578 |
|
Random Effects |
Tropical |
0.7197 |
0.5000 |
1.0359 |
0.0767 |
|
Total Fixed Effect |
|
0.7305 |
0.6668 |
0.8002 |
0.0000 |
|
Total Random Effects |
|
0.5080 |
0.3361 |
0.7679 |
0.0013 |
Cochran’s Q
Selected by Group
|
Group |
Cochran’s Q |
Degrees of Freedom |
Probability |
Tau-square |
|
Central |
2.5072 |
2 |
0.2855 |
0.0277 |
|
Northern |
1.0593 |
3 |
0.7869 |
0.0000 |
|
Tropical |
18.4213 |
3 |
0.0004 |
0.0969 |
|
Within |
21.9878 |
8 |
0.0049 |
|
|
Between |
103.6383 |
2 |
0.0000 |
|
|
Total |
125.6261 |
10 |
0.0000 |
0.3818 |
I-Square
Selected by Group
|
Group |
I-square % |
Lower 95% |
Upper 95% |
|
Central |
20.2284 |
0.0000 |
91.7022 |
|
* |
|
0.0000 |
77.9553 |
|
Northern |
0.0000 |
0.0000 |
84.6878 |
|
* |
|
0.0000 |
67.9090 |
|
Tropical |
83.7145 |
58.8130 |
93.5607 |
|
* |
|
43.4256 |
91.9141 |
|
Total |
92.0399 |
87.7435 |
94.8302 |
|
* |
|
88.2994 |
94.1658 |
* CI using inverse noncentral chi-square function.
Example 3: Meta Analysis with Mantel-Haenszel Weights
Data on 22 randomised controlled trials of streptokinase in the prevention of death following myocardial infarction is given in the form of 2 x 2 tables in ISIS-2 (1988).
Open the data file META and select Study to Ctrl Total (L7-C11) as [Variable]s. In Excel Add-In Mode, if the program asks if there are case labels in column 1, select No. On the second dialogue, assign the following tasks to the selected variables.
Next select Risk Ratio as the summary effect size type and on the next dialogue select the Mantel-Haenszel method. Click [Finish] to display results.
Meta Analysis
Results
|
|
Risk Ratio |
Lower 95% |
Upper 95% |
-3.5062 2.9695 |
|
Fletcher 1959 |
0.2292 |
0.0300 |
1.7499 |
———+——|– |
|
Dewar 1963 |
0.5714 |
0.1962 |
1.6647 |
—–+–|– |
|
1st European 1969 |
1.3494 |
0.7429 |
2.4509 |
–|+— |
|
Heikinheimo1971 |
1.2232 |
0.6688 |
2.2371 |
–|+– |
|
Italian 1971 |
1.0105 |
0.5510 |
1.8531 |
—|– |
|
2nd European 1971 |
0.7026 |
0.5338 |
0.9247 |
-+-| |
|
2nd Frankfurt 1973 |
0.4571 |
0.2522 |
0.8282 |
–+—| |
|
1st Australian 1973 |
0.7786 |
0.4780 |
1.2683 |
—+|- |
|
NHLBI SMIT 1974 |
2.3774 |
0.6490 |
8.7086 |
–|—+—– |
|
Valere 1975 |
1.0476 |
0.4809 |
2.2821 |
—-|— |
|
Frank 1975 |
0.9636 |
0.3316 |
2.8005 |
—–|—- |
|
UK Collaborative 1976 |
0.8956 |
0.6261 |
1.2809 |
-+|- |
|
Klein 1976 |
2.5714 |
0.3394 |
19.4813 |
—–|—+——— |
|
Austrian 1977 |
0.6080 |
0.4173 |
0.8861 |
-+–| |
|
Lasierra 1977 |
0.2821 |
0.0340 |
2.3403 |
———+—–|—- |
|
N German 1977 |
1.1609 |
0.8403 |
1.6038 |
-|– |
|
Witchitz 1977 |
0.8125 |
0.2634 |
2.5062 |
—–+|—- |
|
2nd Australian 1977 |
0.8497 |
0.5369 |
1.3446 |
–+|- |
|
3rd European 1977 |
0.5096 |
0.3327 |
0.7805 |
–+–| |
|
ISAM 1986 |
0.8801 |
0.6195 |
1.2503 |
-+|- |
|
GISSI-1 1986 |
0.8274 |
0.7491 |
0.9138 |
-+| |
|
ISIS-2 1988 |
0.7690 |
0.7044 |
0.8395 |
-+| |
|
Fixed Effect (MH) |
0.7988 |
0.7546 |
0.8455 |
-+| |
|
Random Effects (MH) |
0.8112 |
0.7333 |
0.8973 |
-+| |
Cochran’s Q
|
|
Cochran’s Q (MH) |
Degrees of Freedom |
Probability |
Tau-square |
|
Total |
30.4116 |
21 |
0.0840 |
0.0840 |
I-Square
|
|
I-square (MH) % |
Lower 95% |
Upper 95% |
|
Total |
30.9474 |
0.0000 |
58.9457 |
|
* |
|
0.0000 |
58.0966 |
* CI using inverse noncentral chi-square function.
Begg-Mazumdar Rank Correlation
|
|
Correlation Coefficient |
Z-Statistic |
1-Tail Probability |
2-Tail Probability |
|
Kendall Rank |
0.6710 |
4.3707 |
0.0000 |
0.0000 |
|
Kendall Rank with CC |
0.6753 |
4.3989 |
0.0000 |
0.0000 |
|
|
Lower 95% |
Upper 95% |
|
Kendall Rank |
0.3478 |
0.8517 |
|
Kendall Rank with CC |
0.3547 |
0.8538 |
Egger Regression
|
|
Coefficient |
Standard Error |
t-Statistic |
Degrees of Freedom |
|
Intercept |
0.1670 |
0.3567 |
0.4681 |
20 |
|
|
1-Tail Probability |
2-Tail Probability |
Lower 95% |
Upper 95% |
|
Intercept |
0.3224 |
0.6448 |
-0.5771 |
0.9111 |
Example 4: Cumulative Meta Analysis
Using the data from the last example, select Odds Ratio as the summary effect size type and on the next dialogue select the inverse variance method for weights and select cumulative fixed effect (3: CUM-Fx) analysis to run. On the Output Options Dialogue select only the Meta Analysis Results and Forest Plot output options and click [Opt] situated next to results. After selecting only the Effect Size, Standard Error, Z-Statistic and 2-Tail Probability options, come back to the Output Options Dialogue and click [Finish] to display results.
Meta Analysis
Results
Cumulative, Fixed Effect
|
|
Odds Ratio |
Lower 95% |
Upper 95% |
Z-Statistic |
2-Tail Probability |
|
Fletcher 1959 |
0.1591 |
0.0146 |
1.7318 |
-1.5091 |
0.1313 |
|
Dewar 1963 |
0.3547 |
0.1048 |
1.2001 |
-1.6666 |
0.0956 |
|
1st European 1969 |
0.9889 |
0.5216 |
1.8749 |
-0.0341 |
0.9728 |
|
Heikinheimo1971 |
1.1063 |
0.6980 |
1.7534 |
0.4298 |
0.6673 |
|
Italian 1971 |
1.0760 |
0.7342 |
1.5770 |
0.3756 |
0.7072 |
|
2nd European 1971 |
0.8088 |
0.6243 |
1.0477 |
-1.6068 |
0.1081 |
|
2nd Frankfurt 1973 |
0.7417 |
0.5813 |
0.9464 |
-2.4029 |
0.0163 |
|
1st Australian 1973 |
0.7438 |
0.5953 |
0.9294 |
-2.6044 |
0.0092 |
|
NHLBI SMIT 1974 |
0.7667 |
0.6153 |
0.9554 |
-2.3663 |
0.0180 |
|
Valere 1975 |
0.7784 |
0.6279 |
0.9649 |
-2.2855 |
0.0223 |
|
Frank 1975 |
0.7835 |
0.6341 |
0.9680 |
-2.2617 |
0.0237 |
|
UK Collaborative 1976 |
0.8006 |
0.6622 |
0.9680 |
-2.2962 |
0.0217 |
|
Klein 1976 |
0.8077 |
0.6685 |
0.9759 |
-2.2128 |
0.0269 |
|
Austrian 1977 |
0.7621 |
0.6408 |
0.9063 |
-3.0721 |
0.0021 |
|
Lasierra 1977 |
0.7573 |
0.6371 |
0.9003 |
-3.1504 |
0.0016 |
|
N German 1977 |
0.8107 |
0.6908 |
0.9513 |
-2.5713 |
0.0101 |
|
Witchitz 1977 |
0.8102 |
0.6912 |
0.9498 |
-2.5958 |
0.0094 |
|
2nd Australian 1977 |
0.8100 |
0.6946 |
0.9445 |
-2.6877 |
0.0072 |
|
3rd European 1977 |
0.7709 |
0.6650 |
0.8938 |
-3.4478 |
0.0006 |
|
ISAM 1986 |
0.7838 |
0.6830 |
0.8994 |
-3.4697 |
0.0005 |
|
GISSI-1 1986 |
0.7974 |
0.7308 |
0.8700 |
-5.0925 |
0.0000 |
|
ISIS-2 1988 |
0.7741 |
0.7253 |
0.8261 |
-7.7111 |
0.0000 |
|
Fixed Effect |
0.7741 |
0.7253 |
0.8261 |
-7.7111 |
0.0000 |
