smoking: Meta-Analysis of Interventions to Promote Smoking Cessation
In mvmeta: Multivariate and Univariate Meta-Analysis and Meta-Regression
Description
Usage
Format
Details
Note
Source
Examples
Description
The dataset contains the results of 24 trials comparing four alternative interventions to promote smoking cessation. The trials have different designs, comparing two or three different interventions. The data consist of the number of successes out of the total participants, and the estimated log-odds ratio for arms B, C, and D relative to arm A, as well as the (co)variance matrix of these three estimates.
Usage
1
Format
A data frame with 24 observations on the following 19 variables:
study: study ID.
design: design of the trial, reporting the interventions being compared.
dA, dB, dC, dD: number of successes for each intervention.
nA, nB, nC, nD: number of participants for each intervention.
yB, yC, yD: estimated log-odds ratios for interventions B, C and D versus intervention A.
SBB, SBC, SBD, SCC, SCD, SDD: variances and co-variances of the estimated log-odds ratios for interventions B, C and D versus intervention A. The order corresponds to the lower triangular elements of the (co)variance matrix taken by column.
Details
Intervention A is chosen as the reference category. Trials without an arm A (trials 2 and 21-24) are augmented with an arm A with 0.01 individuals and 0.001 successes. Trials containing zero cells (trials 9 and 20) have 1 individual with 0.5 successes added to each intervention. Details on the data augmentation and estimation of (co)variances of the log-odds ratios are provided by White (2011).
Note
The data provide an example of application of network meta-analysis, also referred to as indirect mixed-treatment comparison. Additional information using examples based on these data are provided by Lu and Ades (2006), White (2011) and Higgins and colleagues (2012).
Source
Lu G, Ades AE (2006). Assessing evidence inconsistency in mixed treatment comparisons. Journal of the American Statistical Association. 101:447–459.
Higgins JPT, Jackson D, Barrett JK et al (2012). Consistency and inconsistency in network meta-analysis: concepts and models for multi-arm studies. Research Synthesis Methods. 3(2):98–110.
White IR (2011). Multivariate random-effects meta-regression. The Stata Journal. 11:255–270.
Sera F, Armstrong B, Blangiardo M, Gasparrini A (2019). An extended mixed-effects framework for meta-analysis.Statistics in Medicine. 2019;38(29):5429-5444. [Freely available here].
Examples
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### REPRODUCE THE RESULTS IN WHITE (2011)
# INSPECT THE DATA
head(smoking)
names(smoking)
# UNSTRUCTURED BETWEEN-STUDY (CO)VARIANCE
y <- as.matrix(smoking[11:13])
S <- as.matrix(smoking[14:19])
model <- mvmeta(y,S)
summary(model)
# STRUCTURED BETWEEN-STUDY (CO)VARIANCE (PROPORTIONAL)
model <- mvmeta(y,S,bscov="prop",control=list(Psifix=diag(3)+1))
summary(model)
# SEE help(mvmetaCovStruct) for additional info and examples
Example output
This is mvmeta 0.4.7. For an overview type: help('mvmeta-package').
study design dA nA dB nB dC nC dD nD yB yC
1 1 acd 9.000 140.00 NA NA 23 140 10 138 NA 1.0512930
2 2 bcd 0.001 0.01 11 78 12 85 29 170 0.39042714 0.3916717
3 3 ab 79.000 702.00 77 694 NA NA NA NA -0.01596494 NA
4 4 ab 18.000 671.00 21 535 NA NA NA NA 0.39350453 NA
5 5 ab 8.000 116.00 19 146 NA NA NA NA 0.70294160 NA
6 6 ac 75.000 731.00 NA NA 363 714 NA NA NA 2.2022893
yD SBB SBC SBD SCC SCD
1 0.1285276 NA NA NA 1.707700e-01 0.1187447
2 0.6157604 1.111217e+03 1111.111 1111.111 1.111208e+03 1111.1110840
3 NA 2.887112e-02 NA NA NA NA
4 NA 1.066515e-01 NA NA NA NA
5 NA 1.947649e-01 NA NA NA NA
6 NA NA NA NA 2.046155e-02 NA
SDD
1 0.2265572
2 1111.1525879
3 NA
4 NA
5 NA
6 NA
[1] "study" "design" "dA" "nA" "dB" "nB" "dC" "nC"
[9] "dD" "nD" "yB" "yC" "yD" "SBB" "SBC" "SBD"
[17] "SCC" "SCD" "SDD"
Call: mvmeta(formula = y ~ 1, S = S)
Multivariate random-effects meta-analysis
Dimension: 3
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
yB 0.3326 0.2162 1.5383 0.1240 -0.0912 0.7564
yC 0.6810 0.2025 3.3623 0.0008 0.2840 1.0780 ***
yD 0.8357 0.3414 2.4479 0.0144 0.1666 1.5049 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Between-study random-effects (co)variance components
Structure: General positive-definite
Std. Dev Corr
yB 0.3141 yB yC
yC 0.7498 0.9362
yD 0.7225 0.8559 0.6196
Multivariate Cochran Q-test for heterogeneity:
Q = 204.2165 (df = 28), p-value = 0.0000
I-square statistic = 86.3%
24 studies, 31 observations, 3 fixed and 6 random-effects parameters
logLik AIC BIC
-53.8269 125.6539 137.6437
Call: mvmeta(formula = y ~ 1, S = S, bscov = "prop", control = list(Psifix = diag(3) +
1))
Multivariate random-effects meta-analysis
Dimension: 3
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
yB 0.3985 0.3299 1.2078 0.2271 -0.2482 1.0451
yC 0.7024 0.1960 3.5826 0.0003 0.3181 1.0866 ***
yD 0.8659 0.3733 2.3193 0.0204 0.1342 1.5976 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Between-study random-effects (co)variance components
Structure: Proportional to fixed matrix
Std. Dev Corr
yB 0.6744 yB yC
yC 0.6744 0.5
yD 0.6744 0.5 0.5
Multivariate Cochran Q-test for heterogeneity:
Q = 204.2165 (df = 28), p-value = 0.0000
I-square statistic = 86.3%
24 studies, 31 observations, 3 fixed and 1 random-effects parameters
logLik AIC BIC
-54.9462 117.8924 123.2212
mvmeta documentation built on Dec. 10, 2019, 5:07 p.m.
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Description Usage Format Details Note Source Examples
Description
The dataset contains the results of 24 trials comparing four alternative interventions to promote smoking cessation. The trials have different designs, comparing two or three different interventions. The data consist of the number of successes out of the total participants, and the estimated log-odds ratio for arms B, C, and D relative to arm A, as well as the (co)variance matrix of these three estimates.
Usage
1 |
Format
A data frame with 24 observations on the following 19 variables:
study: study ID.design: design of the trial, reporting the interventions being compared.dA, dB, dC, dD: number of successes for each intervention.nA, nB, nC, nD: number of participants for each intervention.yB, yC, yD: estimated log-odds ratios for interventions B, C and D versus intervention A.SBB, SBC, SBD, SCC, SCD, SDD: variances and co-variances of the estimated log-odds ratios for interventions B, C and D versus intervention A. The order corresponds to the lower triangular elements of the (co)variance matrix taken by column.
Details
Intervention A is chosen as the reference category. Trials without an arm A (trials 2 and 21-24) are augmented with an arm A with 0.01 individuals and 0.001 successes. Trials containing zero cells (trials 9 and 20) have 1 individual with 0.5 successes added to each intervention. Details on the data augmentation and estimation of (co)variances of the log-odds ratios are provided by White (2011).
Note
The data provide an example of application of network meta-analysis, also referred to as indirect mixed-treatment comparison. Additional information using examples based on these data are provided by Lu and Ades (2006), White (2011) and Higgins and colleagues (2012).
Source
Lu G, Ades AE (2006). Assessing evidence inconsistency in mixed treatment comparisons. Journal of the American Statistical Association. 101:447–459.
Higgins JPT, Jackson D, Barrett JK et al (2012). Consistency and inconsistency in network meta-analysis: concepts and models for multi-arm studies. Research Synthesis Methods. 3(2):98–110.
White IR (2011). Multivariate random-effects meta-regression. The Stata Journal. 11:255–270.
Sera F, Armstrong B, Blangiardo M, Gasparrini A (2019). An extended mixed-effects framework for meta-analysis.Statistics in Medicine. 2019;38(29):5429-5444. [Freely available here].
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ### REPRODUCE THE RESULTS IN WHITE (2011)
# INSPECT THE DATA
head(smoking)
names(smoking)
# UNSTRUCTURED BETWEEN-STUDY (CO)VARIANCE
y <- as.matrix(smoking[11:13])
S <- as.matrix(smoking[14:19])
model <- mvmeta(y,S)
summary(model)
# STRUCTURED BETWEEN-STUDY (CO)VARIANCE (PROPORTIONAL)
model <- mvmeta(y,S,bscov="prop",control=list(Psifix=diag(3)+1))
summary(model)
# SEE help(mvmetaCovStruct) for additional info and examples
|
Example output
This is mvmeta 0.4.7. For an overview type: help('mvmeta-package').
study design dA nA dB nB dC nC dD nD yB yC
1 1 acd 9.000 140.00 NA NA 23 140 10 138 NA 1.0512930
2 2 bcd 0.001 0.01 11 78 12 85 29 170 0.39042714 0.3916717
3 3 ab 79.000 702.00 77 694 NA NA NA NA -0.01596494 NA
4 4 ab 18.000 671.00 21 535 NA NA NA NA 0.39350453 NA
5 5 ab 8.000 116.00 19 146 NA NA NA NA 0.70294160 NA
6 6 ac 75.000 731.00 NA NA 363 714 NA NA NA 2.2022893
yD SBB SBC SBD SCC SCD
1 0.1285276 NA NA NA 1.707700e-01 0.1187447
2 0.6157604 1.111217e+03 1111.111 1111.111 1.111208e+03 1111.1110840
3 NA 2.887112e-02 NA NA NA NA
4 NA 1.066515e-01 NA NA NA NA
5 NA 1.947649e-01 NA NA NA NA
6 NA NA NA NA 2.046155e-02 NA
SDD
1 0.2265572
2 1111.1525879
3 NA
4 NA
5 NA
6 NA
[1] "study" "design" "dA" "nA" "dB" "nB" "dC" "nC"
[9] "dD" "nD" "yB" "yC" "yD" "SBB" "SBC" "SBD"
[17] "SCC" "SCD" "SDD"
Call: mvmeta(formula = y ~ 1, S = S)
Multivariate random-effects meta-analysis
Dimension: 3
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
yB 0.3326 0.2162 1.5383 0.1240 -0.0912 0.7564
yC 0.6810 0.2025 3.3623 0.0008 0.2840 1.0780 ***
yD 0.8357 0.3414 2.4479 0.0144 0.1666 1.5049 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Between-study random-effects (co)variance components
Structure: General positive-definite
Std. Dev Corr
yB 0.3141 yB yC
yC 0.7498 0.9362
yD 0.7225 0.8559 0.6196
Multivariate Cochran Q-test for heterogeneity:
Q = 204.2165 (df = 28), p-value = 0.0000
I-square statistic = 86.3%
24 studies, 31 observations, 3 fixed and 6 random-effects parameters
logLik AIC BIC
-53.8269 125.6539 137.6437
Call: mvmeta(formula = y ~ 1, S = S, bscov = "prop", control = list(Psifix = diag(3) +
1))
Multivariate random-effects meta-analysis
Dimension: 3
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
yB 0.3985 0.3299 1.2078 0.2271 -0.2482 1.0451
yC 0.7024 0.1960 3.5826 0.0003 0.3181 1.0866 ***
yD 0.8659 0.3733 2.3193 0.0204 0.1342 1.5976 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Between-study random-effects (co)variance components
Structure: Proportional to fixed matrix
Std. Dev Corr
yB 0.6744 yB yC
yC 0.6744 0.5
yD 0.6744 0.5 0.5
Multivariate Cochran Q-test for heterogeneity:
Q = 204.2165 (df = 28), p-value = 0.0000
I-square statistic = 86.3%
24 studies, 31 observations, 3 fixed and 1 random-effects parameters
logLik AIC BIC
-54.9462 117.8924 123.2212
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