mvmeta.mm: Method of Moments Estimator for mvmeta Models
In mvmeta: Multivariate and Univariate Meta-Analysis and Meta-Regression
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
See Also
Examples
Description
This function implements a method of moments estimator for multivariate and univariate random-effects meta-analysis and meta-regression. It is meant to be used internally and not directly run by the users.
Usage
1
Arguments
Assuming a meta-analysis or meta-regression based on m studies, k outcomes and p predictors:
Xlist
a m-dimensional list of study-specific design matrices for the fixed-effects part of the model. Rows corresponding to missing outcomes have been excluded.
ylist
a m-dimensional list of study-specific vectors of estimated outcomes. Entries corresponding to missing outcomes have been excluded.
Slist
a m-dimensional list of within-study (co)variance matrices of estimated outcomes. Rows and columns corresponding to missing outcomes have been excluded.
nalist
a m-dimensional list of k-dimensional study-specific logical vectors, identifying missing outcomes.
k, m, p, nall
numeric scalars: number of outcomes, number of studies included in estimation (equal to the length of lists above), number of predictors (including the intercept), number of observations (excluding missing).
control
list of parameters for controlling the fitting process, usually internally set to default values by mvmeta.control.
...
further arguments passed to or from other methods. Currently not used.
Details
The estimation involves kp fixed-effects coefficients and k(k+1)/2 random-effects parameters, corresponding to the lower triangular entries of the between-study (co)variance matrix.
The approach implemented here represents the multivariate extension of the traditional estimator proposed by DerSimonian and Laird (1986), and simplifies to the standard method in the univariate case. This non-iterative routine forces the positive semi-definiteness of the estimated between-study (co)variance matrix by setting its negative eigenvalues to zero.
The specific method of moment estimator used here is described in Jackson and collaborators (2013), and represents a generalization of that developed by Chen and collaborators (2012). However, this general version is computationally more intensive, and may turn out to be slow when applied to meta-analysis of a relatively high number of studies. An alternative and computationally faster method of moment estimator was previously proposed by Jackson and collaborators (2010), although it is not invariant to reparameterization. This latter estimator is not implemented yet in mvmeta. See references below.
Value
This function returns an intermediate list object, whose components are then processed by mvmeta.fit. Other components are added later through mvmeta to finalize an object of class "mvmeta".
Note
As stated earlier, this function is called internally by mvmeta.fit, and is not meant to be used directly. In particular, its code does not contain any check on the arguments provided, which are expected in specific formats. The function is however exported in the namespace and documented for completeness.
The arguments above are prepared by mvmeta.fit from its arguments X, y and S. The list structure, although requiring more elaborate coding, is computationally more efficient, as it avoids the specification of sparse block-diagonal matrices, especially for meta-analysis involving a large number of studies.
Some parameters of the fitting procedures are determined by the control argument, with default set by mvmeta.control. No missing values are accepted in the fitting functions. See details on missing values.
Author(s)
Antonio Gasparrini, antonio.gasparrini@lshtm.ac.uk
References
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].
Gasparrini A, Armstrong B, Kenward MG (2012). Multivariate meta-analysis for non-linear and other multi-parameter associations. Statistics in Medicine. 31(29):3821–3839. [Freely available here].
Jackson D, White IR, Riley RD (2013). A matrix based method of moments for fitting the multivariate random effects model for meta-analysis and meta-regression. Biometrical Journal. 55(2):231-245.
Chen H, Manning AK, Dupuis J (2012). A method of moments estimator for random effect multivariate meta-analysis. Biometrics. 68(4):1278-1284.
Jackson D, White IR, Thompson SG (2010). Extending DerSimonian and Laird's methodology to perform multivariate random effects meta-analyses. Statistics in Medicine. 29(12):1282–1297.
DerSimonian R, Laird N (1986). Meta-analysis in clinical trials. Controlled Clinical Trials. 7(3):177-188.
See Also
See mvmeta for the general usage of the functions. See mvmeta.control to determine specific parameters of the fitting procedures. Use the triple colon operator (':::') to access the code of the internal functions, such as fbtr. See mvmeta-package for an overview of the package and modelling framework.
Examples
1
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3
4
5
6
7
8
9
10
11
12
13
# MM ESTIMATOR: UNIVARIATE MODEL
model <- mvmeta(PD~pubyear,S=berkey98[,5],data=berkey98,method="mm")
summary(model)
# MM ESTIMATOR: REPRODUCE THE RESULTS IN CHEN ET AL. (2012)
S <- as.matrix(hsls[5:10])
model <- mvmeta(cbind(b1,b2,b3),S,data=hsls,method="mm")
summary(model)
# MM ESTIMATOR: REPRODUCE THE RESULTS IN JACKSON ET AL. (2013)
S <- inputcov(hyp[c("sbp_se","dbp_se")],cor=hyp$rho)
model <- mvmeta(cbind(sbp,dbp),S=S,data=hyp,method="mm")
summary(model)
Example output
This is mvmeta 0.4.7. For an overview type: help('mvmeta-package').
Call: mvmeta(formula = PD ~ pubyear, S = berkey98[, 5], data = berkey98,
method = "mm")
Univariate random-effects meta-regression
Dimension: 1
Estimation method: Method of moments
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) -7.8136 40.9068 -0.1910 0.8485 -87.9895 72.3622
pubyear 0.0041 0.0206 0.1999 0.8416 -0.0363 0.0445
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Between-study random-effects (co)variance components
Std. Dev
0.1329
Univariate Cochran Q-test for residual heterogeneity:
Q = 11.8031 (df = 3), p-value = 0.0081
I-square statistic = 74.6%
5 studies, 5 observations, 2 fixed and 1 random-effects parameters
Call: mvmeta(formula = cbind(b1, b2, b3) ~ 1, S = S, data = hsls, method = "mm")
Multivariate random-effects meta-analysis
Dimension: 3
Estimation method: Method of moments
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
b1 -0.0604 0.2684 -0.2250 0.8220 -0.5864 0.4656
b2 6.1821 0.2887 21.4109 0.0000 5.6162 6.7480 ***
b3 -0.7009 0.1894 -3.6996 0.0002 -1.0722 -0.3296 ***
---
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
b1 0.5296 b1 b2
b2 0.3201 -0.55870
b3 0.2308 0.02538 0.81492
(Note: Truncated estimate - 1 negative eigenvalues set to 0)
Multivariate Cochran Q-test for heterogeneity:
Q = 54.6278 (df = 21), p-value = 0.0001
I-square statistic = 61.6%
8 studies, 24 observations, 3 fixed and 1 random-effects parameters
Call: mvmeta(formula = cbind(sbp, dbp) ~ 1, S = S, data = hyp, method = "mm")
Multivariate random-effects meta-analysis
Dimension: 2
Estimation method: Method of moments
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
sbp -9.1702 0.5541 -16.5494 0.0000 -10.2563 -8.0842 ***
dbp -4.3101 0.3625 -11.8885 0.0000 -5.0207 -3.5995 ***
---
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
sbp 1.4265 sbp
dbp 1.0242 0.1377
Multivariate Cochran Q-test for heterogeneity:
Q = 1543.4006 (df = 18), p-value = 0.0000
I-square statistic = 98.8%
10 studies, 20 observations, 2 fixed and 1 random-effects parameters
mvmeta documentation built on Dec. 10, 2019, 5:07 p.m.
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Description Usage Arguments Details Value Note Author(s) References See Also Examples
Description
This function implements a method of moments estimator for multivariate and univariate random-effects meta-analysis and meta-regression. It is meant to be used internally and not directly run by the users.
Usage
1 |
Arguments
Assuming a meta-analysis or meta-regression based on m studies, k outcomes and p predictors:
Xlist |
a m-dimensional list of study-specific design matrices for the fixed-effects part of the model. Rows corresponding to missing outcomes have been excluded. |
ylist |
a m-dimensional list of study-specific vectors of estimated outcomes. Entries corresponding to missing outcomes have been excluded. |
Slist |
a m-dimensional list of within-study (co)variance matrices of estimated outcomes. Rows and columns corresponding to missing outcomes have been excluded. |
nalist |
a m-dimensional list of k-dimensional study-specific logical vectors, identifying missing outcomes. |
k, m, p, nall |
numeric scalars: number of outcomes, number of studies included in estimation (equal to the length of lists above), number of predictors (including the intercept), number of observations (excluding missing). |
control |
list of parameters for controlling the fitting process, usually internally set to default values by |
... |
further arguments passed to or from other methods. Currently not used. |
Details
The estimation involves kp fixed-effects coefficients and k(k+1)/2 random-effects parameters, corresponding to the lower triangular entries of the between-study (co)variance matrix.
The approach implemented here represents the multivariate extension of the traditional estimator proposed by DerSimonian and Laird (1986), and simplifies to the standard method in the univariate case. This non-iterative routine forces the positive semi-definiteness of the estimated between-study (co)variance matrix by setting its negative eigenvalues to zero.
The specific method of moment estimator used here is described in Jackson and collaborators (2013), and represents a generalization of that developed by Chen and collaborators (2012). However, this general version is computationally more intensive, and may turn out to be slow when applied to meta-analysis of a relatively high number of studies. An alternative and computationally faster method of moment estimator was previously proposed by Jackson and collaborators (2010), although it is not invariant to reparameterization. This latter estimator is not implemented yet in mvmeta. See references below.
Value
This function returns an intermediate list object, whose components are then processed by mvmeta.fit. Other components are added later through mvmeta to finalize an object of class "mvmeta".
Note
As stated earlier, this function is called internally by mvmeta.fit, and is not meant to be used directly. In particular, its code does not contain any check on the arguments provided, which are expected in specific formats. The function is however exported in the namespace and documented for completeness.
The arguments above are prepared by mvmeta.fit from its arguments X, y and S. The list structure, although requiring more elaborate coding, is computationally more efficient, as it avoids the specification of sparse block-diagonal matrices, especially for meta-analysis involving a large number of studies.
Some parameters of the fitting procedures are determined by the control argument, with default set by mvmeta.control. No missing values are accepted in the fitting functions. See details on missing values.
Author(s)
Antonio Gasparrini, antonio.gasparrini@lshtm.ac.uk
References
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].
Gasparrini A, Armstrong B, Kenward MG (2012). Multivariate meta-analysis for non-linear and other multi-parameter associations. Statistics in Medicine. 31(29):3821–3839. [Freely available here].
Jackson D, White IR, Riley RD (2013). A matrix based method of moments for fitting the multivariate random effects model for meta-analysis and meta-regression. Biometrical Journal. 55(2):231-245.
Chen H, Manning AK, Dupuis J (2012). A method of moments estimator for random effect multivariate meta-analysis. Biometrics. 68(4):1278-1284.
Jackson D, White IR, Thompson SG (2010). Extending DerSimonian and Laird's methodology to perform multivariate random effects meta-analyses. Statistics in Medicine. 29(12):1282–1297.
DerSimonian R, Laird N (1986). Meta-analysis in clinical trials. Controlled Clinical Trials. 7(3):177-188.
See Also
See mvmeta for the general usage of the functions. See mvmeta.control to determine specific parameters of the fitting procedures. Use the triple colon operator (':::') to access the code of the internal functions, such as fbtr. See mvmeta-package for an overview of the package and modelling framework.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 | # MM ESTIMATOR: UNIVARIATE MODEL
model <- mvmeta(PD~pubyear,S=berkey98[,5],data=berkey98,method="mm")
summary(model)
# MM ESTIMATOR: REPRODUCE THE RESULTS IN CHEN ET AL. (2012)
S <- as.matrix(hsls[5:10])
model <- mvmeta(cbind(b1,b2,b3),S,data=hsls,method="mm")
summary(model)
# MM ESTIMATOR: REPRODUCE THE RESULTS IN JACKSON ET AL. (2013)
S <- inputcov(hyp[c("sbp_se","dbp_se")],cor=hyp$rho)
model <- mvmeta(cbind(sbp,dbp),S=S,data=hyp,method="mm")
summary(model)
|
Example output
This is mvmeta 0.4.7. For an overview type: help('mvmeta-package').
Call: mvmeta(formula = PD ~ pubyear, S = berkey98[, 5], data = berkey98,
method = "mm")
Univariate random-effects meta-regression
Dimension: 1
Estimation method: Method of moments
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) -7.8136 40.9068 -0.1910 0.8485 -87.9895 72.3622
pubyear 0.0041 0.0206 0.1999 0.8416 -0.0363 0.0445
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Between-study random-effects (co)variance components
Std. Dev
0.1329
Univariate Cochran Q-test for residual heterogeneity:
Q = 11.8031 (df = 3), p-value = 0.0081
I-square statistic = 74.6%
5 studies, 5 observations, 2 fixed and 1 random-effects parameters
Call: mvmeta(formula = cbind(b1, b2, b3) ~ 1, S = S, data = hsls, method = "mm")
Multivariate random-effects meta-analysis
Dimension: 3
Estimation method: Method of moments
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
b1 -0.0604 0.2684 -0.2250 0.8220 -0.5864 0.4656
b2 6.1821 0.2887 21.4109 0.0000 5.6162 6.7480 ***
b3 -0.7009 0.1894 -3.6996 0.0002 -1.0722 -0.3296 ***
---
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
b1 0.5296 b1 b2
b2 0.3201 -0.55870
b3 0.2308 0.02538 0.81492
(Note: Truncated estimate - 1 negative eigenvalues set to 0)
Multivariate Cochran Q-test for heterogeneity:
Q = 54.6278 (df = 21), p-value = 0.0001
I-square statistic = 61.6%
8 studies, 24 observations, 3 fixed and 1 random-effects parameters
Call: mvmeta(formula = cbind(sbp, dbp) ~ 1, S = S, data = hyp, method = "mm")
Multivariate random-effects meta-analysis
Dimension: 2
Estimation method: Method of moments
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
sbp -9.1702 0.5541 -16.5494 0.0000 -10.2563 -8.0842 ***
dbp -4.3101 0.3625 -11.8885 0.0000 -5.0207 -3.5995 ***
---
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
sbp 1.4265 sbp
dbp 1.0242 0.1377
Multivariate Cochran Q-test for heterogeneity:
Q = 1543.4006 (df = 18), p-value = 0.0000
I-square statistic = 98.8%
10 studies, 20 observations, 2 fixed and 1 random-effects parameters
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