mixmeta: Fitting Standard and Extended Meta-Analysis and...
In mixmeta: An Extended Mixed-Effects Framework for Meta-Analysis
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
The function mixmeta performs various meta-analytical models under a common mixed-effects framework, including standard univariate fixed and random-effects meta-analysis and meta-regression, and non-standard extensions such as multivariate, multilevel, longitudinal, and dose-response models. The function mixmeta.fit is a wrapper for actual fitting functions based on different estimation methods, usually called internally. See mixmeta-package for an overview.
Usage
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Arguments
Assuming a meta-analysis or meta-regression based on n units aggregated within m (outer-level) groups, k outcomes, p fixed-effects predictors, and q random-effects predictors:
formula
an object of class "formula" (or one that can be coerced to that class) offering a symbolic description of the linear predictor for the fixed-effects part of the model. Alternatively, for meta-analysis with no fixed-effects predictors, a single vector (for univariate models) or matrix-type object (for multivariate models). Terms in formula must be vector or matrix-type objects, optionally provided in the data argument below. See mixmetaFormula.
S
series of within-unit variances (or (co)variance matrices for multivariate models) of the estimated outcome(s). For univariate models, this is usually a n-dimensional vector. For multivariate models, it can be provided as: a m-dimensional list of k x k matrices; a tri-dimensional k x k x n array; a matrix or data frame with n rows and k(k+1)/2 or k columns, depending on the availability of the within-unit correlations. mixmeta.fit accepts only the last option. Optionally, for more complex error structures, this argument can be omitted and passed through addSlist in control. See Details below.
data
an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in formula and random. If not found in data, the variables are taken from environment(formula), typically the environment from which mixmeta is called.
random
a one-sided formula (or a list of formulae for multilevel models) offering a symbolic description of the linear predictor(s) and grouping structure for the random-effects part of the model. The usual form is ~ z1 + ... + zq | g, with the grouping factor separated from the linear predictor by the symbol '|'. Multiple levels with the same linear predictor can be defined by separating multiple grouping factors using the symbol '/'. Alternatively, in a list form the grouping factors can also be provided as list names. In both cases, the levels are considered nested (from outer to inner following the order). See mixmetaFormula and Details below.
method
estimation method: "fixed" for fixed-effects models, "ml" or "reml" for random-effects models fitted through (restricted) maximum likelihood, "mm" for random-effects models fitted through method of moments, and "vc" for random-effects models fitted through variance components. See Details below. If "model.frame", the model frame is returned, as in lm or glm.
bscov
a character vector defining the structure of the random-effects (co)variance matrices. Default to "unstr" (unstructured). Names corresponding to grouping factors (see random above) can be used to refer to specific random-effects levels for non-default values. If unnamed, the values can be recycled. Among various (co)variance structures, the user can select "diag" (diagonal), "cs" (compound symmetry), "hcs" (heterogeneous compound symmetry), "ar1" (autoregressive of first order), or "fixed" (fixed). See also Details.
offset
optionally, a n-dimensional numeric vector used to specify an a priori known component in the linear predictor. One or more offset terms can be included in the formula instead or as well. See model.offset.
subset
an optional vector specifying a subset of observations to be used in the fitting process.
contrasts
an optional list. See the contrasts.arg of model.matrix.
na.action
a function which indicates what should happen when the data contain NAs. Default to na.action setting of options, usually na.omit. na.exclude can be useful. See details on missing values in mixmeta.
model
a logical value indicating whether the model frame should be included as a component of the returned value. See the model.frame method function.
control
list of parameters for controlling the fitting process. These are passed to mixmeta.control to replace otherwise selected default values.
X
a n x p design matrix containing the p fixed-effects predictors, appropriately ordered by groups. Usually produced internally by mixmeta from formula above.
Z
a n x q design matrix (or a list of design matrices for multilevel models) containing the q random-effects predictors, appropriately ordered by groups. Usually produced internally by mixmeta from random above.
y
a n-dimensional vector (for univariate models) or m x k matrix (for multivariate models) of outcomes, appropriately ordered by groups. Usually produced internally by mixmeta from formula above.
groups
matrix with n rows, with each column identifying the groups for each level of random-effects, appropriately ordered. Usually produced internally by mixmeta from random above.
Details
The function mixmeta resembles standard regression functions in R. See lme in particular, or lm or glm, for information on most of the arguments. Internally, this function assembles the data components, defines the (potentially multiple) grouping levels and re-order the data accordingly, and then pass them to mixmeta.fit. This is a wrapper for actual fitting functions that are automatically selected. Functions other than mixmeta are not expected to be called directly for model fitting.
Fixed or random-effects models for meta-analysis are simply defined using y ~ 1 in formula, where y is a response vector optionally stored in data. In meta-regression models, other terms are added in the right-hand side of the formula as y ~ x1 + ... + xp, defining the linear meta-predictor. Factors, variable transformations and interactions are allowed, following the usual formula specification (see mixmetaFormula).
In this standard usage, each of the n rows is assumed to represent a single estimate of an outcome from a set of independent studies. In random-effects models, the grouping structure is automatically derived by assigning a group to each row of data (with m=n). Extensions to multivariate models (k>1) are straightforward, and only require using a matrix in the left-hand side, where each of the k columns represents a different outcome, or the form cbind(y1, ..., yk) ~ 1. See mixmetaFormula.
Non-standard random-effects models can be specified through the optional argument random. This is commonly represented by a one-sided formula, whose basic random-intercept form is ~ 1 | g, where g is a grouping factor. A more complex linear meta-predictor for the random-effects part can be also specified by ~ z1 + ... + zq | g. The argument random also accepts a list of one-sided formulae referring to multiple random-effects levels (see mixmetaFormula). The use of random extends the standard meta-analytical setting by relaxing the assumption of independence between units, allowing multiple estimates from the same group (with m<n) and multiple nested grouping levels. This provides the possibility to fit longitudinal, multilevel, and dose-response meta-analysis, among other extensions. See the examples below.
The argument bscov allows the definition of specific structures for the random-effects (co)variance matrices corresponding the each level. The default unstructured form requires kq(kq+1)/2 parameters for a single-level meta-analysis. The choice of other structures reduces the number of parameters, although requiring stronger assumptions. More information and complete list of options is available at a specific help page (see mixmetaCovStruct).
The within-unit (co)variances are provided through the argument S, usually as a matrix. If the correlations are available, each of the m row represents the k(k+1)/2 vectorized entries of the lower triangle of the related (co)variance matrix, taken by column (see xpndMat). If correlations are not available, each row represents the k variances, and the correlations are inputted internally through the argument Scor of the control list (see inputcov). For more complex error structures that span multiple units, the argument S can be omitted and passed through addSlist in control, although requiring the observations to be re-ordered accordingly to groups (see mixmeta.control).
Different estimator are available in the package mixmeta and chosen through the argument method, with related fitting functions called internally. In the current version, the options are:
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method="fixed": Fixed-effects estimator
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method="ml": Maximum likelihood (ML) estimator
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method="reml": Restricted maximum likelihood (REML) estimator
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method="mm": Method of moments estimator
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method="vc": Variance components estimator
Note that non-standard random-effects models and the use of structured (co)variance matrices are only available for "ml" and "reml" methods. See their help pages for further details on the estimation procedures, following the links above.
Missing values are allowed in both sides of formula. In the case of missing predictors (right-hand side of formula), the related unit is entirely excluded from estimation. In contrast, a unit still contributes to estimation if at least outcome is non-missing. This behaviour is different from standard regression functions such as lm or glm. Before the call to mixmeta.fit, units matching such stricter missing definition are removed from the the model frame. The missing pattern in S must be consistent with that in y. See further details on handling missing values in mixmeta.
The fitting procedure can be controlled through the additional terms specified in control, which are passed to the function mixmeta.control.
Value
The mixmeta function typically returns a list object of class "mixmeta" representing the meta-analytical model fit, as described in mixmetaObject. When method="data.frame", the model is not fitted and the model frame is returned, namely a data frame with special attributes (see the default method model.frame) and, in this case, the additional class "data.frame.mixmeta".
The wrapper function mixmeta.fit is usually called internally in mixmeta, and returns an intermediate list object with some of the components expected in the "mixmeta" class.
Several method functions for regression objects are available, either default or specifically written for the "mixmeta" class. See mixmetaObject for a complete list.
Author(s)
Antonio Gasparrini <antonio.gasparrini@lshtm.ac.uk> and Francesco Sera <francesco.sera@lshtm.ac.uk>
References
Sera F, 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].
See Also
See additional info on the estimation procedures at the related page of the fitting functions See mixmetaFormula for the use of formulae to define the fixed and random parts of the model. See alternative (co)variance structures for likelihood-based estimation methods. See handling of missing values in mixmeta. See lme, lm or glm for standard regression functions. See mixmeta-package for an overview of this modelling framework.
Examples
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### STANDARD MODELS
# RANDOM-EFFECTS META-ANALYSIS, ESTIMATED WITH REML
model <- mixmeta(logor, logorvar, data=bcg)
summary(model)
# RANDOM-EFFECTS META-REGRESSION, ESTIMATED WITH ML
model <- mixmeta(logor~ablat, logorvar, data=bcg, method="ml")
summary(model)
### MAIN METHOD FUNCTIONS
# COEFFICIENTS AND (CO)VARIANCE MATRIX
coef(model)
vcov(model)
# RESIDUALS AND FITTED VALUES
residuals(model)
fitted(model)
# MODEL FRAME AND MODEL MATRIX
model.frame(model)
model.matrix(model)
# LOG-LIKELIHOOD AND AIC VALUE
logLik(model)
AIC(model)
# COCHRAN Q TEST FOR RESIDUAL HETEROGENEITY
qtest(model)
### PREDICTIONS
# PREDICTED EFFECTS
predict(model)
predict(model, se=TRUE)
predict(model, newdata=data.frame(ablat=2:5*10), ci=TRUE)
# BEST LINEAR UNBIASED PREDICTION
blup(model)
blup(model, pi=TRUE)
# SEE help(predict.mixmeta) AND help(BLUP.mixmeta) FOR MORE INFO
### MULTIVARIATE MODELS
### BIVARIATE MODELS
model <- mixmeta(cbind(PD,AL) ~ pubyear, S=berkey98[5:7], data=berkey98)
summary(model)
residuals(model)
### MULTIVARIATE META-ANALYSIS WITH MORE THAN 2 OUTCOMES
y <- as.matrix(fibrinogen[2:5])
S <- as.matrix(fibrinogen[6:15])
model <- mixmeta(y, S)
summary(model)
predict(model, se=TRUE)
predict(model, se=TRUE, aggregate="outcome")
### OTHER EXTENSIONS
# MULTILEVEL META-ANALYSIS
model <- mixmeta(effect, var, random= ~ 1|district/study, data=school)
summary(model)
# SEE help(school) AND help(thrombolytic) FOR MORE EXAMPLES
# DOSE-RESPONSE META-ANALYSIS (SIMPLIFIED)
model <- mixmeta(logrr ~ 0 + dose, S=se^2, random= ~ 0 + dose|id, data=alcohol,
subset=!is.na(se))
summary(model)
# SEE help(alcohol) FOR MORE EXAMPLES
# LONGITUDINAL META-ANALYSIS
model <- mixmeta(logOR~time, S=logORvar, random=~I(time-15)|study, data=gliomas)
summary(model)
# SEE help(gliomas) AND help(dbs) FOR MORE EXAMPLES
### FIXED-EFFECTS MODELS AND ALTERNATIVE ESTIMATORS
# FIXED-EFFECTS MODEL
model <- mixmeta(sbp~ish, S=sbp_se^2, data=hyp, method="fixed")
summary(model)
# METHOD OF MOMENTS
S <- as.matrix(hsls[5:10])
model <- mixmeta(cbind(b1,b2,b3), S, data=hsls, method="mm")
summary(model)
# VARIANCE COMPONENTS ESTIMATOR
model <- mixmeta(cbind(PD,AL)~pubyear, S=berkey98[5:7], data=berkey98,
method="vc")
summary(model)
### IN THE PRESENCE OF MISSING VALUES
# RUN THE MODEL
y <- as.matrix(smoking[11:13])
S <- as.matrix(smoking[14:19])
model <- mixmeta(y, S)
summary(model)
model.frame(model)
# SEE help(na.omit.data.frame.mixmeta) FOR MORE EXAMPLES
### WHEN WITHIN-STUDY COVIARIANCES ARE NOT AVAILABLE AND/OR NEED TO BE INPUTTED
# GENERATE S
(S <- inputcov(hyp[c("sbp_se","dbp_se")], cor=hyp$rho))
# RUN THE MODEL
model <- mixmeta(cbind(sbp,dbp), S=S, data=hyp)
# INPUTTING THE CORRELATION DIRECTLY IN THE MODEL
model <- mixmeta(cbind(y1,y2), cbind(V1,V2), data=p53, control=list(Scor=0.95))
summary(model)
# SEE help(hyp) AND help(p53) FOR MORE EXAMPLES
### STRUCTURING THE BETWEEN-STUDY (CO)VARIANCE
# DIAGONAL
S <- as.matrix(hsls[5:10])
model <- mixmeta(cbind(b1,b2,b3), S, data=hsls, bscov="diag")
summary(model)
model$Psi
# COMPOUND SYMMETRY
model <- mixmeta(cbind(b1,b2,b3), S, data=hsls, bscov="cs")
summary(model)
model$Psi
# SEE help(mixmetaCovStruct) FOR DETAILS AND ADDITIONAL EXAMPLES
### USE OF THE CONTROL LIST
# PRINT THE ITERATIONS AND CHANGE THE DEFAULT FOR STARTING VALUES
y <- as.matrix(smoking[11:13])
S <- as.matrix(smoking[14:19])
model <- mixmeta(y, S, control=list(showiter=TRUE, igls.inititer=20))
# SEE help(mixmeta.control) FOR FURTHER DETAILS
Example output
This is mixmeta 1.1.0. For an overview type: help('mixmeta-package').
Call: mixmeta(formula = logor, S = logorvar, data = bcg)
Univariate random-effects meta-analysis
Dimension: 1
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) -0.7452 0.1860 -4.0057 0.0001 -1.1098 -0.3806 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: General positive-definite
Std. Dev
0.5812
Univariate Cochran Q-test for heterogeneity:
Q = 163.1649 (df = 12), p-value = 0.0000
I-square statistic = 92.6%
13 units, 1 outcome, 13 observations, 1 fixed and 1 random-effects parameters
logLik AIC BIC
-12.5757 29.1513 30.1211
Call: mixmeta(formula = logor ~ ablat, S = logorvar, data = bcg, method = "ml")
Univariate random-effects meta-regression
Dimension: 1
Estimation method: ML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) 0.3711 0.1060 3.5016 0.0005 0.1634 0.5788 ***
ablat -0.0327 0.0034 -9.7054 0.0000 -0.0393 -0.0261 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: General positive-definite
Std. Dev
0.0632
Univariate Cochran Q-test for residual heterogeneity:
Q = 25.0954 (df = 11), p-value = 0.0088
I-square statistic = 56.2%
13 units, 1 outcome, 13 observations, 2 fixed and 1 random-effects parameters
logLik AIC BIC
-6.9634 19.9269 21.6217
(Intercept) ablat
0.37106929 -0.03272247
(Intercept) ablat
(Intercept) 0.0112301825 -0.0003119412
ablat -0.0003119412 0.0000113675
1 2 3 4 5 6
0.13002547 -0.23752393 -0.38301972 -0.12594416 -0.16481820 0.11059758
7 8 9 10 11 12
-1.38311810 0.06634348 0.04069150 -0.39793555 -0.12291438 1.15540705
13
0.69143050
1 2 3 4 5 6
-1.06871959 -1.42866681 -1.00327464 -1.33049939 -0.05432288 -1.06871959
7 8 9 10 11 12
-0.25065773 -0.05432288 -0.51243753 -1.00327464 -0.21793526 -0.70877237
13
-0.70877237
logor ablat
1 -0.93869412 44
2 -1.66619074 55
3 -1.38629436 42
4 -1.45644355 52
5 -0.21914108 13
6 -0.95812201 44
7 -1.63377583 19
8 0.01202060 13
9 -0.47174603 27
10 -1.40121019 42
11 -0.34084964 18
12 0.44663468 33
13 -0.01734187 33
(Intercept) ablat
1 1 44
2 1 55
3 1 42
4 1 52
5 1 13
6 1 44
7 1 19
8 1 13
9 1 27
10 1 42
11 1 18
12 1 33
13 1 33
attr(,"assign")
[1] 0 1
'log Lik.' -6.963434 (df=3)
[1] 19.92687
Univariate Cochran Q-test for residual heterogeneity
Q = 25.095 (df = 11), p-value = 0.009
1 2 3 4 5 6
-1.06871959 -1.42866681 -1.00327464 -1.33049939 -0.05432288 -1.06871959
7 8 9 10 11 12
-0.25065773 -0.05432288 -0.51243753 -1.00327464 -0.21793526 -0.70877237
13
-0.70877237
fit se
1 -1.06871959 0.07607129
2 -1.42866681 0.10631719
3 -1.00327464 0.07126987
4 -1.33049939 0.09760135
5 -0.05432288 0.07099872
6 -1.06871959 0.07607129
7 -0.25065773 0.05899224
8 -0.05432288 0.07099872
9 -0.51243753 0.05169396
10 -1.00327464 0.07126987
11 -0.21793526 0.06069076
12 -0.70877237 0.05496610
13 -0.70877237 0.05496610
fit ci.lb ci.ub
1 -0.2833802 -0.3959636 -0.1707968
2 -0.6106049 -0.7132828 -0.5079271
3 -0.9378297 -1.0687648 -0.8068946
4 -1.2650544 -1.4452733 -1.0848356
1 2 3 4 5 6
-1.06727983 -1.43314415 -1.00677609 -1.35121295 -0.06610215 -1.03691247
7 8 9 10 11 12
-0.27459907 -0.02118545 -0.50976905 -1.02331002 -0.24767993 -0.70018738
13
-0.67221714
blup pi.lb pi.ub
1 -1.06727983 -1.2607239 -0.87383580
2 -1.43314415 -1.6749965 -1.19129181
3 -1.00677609 -1.1931430 -0.82040915
4 -1.35121295 -1.5735376 -1.12888824
5 -0.06610215 -0.2494790 0.11727468
6 -1.03691247 -1.2190471 -0.85477783
7 -0.27459907 -0.4433103 -0.10588783
8 -0.02118545 -0.1856617 0.14329077
9 -0.50976905 -0.6666730 -0.35286513
10 -1.02331002 -1.2079710 -0.83864906
11 -0.24767993 -0.4082821 -0.08707778
12 -0.70018738 -0.8640554 -0.53631935
13 -0.67221714 -0.8339415 -0.51049282
Call: mixmeta(formula = cbind(PD, AL) ~ pubyear, S = berkey98[5:7],
data = berkey98)
Multivariate random-effects meta-regression
Dimension: 2
Estimation method: REML
Fixed-effects coefficients
PD :
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) -9.2817 43.3421 -0.2142 0.8304 -94.2306 75.6671
pubyear 0.0049 0.0219 0.2225 0.8239 -0.0380 0.0477
AL :
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) 22.5409 59.4284 0.3793 0.7045 -93.9365 139.0183
pubyear -0.0115 0.0300 -0.3850 0.7002 -0.0703 0.0472
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: General positive-definite
Std. Dev Corr
PD 0.1430 PD
AL 0.2021 0.5614
Multivariate Cochran Q-test for residual heterogeneity:
Q = 125.7557 (df = 6), p-value = 0.0000
I-square statistic = 95.2%
5 units, 2 outcomes, 10 observations, 4 fixed and 3 random-effects parameters
logLik AIC BIC
2.0732 9.8537 8.3960
PD AL
Pihlstrom 0.11124337 0.015736234
Lindhe -0.15389507 -0.275800146
Knowles 0.06068963 0.169590714
Ramfjord -0.11820289 0.071881754
Becker 0.17693555 0.003418134
Call: mixmeta(formula = y, S = S)
Multivariate random-effects meta-analysis
Dimension: 4
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
b2 0.1616 0.0754 2.1433 0.0321 0.0138 0.3093 *
b3 0.3926 0.0837 4.6901 0.0000 0.2285 0.5567 ***
b4 0.5620 0.0870 6.4602 0.0000 0.3915 0.7325 ***
b5 0.8973 0.0906 9.9086 0.0000 0.7198 1.0748 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: General positive-definite
Std. Dev Corr
b2 0.2273 b2 b3 b4
b3 0.2861 0.9895
b4 0.3083 0.9742 0.9966
b5 0.3274 0.7062 0.8010 0.8477
Multivariate Cochran Q-test for heterogeneity:
Q = 187.8831 (df = 120), p-value = 0.0001
I-square statistic = 36.1%
31 units, 4 outcomes, 124 observations, 4 fixed and 10 random-effects parameters
logLik AIC BIC
-72.6212 173.2423 212.2672
$fit
b2 b3 b4 b5
1 0.1615843 0.3926019 0.5620076 0.8973289
2 0.1615843 0.3926019 0.5620076 0.8973289
3 0.1615843 0.3926019 0.5620076 0.8973289
4 0.1615843 0.3926019 0.5620076 0.8973289
5 0.1615843 0.3926019 0.5620076 0.8973289
6 0.1615843 0.3926019 0.5620076 0.8973289
7 0.1615843 0.3926019 0.5620076 0.8973289
8 0.1615843 0.3926019 0.5620076 0.8973289
9 0.1615843 0.3926019 0.5620076 0.8973289
10 0.1615843 0.3926019 0.5620076 0.8973289
11 0.1615843 0.3926019 0.5620076 0.8973289
12 0.1615843 0.3926019 0.5620076 0.8973289
13 0.1615843 0.3926019 0.5620076 0.8973289
14 0.1615843 0.3926019 0.5620076 0.8973289
15 0.1615843 0.3926019 0.5620076 0.8973289
16 0.1615843 0.3926019 0.5620076 0.8973289
17 0.1615843 0.3926019 0.5620076 0.8973289
18 0.1615843 0.3926019 0.5620076 0.8973289
19 0.1615843 0.3926019 0.5620076 0.8973289
20 0.1615843 0.3926019 0.5620076 0.8973289
21 0.1615843 0.3926019 0.5620076 0.8973289
22 0.1615843 0.3926019 0.5620076 0.8973289
23 0.1615843 0.3926019 0.5620076 0.8973289
24 0.1615843 0.3926019 0.5620076 0.8973289
25 0.1615843 0.3926019 0.5620076 0.8973289
26 0.1615843 0.3926019 0.5620076 0.8973289
27 0.1615843 0.3926019 0.5620076 0.8973289
28 0.1615843 0.3926019 0.5620076 0.8973289
29 0.1615843 0.3926019 0.5620076 0.8973289
30 0.1615843 0.3926019 0.5620076 0.8973289
31 0.1615843 0.3926019 0.5620076 0.8973289
$se
b2 b3 b4 b5
1 0.07539004 0.08370929 0.08699507 0.09056051
2 0.07539004 0.08370929 0.08699507 0.09056051
3 0.07539004 0.08370929 0.08699507 0.09056051
4 0.07539004 0.08370929 0.08699507 0.09056051
5 0.07539004 0.08370929 0.08699507 0.09056051
6 0.07539004 0.08370929 0.08699507 0.09056051
7 0.07539004 0.08370929 0.08699507 0.09056051
8 0.07539004 0.08370929 0.08699507 0.09056051
9 0.07539004 0.08370929 0.08699507 0.09056051
10 0.07539004 0.08370929 0.08699507 0.09056051
11 0.07539004 0.08370929 0.08699507 0.09056051
12 0.07539004 0.08370929 0.08699507 0.09056051
13 0.07539004 0.08370929 0.08699507 0.09056051
14 0.07539004 0.08370929 0.08699507 0.09056051
15 0.07539004 0.08370929 0.08699507 0.09056051
16 0.07539004 0.08370929 0.08699507 0.09056051
17 0.07539004 0.08370929 0.08699507 0.09056051
18 0.07539004 0.08370929 0.08699507 0.09056051
19 0.07539004 0.08370929 0.08699507 0.09056051
20 0.07539004 0.08370929 0.08699507 0.09056051
21 0.07539004 0.08370929 0.08699507 0.09056051
22 0.07539004 0.08370929 0.08699507 0.09056051
23 0.07539004 0.08370929 0.08699507 0.09056051
24 0.07539004 0.08370929 0.08699507 0.09056051
25 0.07539004 0.08370929 0.08699507 0.09056051
26 0.07539004 0.08370929 0.08699507 0.09056051
27 0.07539004 0.08370929 0.08699507 0.09056051
28 0.07539004 0.08370929 0.08699507 0.09056051
29 0.07539004 0.08370929 0.08699507 0.09056051
30 0.07539004 0.08370929 0.08699507 0.09056051
31 0.07539004 0.08370929 0.08699507 0.09056051
$b2
fit se
1 0.1615843 0.07539004
2 0.1615843 0.07539004
3 0.1615843 0.07539004
4 0.1615843 0.07539004
5 0.1615843 0.07539004
6 0.1615843 0.07539004
7 0.1615843 0.07539004
8 0.1615843 0.07539004
9 0.1615843 0.07539004
10 0.1615843 0.07539004
11 0.1615843 0.07539004
12 0.1615843 0.07539004
13 0.1615843 0.07539004
14 0.1615843 0.07539004
15 0.1615843 0.07539004
16 0.1615843 0.07539004
17 0.1615843 0.07539004
18 0.1615843 0.07539004
19 0.1615843 0.07539004
20 0.1615843 0.07539004
21 0.1615843 0.07539004
22 0.1615843 0.07539004
23 0.1615843 0.07539004
24 0.1615843 0.07539004
25 0.1615843 0.07539004
26 0.1615843 0.07539004
27 0.1615843 0.07539004
28 0.1615843 0.07539004
29 0.1615843 0.07539004
30 0.1615843 0.07539004
31 0.1615843 0.07539004
$b3
fit se
1 0.3926019 0.08370929
2 0.3926019 0.08370929
3 0.3926019 0.08370929
4 0.3926019 0.08370929
5 0.3926019 0.08370929
6 0.3926019 0.08370929
7 0.3926019 0.08370929
8 0.3926019 0.08370929
9 0.3926019 0.08370929
10 0.3926019 0.08370929
11 0.3926019 0.08370929
12 0.3926019 0.08370929
13 0.3926019 0.08370929
14 0.3926019 0.08370929
15 0.3926019 0.08370929
16 0.3926019 0.08370929
17 0.3926019 0.08370929
18 0.3926019 0.08370929
19 0.3926019 0.08370929
20 0.3926019 0.08370929
21 0.3926019 0.08370929
22 0.3926019 0.08370929
23 0.3926019 0.08370929
24 0.3926019 0.08370929
25 0.3926019 0.08370929
26 0.3926019 0.08370929
27 0.3926019 0.08370929
28 0.3926019 0.08370929
29 0.3926019 0.08370929
30 0.3926019 0.08370929
31 0.3926019 0.08370929
$b4
fit se
1 0.5620076 0.08699507
2 0.5620076 0.08699507
3 0.5620076 0.08699507
4 0.5620076 0.08699507
5 0.5620076 0.08699507
6 0.5620076 0.08699507
7 0.5620076 0.08699507
8 0.5620076 0.08699507
9 0.5620076 0.08699507
10 0.5620076 0.08699507
11 0.5620076 0.08699507
12 0.5620076 0.08699507
13 0.5620076 0.08699507
14 0.5620076 0.08699507
15 0.5620076 0.08699507
16 0.5620076 0.08699507
17 0.5620076 0.08699507
18 0.5620076 0.08699507
19 0.5620076 0.08699507
20 0.5620076 0.08699507
21 0.5620076 0.08699507
22 0.5620076 0.08699507
23 0.5620076 0.08699507
24 0.5620076 0.08699507
25 0.5620076 0.08699507
26 0.5620076 0.08699507
27 0.5620076 0.08699507
28 0.5620076 0.08699507
29 0.5620076 0.08699507
30 0.5620076 0.08699507
31 0.5620076 0.08699507
$b5
fit se
1 0.8973289 0.09056051
2 0.8973289 0.09056051
3 0.8973289 0.09056051
4 0.8973289 0.09056051
5 0.8973289 0.09056051
6 0.8973289 0.09056051
7 0.8973289 0.09056051
8 0.8973289 0.09056051
9 0.8973289 0.09056051
10 0.8973289 0.09056051
11 0.8973289 0.09056051
12 0.8973289 0.09056051
13 0.8973289 0.09056051
14 0.8973289 0.09056051
15 0.8973289 0.09056051
16 0.8973289 0.09056051
17 0.8973289 0.09056051
18 0.8973289 0.09056051
19 0.8973289 0.09056051
20 0.8973289 0.09056051
21 0.8973289 0.09056051
22 0.8973289 0.09056051
23 0.8973289 0.09056051
24 0.8973289 0.09056051
25 0.8973289 0.09056051
26 0.8973289 0.09056051
27 0.8973289 0.09056051
28 0.8973289 0.09056051
29 0.8973289 0.09056051
30 0.8973289 0.09056051
31 0.8973289 0.09056051
Call: mixmeta(formula = effect, S = var, data = school, random = ~1 |
district/study)
Univariate extended random-effects meta-analysis
Dimension: 1
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) 0.1847 0.0846 2.1845 0.0289 0.0190 0.3504 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Formula: ~1 | district
Structure: General positive-definite
Std. Dev
0.2551
Formula: ~1 | study
Structure: General positive-definite
Std. Dev
0.1809
Univariate Cochran Q-test for heterogeneity:
Q = 578.8640 (df = 55), p-value = 0.0000
I-square statistic = 90.5%
56 units, 1 outcome, 56 observations, 1 fixed and 2 random-effects parameters
logLik AIC BIC
-7.9587 21.9174 27.9394
Call: mixmeta(formula = logrr ~ 0 + dose, S = se^2, data = alcohol,
random = ~0 + dose | id, subset = !is.na(se))
Univariate extended random-effects meta-regression
Dimension: 1
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
dose 0.0039 0.0013 2.9727 0.0030 0.0013 0.0064 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Formula: ~0 + dose | id
Structure: General positive-definite
Std. Dev
0.0000
Univariate Cochran Q-test for residual heterogeneity:
Q = 43.9080 (df = 39), p-value = 0.2713
I-square statistic = 11.2%
40 units, 1 outcome, 40 observations, 1 fixed and 1 random-effects parameters
logLik AIC BIC
2.6167 -1.2334 2.0937
Call: mixmeta(formula = logOR ~ time, S = logORvar, data = gliomas,
random = ~I(time - 15) | study)
Univariate extended random-effects meta-regression
Dimension: 1
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) 0.2423 0.1555 1.5578 0.1193 -0.0626 0.5471
time 0.0091 0.0124 0.7281 0.4665 -0.0153 0.0335
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Formula: ~I(time - 15) | study
Structure: General positive-definite
Std. Dev Corr
(Intercept) 0.1795 (Intercept)
I(time - 15) 0.0320 1
Univariate Cochran Q-test for residual heterogeneity:
Q = 67.1212 (df = 64), p-value = 0.3706
I-square statistic = 4.7%
66 units, 1 outcome, 66 observations, 2 fixed and 3 random-effects parameters
(2 units removed due to missingness)
logLik AIC BIC
-52.0395 114.0789 124.8734
Call: mixmeta(formula = sbp ~ ish, S = sbp_se^2, data = hyp, method = "fixed")
Univariate fixed-effects meta-regression
Dimension: 1
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) -9.1049 0.1131 -80.5146 0.0000 -9.3266 -8.8833 ***
ish -0.4500 0.2123 -2.1195 0.0340 -0.8660 -0.0339 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Univariate Cochran Q-test for residual heterogeneity:
Q = 154.2734 (df = 8), p-value = 0.0000
I-square statistic = 94.8%
10 units, 1 outcome, 10 observations, 2 fixed and 0 random-effects parameters
logLik AIC BIC
-84.2261 172.4522 173.0574
Call: mixmeta(formula = cbind(b1, b2, b3), 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
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
Multivariate Cochran Q-test for heterogeneity:
Q = 54.6278 (df = 21), p-value = 0.0001
I-square statistic = 61.6%
8 units, 3 outcomes, 24 observations, 3 fixed and 1 random-effects parameters
Call: mixmeta(formula = cbind(PD, AL) ~ pubyear, S = berkey98[5:7],
data = berkey98, method = "vc")
Multivariate random-effects meta-regression
Dimension: 2
Estimation method: Variance components
Fixed-effects coefficients
PD :
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) -9.9362 43.8402 -0.2266 0.8207 -95.8614 75.9890
pubyear 0.0052 0.0221 0.2349 0.8143 -0.0381 0.0485
AL :
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) 23.3783 53.0925 0.4403 0.6597 -80.6811 127.4376
pubyear -0.0120 0.0268 -0.4468 0.6550 -0.0644 0.0405
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: General positive-definite
Std. Dev Corr
PD 0.1450 PD
AL 0.1771 0.4756
Multivariate Cochran Q-test for residual heterogeneity:
Q = 125.7557 (df = 6), p-value = 0.0000
I-square statistic = 95.2%
5 units, 2 outcomes, 10 observations, 4 fixed and 1 random-effects parameters
Call: mixmeta(formula = y, 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
Random-effects (co)variance components
Structure: General positive-definite
Std. Dev Corr
yB 0.3141 yB yC
yC 0.7498 0.9363
yD 0.7225 0.8558 0.6196
Multivariate Cochran Q-test for heterogeneity:
Q = 204.2165 (df = 28), p-value = 0.0000
I-square statistic = 86.3%
24 units, 3 outcomes, 31 observations, 3 fixed and 6 random-effects parameters
logLik AIC BIC
-50.5629 119.1259 131.1157
y.yB y.yC y.yD
1 NA 1.05129302 0.12852758
2 0.39042714 0.39167172 0.61576045
3 -0.01596494 NA NA
4 0.39350453 NA NA
5 0.70294160 NA NA
6 NA 2.20228934 NA
7 NA 0.87035364 NA
8 NA 0.41564852 NA
9 NA 2.77968383 NA
10 NA 2.70539331 NA
11 NA 2.42518735 NA
12 NA 0.44361687 NA
13 NA 0.46459091 NA
14 NA -0.15581043 NA
15 NA -0.23997016 NA
16 NA 0.03895601 NA
17 NA 0.39041227 NA
18 NA 0.10633565 NA
19 NA 0.58339828 NA
20 NA NA 3.52251673
21 1.82566094 1.67397630 NA
22 0.06559721 NA 1.10908353
23 NA 0.52324808 1.20397270
24 NA 0.56580770 0.16034257
sbp_se.sbp_se dbp_se.sbp_se dbp_se.dbp_se
[1,] 0.5184 0.151632 0.0729
[2,] 22.3729 3.065040 2.0736
[3,] 106.2961 10.766733 3.1329
[4,] 0.0900 0.023100 0.0100
[5,] 0.0196 0.004620 0.0025
[6,] 0.3364 0.051156 0.0324
[7,] 0.0900 0.040500 0.0729
[8,] 33.8724 4.650762 1.7161
[9,] 0.1681 0.020295 0.0121
[10,] 0.0400 0.004080 0.0016
Call: mixmeta(formula = cbind(y1, y2), S = cbind(V1, V2), data = p53,
control = list(Scor = 0.95))
Multivariate random-effects meta-analysis
Dimension: 2
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
y1 -0.2821 0.2587 -1.0905 0.2755 -0.7890 0.2249
y2 0.1036 0.3078 0.3366 0.7364 -0.4997 0.7069
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: General positive-definite
Std. Dev Corr
y1 0.4089 y1
y2 0.6195 1
Multivariate Cochran Q-test for heterogeneity:
Q = 24.1472 (df = 7), p-value = 0.0011
I-square statistic = 71.0%
6 units, 2 outcomes, 9 observations, 2 fixed and 3 random-effects parameters
logLik AIC BIC
-4.9888 19.9775 19.7071
Call: mixmeta(formula = cbind(b1, b2, b3), S = S, data = hsls, bscov = "diag")
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
b1 -0.0049 0.2239 -0.0219 0.9825 -0.4437 0.4339
b2 6.1380 0.3477 17.6551 0.0000 5.4566 6.8194 ***
b3 -0.6706 0.1597 -4.1988 0.0000 -0.9836 -0.3575 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: Diagonal
Std. Dev Corr
b1 0.3973 b1 b2
b2 0.5618 0
b3 0.0060 0 0
Multivariate Cochran Q-test for heterogeneity:
Q = 54.6278 (df = 21), p-value = 0.0001
I-square statistic = 61.6%
8 units, 3 outcomes, 24 observations, 3 fixed and 3 random-effects parameters
logLik AIC BIC
-26.7977 65.5954 71.8626
b1 b2 b3
b1 0.1578586 0.0000000 0.000000e+00
b2 0.0000000 0.3156256 0.000000e+00
b3 0.0000000 0.0000000 3.585253e-05
Call: mixmeta(formula = cbind(b1, b2, b3), S = S, data = hsls, bscov = "cs")
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
b1 -0.0275 0.1980 -0.1388 0.8896 -0.4156 0.3606
b2 6.1728 0.3011 20.4981 0.0000 5.5825 6.7630 ***
b3 -0.7089 0.2173 -3.2621 0.0011 -1.1348 -0.2829 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: Compound symmetry
Std. Dev Corr
b1 0.3169 b1 b2
b2 0.3169 -0.1392
b3 0.3169 -0.1392 -0.1392
Multivariate Cochran Q-test for heterogeneity:
Q = 54.6278 (df = 21), p-value = 0.0001
I-square statistic = 61.6%
8 units, 3 outcomes, 24 observations, 3 fixed and 2 random-effects parameters
logLik AIC BIC
-27.8862 65.7724 70.9950
b1 b2 b3
b1 0.10040324 -0.01397525 -0.01397525
b2 -0.01397525 0.10040324 -0.01397525
b3 -0.01397525 -0.01397525 0.10040324
IGLS iterations:
iter 0: value 120.5032
iter 1: value 50.86766
iter 2: value 50.6475
iter 3: value 50.65019
iter 4: value 50.64327
iter 5: value 50.63971
iter 6: value 50.63825
iter 7: value 50.63765
iter 8: value 50.63739
iter 9: value 50.63727
iter 10: value 50.63722
iter 11: value 50.63719
iter 12: value 50.63718
iter 13: value 50.63717
iter 14: value 50.63717
iter 15: value 50.63716
iter 16: value 50.63716
iter 17: value 50.63716
iter 18: value 50.63716
iter 19: value 50.63716
Newton iterations:
initial value 50.637162
iter 2 value 50.614498
iter 3 value 50.597309
iter 4 value 50.577756
iter 5 value 50.572085
iter 6 value 50.565450
iter 7 value 50.563093
iter 8 value 50.562999
iter 9 value 50.562951
iter 10 value 50.562949
iter 10 value 50.562949
iter 10 value 50.562949
final value 50.562949
converged
mixmeta documentation built on Oct. 16, 2021, 5:09 p.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
The function mixmeta performs various meta-analytical models under a common mixed-effects framework, including standard univariate fixed and random-effects meta-analysis and meta-regression, and non-standard extensions such as multivariate, multilevel, longitudinal, and dose-response models. The function mixmeta.fit is a wrapper for actual fitting functions based on different estimation methods, usually called internally. See mixmeta-package for an overview.
Usage
1 2 3 4 |
Arguments
Assuming a meta-analysis or meta-regression based on n units aggregated within m (outer-level) groups, k outcomes, p fixed-effects predictors, and q random-effects predictors:
formula |
an object of class |
S |
series of within-unit variances (or (co)variance matrices for multivariate models) of the estimated outcome(s). For univariate models, this is usually a n-dimensional vector. For multivariate models, it can be provided as: a m-dimensional list of k x k matrices; a tri-dimensional k x k x n array; a matrix or data frame with n rows and k(k+1)/2 or k columns, depending on the availability of the within-unit correlations. |
data |
an optional data frame, list or environment (or object coercible by |
random |
a one-sided formula (or a list of formulae for multilevel models) offering a symbolic description of the linear predictor(s) and grouping structure for the random-effects part of the model. The usual form is |
method |
estimation method: |
bscov |
a character vector defining the structure of the random-effects (co)variance matrices. Default to |
offset |
optionally, a n-dimensional numeric vector used to specify an a priori known component in the linear predictor. One or more |
subset |
an optional vector specifying a subset of observations to be used in the fitting process. |
contrasts |
an optional list. See the |
na.action |
a function which indicates what should happen when the data contain |
model |
a logical value indicating whether the model frame should be included as a component of the returned value. See the |
control |
list of parameters for controlling the fitting process. These are passed to |
X |
a n x p design matrix containing the p fixed-effects predictors, appropriately ordered by |
Z |
a n x q design matrix (or a list of design matrices for multilevel models) containing the q random-effects predictors, appropriately ordered by |
y |
a n-dimensional vector (for univariate models) or m x k matrix (for multivariate models) of outcomes, appropriately ordered by |
groups |
matrix with n rows, with each column identifying the groups for each level of random-effects, appropriately ordered. Usually produced internally by |
Details
The function mixmeta resembles standard regression functions in R. See lme in particular, or lm or glm, for information on most of the arguments. Internally, this function assembles the data components, defines the (potentially multiple) grouping levels and re-order the data accordingly, and then pass them to mixmeta.fit. This is a wrapper for actual fitting functions that are automatically selected. Functions other than mixmeta are not expected to be called directly for model fitting.
Fixed or random-effects models for meta-analysis are simply defined using y ~ 1 in formula, where y is a response vector optionally stored in data. In meta-regression models, other terms are added in the right-hand side of the formula as y ~ x1 + ... + xp, defining the linear meta-predictor. Factors, variable transformations and interactions are allowed, following the usual formula specification (see mixmetaFormula).
In this standard usage, each of the n rows is assumed to represent a single estimate of an outcome from a set of independent studies. In random-effects models, the grouping structure is automatically derived by assigning a group to each row of data (with m=n). Extensions to multivariate models (k>1) are straightforward, and only require using a matrix in the left-hand side, where each of the k columns represents a different outcome, or the form cbind(y1, ..., yk) ~ 1. See mixmetaFormula.
Non-standard random-effects models can be specified through the optional argument random. This is commonly represented by a one-sided formula, whose basic random-intercept form is ~ 1 | g, where g is a grouping factor. A more complex linear meta-predictor for the random-effects part can be also specified by ~ z1 + ... + zq | g. The argument random also accepts a list of one-sided formulae referring to multiple random-effects levels (see mixmetaFormula). The use of random extends the standard meta-analytical setting by relaxing the assumption of independence between units, allowing multiple estimates from the same group (with m<n) and multiple nested grouping levels. This provides the possibility to fit longitudinal, multilevel, and dose-response meta-analysis, among other extensions. See the examples below.
The argument bscov allows the definition of specific structures for the random-effects (co)variance matrices corresponding the each level. The default unstructured form requires kq(kq+1)/2 parameters for a single-level meta-analysis. The choice of other structures reduces the number of parameters, although requiring stronger assumptions. More information and complete list of options is available at a specific help page (see mixmetaCovStruct).
The within-unit (co)variances are provided through the argument S, usually as a matrix. If the correlations are available, each of the m row represents the k(k+1)/2 vectorized entries of the lower triangle of the related (co)variance matrix, taken by column (see xpndMat). If correlations are not available, each row represents the k variances, and the correlations are inputted internally through the argument Scor of the control list (see inputcov). For more complex error structures that span multiple units, the argument S can be omitted and passed through addSlist in control, although requiring the observations to be re-ordered accordingly to groups (see mixmeta.control).
Different estimator are available in the package mixmeta and chosen through the argument method, with related fitting functions called internally. In the current version, the options are:
-
method="fixed":Fixed-effects estimator -
method="ml":Maximum likelihood (ML) estimator -
method="reml":Restricted maximum likelihood (REML) estimator -
method="mm":Method of moments estimator -
method="vc":Variance components estimator
Note that non-standard random-effects models and the use of structured (co)variance matrices are only available for "ml" and "reml" methods. See their help pages for further details on the estimation procedures, following the links above.
Missing values are allowed in both sides of formula. In the case of missing predictors (right-hand side of formula), the related unit is entirely excluded from estimation. In contrast, a unit still contributes to estimation if at least outcome is non-missing. This behaviour is different from standard regression functions such as lm or glm. Before the call to mixmeta.fit, units matching such stricter missing definition are removed from the the model frame. The missing pattern in S must be consistent with that in y. See further details on handling missing values in mixmeta.
The fitting procedure can be controlled through the additional terms specified in control, which are passed to the function mixmeta.control.
Value
The mixmeta function typically returns a list object of class "mixmeta" representing the meta-analytical model fit, as described in mixmetaObject. When method="data.frame", the model is not fitted and the model frame is returned, namely a data frame with special attributes (see the default method model.frame) and, in this case, the additional class "data.frame.mixmeta".
The wrapper function mixmeta.fit is usually called internally in mixmeta, and returns an intermediate list object with some of the components expected in the "mixmeta" class.
Several method functions for regression objects are available, either default or specifically written for the "mixmeta" class. See mixmetaObject for a complete list.
Author(s)
Antonio Gasparrini <antonio.gasparrini@lshtm.ac.uk> and Francesco Sera <francesco.sera@lshtm.ac.uk>
References
Sera F, 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].
See Also
See additional info on the estimation procedures at the related page of the fitting functions See mixmetaFormula for the use of formulae to define the fixed and random parts of the model. See alternative (co)variance structures for likelihood-based estimation methods. See handling of missing values in mixmeta. See lme, lm or glm for standard regression functions. See mixmeta-package for an overview of this modelling framework.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 | ### STANDARD MODELS
# RANDOM-EFFECTS META-ANALYSIS, ESTIMATED WITH REML
model <- mixmeta(logor, logorvar, data=bcg)
summary(model)
# RANDOM-EFFECTS META-REGRESSION, ESTIMATED WITH ML
model <- mixmeta(logor~ablat, logorvar, data=bcg, method="ml")
summary(model)
### MAIN METHOD FUNCTIONS
# COEFFICIENTS AND (CO)VARIANCE MATRIX
coef(model)
vcov(model)
# RESIDUALS AND FITTED VALUES
residuals(model)
fitted(model)
# MODEL FRAME AND MODEL MATRIX
model.frame(model)
model.matrix(model)
# LOG-LIKELIHOOD AND AIC VALUE
logLik(model)
AIC(model)
# COCHRAN Q TEST FOR RESIDUAL HETEROGENEITY
qtest(model)
### PREDICTIONS
# PREDICTED EFFECTS
predict(model)
predict(model, se=TRUE)
predict(model, newdata=data.frame(ablat=2:5*10), ci=TRUE)
# BEST LINEAR UNBIASED PREDICTION
blup(model)
blup(model, pi=TRUE)
# SEE help(predict.mixmeta) AND help(BLUP.mixmeta) FOR MORE INFO
### MULTIVARIATE MODELS
### BIVARIATE MODELS
model <- mixmeta(cbind(PD,AL) ~ pubyear, S=berkey98[5:7], data=berkey98)
summary(model)
residuals(model)
### MULTIVARIATE META-ANALYSIS WITH MORE THAN 2 OUTCOMES
y <- as.matrix(fibrinogen[2:5])
S <- as.matrix(fibrinogen[6:15])
model <- mixmeta(y, S)
summary(model)
predict(model, se=TRUE)
predict(model, se=TRUE, aggregate="outcome")
### OTHER EXTENSIONS
# MULTILEVEL META-ANALYSIS
model <- mixmeta(effect, var, random= ~ 1|district/study, data=school)
summary(model)
# SEE help(school) AND help(thrombolytic) FOR MORE EXAMPLES
# DOSE-RESPONSE META-ANALYSIS (SIMPLIFIED)
model <- mixmeta(logrr ~ 0 + dose, S=se^2, random= ~ 0 + dose|id, data=alcohol,
subset=!is.na(se))
summary(model)
# SEE help(alcohol) FOR MORE EXAMPLES
# LONGITUDINAL META-ANALYSIS
model <- mixmeta(logOR~time, S=logORvar, random=~I(time-15)|study, data=gliomas)
summary(model)
# SEE help(gliomas) AND help(dbs) FOR MORE EXAMPLES
### FIXED-EFFECTS MODELS AND ALTERNATIVE ESTIMATORS
# FIXED-EFFECTS MODEL
model <- mixmeta(sbp~ish, S=sbp_se^2, data=hyp, method="fixed")
summary(model)
# METHOD OF MOMENTS
S <- as.matrix(hsls[5:10])
model <- mixmeta(cbind(b1,b2,b3), S, data=hsls, method="mm")
summary(model)
# VARIANCE COMPONENTS ESTIMATOR
model <- mixmeta(cbind(PD,AL)~pubyear, S=berkey98[5:7], data=berkey98,
method="vc")
summary(model)
### IN THE PRESENCE OF MISSING VALUES
# RUN THE MODEL
y <- as.matrix(smoking[11:13])
S <- as.matrix(smoking[14:19])
model <- mixmeta(y, S)
summary(model)
model.frame(model)
# SEE help(na.omit.data.frame.mixmeta) FOR MORE EXAMPLES
### WHEN WITHIN-STUDY COVIARIANCES ARE NOT AVAILABLE AND/OR NEED TO BE INPUTTED
# GENERATE S
(S <- inputcov(hyp[c("sbp_se","dbp_se")], cor=hyp$rho))
# RUN THE MODEL
model <- mixmeta(cbind(sbp,dbp), S=S, data=hyp)
# INPUTTING THE CORRELATION DIRECTLY IN THE MODEL
model <- mixmeta(cbind(y1,y2), cbind(V1,V2), data=p53, control=list(Scor=0.95))
summary(model)
# SEE help(hyp) AND help(p53) FOR MORE EXAMPLES
### STRUCTURING THE BETWEEN-STUDY (CO)VARIANCE
# DIAGONAL
S <- as.matrix(hsls[5:10])
model <- mixmeta(cbind(b1,b2,b3), S, data=hsls, bscov="diag")
summary(model)
model$Psi
# COMPOUND SYMMETRY
model <- mixmeta(cbind(b1,b2,b3), S, data=hsls, bscov="cs")
summary(model)
model$Psi
# SEE help(mixmetaCovStruct) FOR DETAILS AND ADDITIONAL EXAMPLES
### USE OF THE CONTROL LIST
# PRINT THE ITERATIONS AND CHANGE THE DEFAULT FOR STARTING VALUES
y <- as.matrix(smoking[11:13])
S <- as.matrix(smoking[14:19])
model <- mixmeta(y, S, control=list(showiter=TRUE, igls.inititer=20))
# SEE help(mixmeta.control) FOR FURTHER DETAILS
|
Example output
This is mixmeta 1.1.0. For an overview type: help('mixmeta-package').
Call: mixmeta(formula = logor, S = logorvar, data = bcg)
Univariate random-effects meta-analysis
Dimension: 1
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) -0.7452 0.1860 -4.0057 0.0001 -1.1098 -0.3806 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: General positive-definite
Std. Dev
0.5812
Univariate Cochran Q-test for heterogeneity:
Q = 163.1649 (df = 12), p-value = 0.0000
I-square statistic = 92.6%
13 units, 1 outcome, 13 observations, 1 fixed and 1 random-effects parameters
logLik AIC BIC
-12.5757 29.1513 30.1211
Call: mixmeta(formula = logor ~ ablat, S = logorvar, data = bcg, method = "ml")
Univariate random-effects meta-regression
Dimension: 1
Estimation method: ML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) 0.3711 0.1060 3.5016 0.0005 0.1634 0.5788 ***
ablat -0.0327 0.0034 -9.7054 0.0000 -0.0393 -0.0261 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: General positive-definite
Std. Dev
0.0632
Univariate Cochran Q-test for residual heterogeneity:
Q = 25.0954 (df = 11), p-value = 0.0088
I-square statistic = 56.2%
13 units, 1 outcome, 13 observations, 2 fixed and 1 random-effects parameters
logLik AIC BIC
-6.9634 19.9269 21.6217
(Intercept) ablat
0.37106929 -0.03272247
(Intercept) ablat
(Intercept) 0.0112301825 -0.0003119412
ablat -0.0003119412 0.0000113675
1 2 3 4 5 6
0.13002547 -0.23752393 -0.38301972 -0.12594416 -0.16481820 0.11059758
7 8 9 10 11 12
-1.38311810 0.06634348 0.04069150 -0.39793555 -0.12291438 1.15540705
13
0.69143050
1 2 3 4 5 6
-1.06871959 -1.42866681 -1.00327464 -1.33049939 -0.05432288 -1.06871959
7 8 9 10 11 12
-0.25065773 -0.05432288 -0.51243753 -1.00327464 -0.21793526 -0.70877237
13
-0.70877237
logor ablat
1 -0.93869412 44
2 -1.66619074 55
3 -1.38629436 42
4 -1.45644355 52
5 -0.21914108 13
6 -0.95812201 44
7 -1.63377583 19
8 0.01202060 13
9 -0.47174603 27
10 -1.40121019 42
11 -0.34084964 18
12 0.44663468 33
13 -0.01734187 33
(Intercept) ablat
1 1 44
2 1 55
3 1 42
4 1 52
5 1 13
6 1 44
7 1 19
8 1 13
9 1 27
10 1 42
11 1 18
12 1 33
13 1 33
attr(,"assign")
[1] 0 1
'log Lik.' -6.963434 (df=3)
[1] 19.92687
Univariate Cochran Q-test for residual heterogeneity
Q = 25.095 (df = 11), p-value = 0.009
1 2 3 4 5 6
-1.06871959 -1.42866681 -1.00327464 -1.33049939 -0.05432288 -1.06871959
7 8 9 10 11 12
-0.25065773 -0.05432288 -0.51243753 -1.00327464 -0.21793526 -0.70877237
13
-0.70877237
fit se
1 -1.06871959 0.07607129
2 -1.42866681 0.10631719
3 -1.00327464 0.07126987
4 -1.33049939 0.09760135
5 -0.05432288 0.07099872
6 -1.06871959 0.07607129
7 -0.25065773 0.05899224
8 -0.05432288 0.07099872
9 -0.51243753 0.05169396
10 -1.00327464 0.07126987
11 -0.21793526 0.06069076
12 -0.70877237 0.05496610
13 -0.70877237 0.05496610
fit ci.lb ci.ub
1 -0.2833802 -0.3959636 -0.1707968
2 -0.6106049 -0.7132828 -0.5079271
3 -0.9378297 -1.0687648 -0.8068946
4 -1.2650544 -1.4452733 -1.0848356
1 2 3 4 5 6
-1.06727983 -1.43314415 -1.00677609 -1.35121295 -0.06610215 -1.03691247
7 8 9 10 11 12
-0.27459907 -0.02118545 -0.50976905 -1.02331002 -0.24767993 -0.70018738
13
-0.67221714
blup pi.lb pi.ub
1 -1.06727983 -1.2607239 -0.87383580
2 -1.43314415 -1.6749965 -1.19129181
3 -1.00677609 -1.1931430 -0.82040915
4 -1.35121295 -1.5735376 -1.12888824
5 -0.06610215 -0.2494790 0.11727468
6 -1.03691247 -1.2190471 -0.85477783
7 -0.27459907 -0.4433103 -0.10588783
8 -0.02118545 -0.1856617 0.14329077
9 -0.50976905 -0.6666730 -0.35286513
10 -1.02331002 -1.2079710 -0.83864906
11 -0.24767993 -0.4082821 -0.08707778
12 -0.70018738 -0.8640554 -0.53631935
13 -0.67221714 -0.8339415 -0.51049282
Call: mixmeta(formula = cbind(PD, AL) ~ pubyear, S = berkey98[5:7],
data = berkey98)
Multivariate random-effects meta-regression
Dimension: 2
Estimation method: REML
Fixed-effects coefficients
PD :
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) -9.2817 43.3421 -0.2142 0.8304 -94.2306 75.6671
pubyear 0.0049 0.0219 0.2225 0.8239 -0.0380 0.0477
AL :
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) 22.5409 59.4284 0.3793 0.7045 -93.9365 139.0183
pubyear -0.0115 0.0300 -0.3850 0.7002 -0.0703 0.0472
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: General positive-definite
Std. Dev Corr
PD 0.1430 PD
AL 0.2021 0.5614
Multivariate Cochran Q-test for residual heterogeneity:
Q = 125.7557 (df = 6), p-value = 0.0000
I-square statistic = 95.2%
5 units, 2 outcomes, 10 observations, 4 fixed and 3 random-effects parameters
logLik AIC BIC
2.0732 9.8537 8.3960
PD AL
Pihlstrom 0.11124337 0.015736234
Lindhe -0.15389507 -0.275800146
Knowles 0.06068963 0.169590714
Ramfjord -0.11820289 0.071881754
Becker 0.17693555 0.003418134
Call: mixmeta(formula = y, S = S)
Multivariate random-effects meta-analysis
Dimension: 4
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
b2 0.1616 0.0754 2.1433 0.0321 0.0138 0.3093 *
b3 0.3926 0.0837 4.6901 0.0000 0.2285 0.5567 ***
b4 0.5620 0.0870 6.4602 0.0000 0.3915 0.7325 ***
b5 0.8973 0.0906 9.9086 0.0000 0.7198 1.0748 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: General positive-definite
Std. Dev Corr
b2 0.2273 b2 b3 b4
b3 0.2861 0.9895
b4 0.3083 0.9742 0.9966
b5 0.3274 0.7062 0.8010 0.8477
Multivariate Cochran Q-test for heterogeneity:
Q = 187.8831 (df = 120), p-value = 0.0001
I-square statistic = 36.1%
31 units, 4 outcomes, 124 observations, 4 fixed and 10 random-effects parameters
logLik AIC BIC
-72.6212 173.2423 212.2672
$fit
b2 b3 b4 b5
1 0.1615843 0.3926019 0.5620076 0.8973289
2 0.1615843 0.3926019 0.5620076 0.8973289
3 0.1615843 0.3926019 0.5620076 0.8973289
4 0.1615843 0.3926019 0.5620076 0.8973289
5 0.1615843 0.3926019 0.5620076 0.8973289
6 0.1615843 0.3926019 0.5620076 0.8973289
7 0.1615843 0.3926019 0.5620076 0.8973289
8 0.1615843 0.3926019 0.5620076 0.8973289
9 0.1615843 0.3926019 0.5620076 0.8973289
10 0.1615843 0.3926019 0.5620076 0.8973289
11 0.1615843 0.3926019 0.5620076 0.8973289
12 0.1615843 0.3926019 0.5620076 0.8973289
13 0.1615843 0.3926019 0.5620076 0.8973289
14 0.1615843 0.3926019 0.5620076 0.8973289
15 0.1615843 0.3926019 0.5620076 0.8973289
16 0.1615843 0.3926019 0.5620076 0.8973289
17 0.1615843 0.3926019 0.5620076 0.8973289
18 0.1615843 0.3926019 0.5620076 0.8973289
19 0.1615843 0.3926019 0.5620076 0.8973289
20 0.1615843 0.3926019 0.5620076 0.8973289
21 0.1615843 0.3926019 0.5620076 0.8973289
22 0.1615843 0.3926019 0.5620076 0.8973289
23 0.1615843 0.3926019 0.5620076 0.8973289
24 0.1615843 0.3926019 0.5620076 0.8973289
25 0.1615843 0.3926019 0.5620076 0.8973289
26 0.1615843 0.3926019 0.5620076 0.8973289
27 0.1615843 0.3926019 0.5620076 0.8973289
28 0.1615843 0.3926019 0.5620076 0.8973289
29 0.1615843 0.3926019 0.5620076 0.8973289
30 0.1615843 0.3926019 0.5620076 0.8973289
31 0.1615843 0.3926019 0.5620076 0.8973289
$se
b2 b3 b4 b5
1 0.07539004 0.08370929 0.08699507 0.09056051
2 0.07539004 0.08370929 0.08699507 0.09056051
3 0.07539004 0.08370929 0.08699507 0.09056051
4 0.07539004 0.08370929 0.08699507 0.09056051
5 0.07539004 0.08370929 0.08699507 0.09056051
6 0.07539004 0.08370929 0.08699507 0.09056051
7 0.07539004 0.08370929 0.08699507 0.09056051
8 0.07539004 0.08370929 0.08699507 0.09056051
9 0.07539004 0.08370929 0.08699507 0.09056051
10 0.07539004 0.08370929 0.08699507 0.09056051
11 0.07539004 0.08370929 0.08699507 0.09056051
12 0.07539004 0.08370929 0.08699507 0.09056051
13 0.07539004 0.08370929 0.08699507 0.09056051
14 0.07539004 0.08370929 0.08699507 0.09056051
15 0.07539004 0.08370929 0.08699507 0.09056051
16 0.07539004 0.08370929 0.08699507 0.09056051
17 0.07539004 0.08370929 0.08699507 0.09056051
18 0.07539004 0.08370929 0.08699507 0.09056051
19 0.07539004 0.08370929 0.08699507 0.09056051
20 0.07539004 0.08370929 0.08699507 0.09056051
21 0.07539004 0.08370929 0.08699507 0.09056051
22 0.07539004 0.08370929 0.08699507 0.09056051
23 0.07539004 0.08370929 0.08699507 0.09056051
24 0.07539004 0.08370929 0.08699507 0.09056051
25 0.07539004 0.08370929 0.08699507 0.09056051
26 0.07539004 0.08370929 0.08699507 0.09056051
27 0.07539004 0.08370929 0.08699507 0.09056051
28 0.07539004 0.08370929 0.08699507 0.09056051
29 0.07539004 0.08370929 0.08699507 0.09056051
30 0.07539004 0.08370929 0.08699507 0.09056051
31 0.07539004 0.08370929 0.08699507 0.09056051
$b2
fit se
1 0.1615843 0.07539004
2 0.1615843 0.07539004
3 0.1615843 0.07539004
4 0.1615843 0.07539004
5 0.1615843 0.07539004
6 0.1615843 0.07539004
7 0.1615843 0.07539004
8 0.1615843 0.07539004
9 0.1615843 0.07539004
10 0.1615843 0.07539004
11 0.1615843 0.07539004
12 0.1615843 0.07539004
13 0.1615843 0.07539004
14 0.1615843 0.07539004
15 0.1615843 0.07539004
16 0.1615843 0.07539004
17 0.1615843 0.07539004
18 0.1615843 0.07539004
19 0.1615843 0.07539004
20 0.1615843 0.07539004
21 0.1615843 0.07539004
22 0.1615843 0.07539004
23 0.1615843 0.07539004
24 0.1615843 0.07539004
25 0.1615843 0.07539004
26 0.1615843 0.07539004
27 0.1615843 0.07539004
28 0.1615843 0.07539004
29 0.1615843 0.07539004
30 0.1615843 0.07539004
31 0.1615843 0.07539004
$b3
fit se
1 0.3926019 0.08370929
2 0.3926019 0.08370929
3 0.3926019 0.08370929
4 0.3926019 0.08370929
5 0.3926019 0.08370929
6 0.3926019 0.08370929
7 0.3926019 0.08370929
8 0.3926019 0.08370929
9 0.3926019 0.08370929
10 0.3926019 0.08370929
11 0.3926019 0.08370929
12 0.3926019 0.08370929
13 0.3926019 0.08370929
14 0.3926019 0.08370929
15 0.3926019 0.08370929
16 0.3926019 0.08370929
17 0.3926019 0.08370929
18 0.3926019 0.08370929
19 0.3926019 0.08370929
20 0.3926019 0.08370929
21 0.3926019 0.08370929
22 0.3926019 0.08370929
23 0.3926019 0.08370929
24 0.3926019 0.08370929
25 0.3926019 0.08370929
26 0.3926019 0.08370929
27 0.3926019 0.08370929
28 0.3926019 0.08370929
29 0.3926019 0.08370929
30 0.3926019 0.08370929
31 0.3926019 0.08370929
$b4
fit se
1 0.5620076 0.08699507
2 0.5620076 0.08699507
3 0.5620076 0.08699507
4 0.5620076 0.08699507
5 0.5620076 0.08699507
6 0.5620076 0.08699507
7 0.5620076 0.08699507
8 0.5620076 0.08699507
9 0.5620076 0.08699507
10 0.5620076 0.08699507
11 0.5620076 0.08699507
12 0.5620076 0.08699507
13 0.5620076 0.08699507
14 0.5620076 0.08699507
15 0.5620076 0.08699507
16 0.5620076 0.08699507
17 0.5620076 0.08699507
18 0.5620076 0.08699507
19 0.5620076 0.08699507
20 0.5620076 0.08699507
21 0.5620076 0.08699507
22 0.5620076 0.08699507
23 0.5620076 0.08699507
24 0.5620076 0.08699507
25 0.5620076 0.08699507
26 0.5620076 0.08699507
27 0.5620076 0.08699507
28 0.5620076 0.08699507
29 0.5620076 0.08699507
30 0.5620076 0.08699507
31 0.5620076 0.08699507
$b5
fit se
1 0.8973289 0.09056051
2 0.8973289 0.09056051
3 0.8973289 0.09056051
4 0.8973289 0.09056051
5 0.8973289 0.09056051
6 0.8973289 0.09056051
7 0.8973289 0.09056051
8 0.8973289 0.09056051
9 0.8973289 0.09056051
10 0.8973289 0.09056051
11 0.8973289 0.09056051
12 0.8973289 0.09056051
13 0.8973289 0.09056051
14 0.8973289 0.09056051
15 0.8973289 0.09056051
16 0.8973289 0.09056051
17 0.8973289 0.09056051
18 0.8973289 0.09056051
19 0.8973289 0.09056051
20 0.8973289 0.09056051
21 0.8973289 0.09056051
22 0.8973289 0.09056051
23 0.8973289 0.09056051
24 0.8973289 0.09056051
25 0.8973289 0.09056051
26 0.8973289 0.09056051
27 0.8973289 0.09056051
28 0.8973289 0.09056051
29 0.8973289 0.09056051
30 0.8973289 0.09056051
31 0.8973289 0.09056051
Call: mixmeta(formula = effect, S = var, data = school, random = ~1 |
district/study)
Univariate extended random-effects meta-analysis
Dimension: 1
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) 0.1847 0.0846 2.1845 0.0289 0.0190 0.3504 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Formula: ~1 | district
Structure: General positive-definite
Std. Dev
0.2551
Formula: ~1 | study
Structure: General positive-definite
Std. Dev
0.1809
Univariate Cochran Q-test for heterogeneity:
Q = 578.8640 (df = 55), p-value = 0.0000
I-square statistic = 90.5%
56 units, 1 outcome, 56 observations, 1 fixed and 2 random-effects parameters
logLik AIC BIC
-7.9587 21.9174 27.9394
Call: mixmeta(formula = logrr ~ 0 + dose, S = se^2, data = alcohol,
random = ~0 + dose | id, subset = !is.na(se))
Univariate extended random-effects meta-regression
Dimension: 1
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
dose 0.0039 0.0013 2.9727 0.0030 0.0013 0.0064 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Formula: ~0 + dose | id
Structure: General positive-definite
Std. Dev
0.0000
Univariate Cochran Q-test for residual heterogeneity:
Q = 43.9080 (df = 39), p-value = 0.2713
I-square statistic = 11.2%
40 units, 1 outcome, 40 observations, 1 fixed and 1 random-effects parameters
logLik AIC BIC
2.6167 -1.2334 2.0937
Call: mixmeta(formula = logOR ~ time, S = logORvar, data = gliomas,
random = ~I(time - 15) | study)
Univariate extended random-effects meta-regression
Dimension: 1
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) 0.2423 0.1555 1.5578 0.1193 -0.0626 0.5471
time 0.0091 0.0124 0.7281 0.4665 -0.0153 0.0335
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Formula: ~I(time - 15) | study
Structure: General positive-definite
Std. Dev Corr
(Intercept) 0.1795 (Intercept)
I(time - 15) 0.0320 1
Univariate Cochran Q-test for residual heterogeneity:
Q = 67.1212 (df = 64), p-value = 0.3706
I-square statistic = 4.7%
66 units, 1 outcome, 66 observations, 2 fixed and 3 random-effects parameters
(2 units removed due to missingness)
logLik AIC BIC
-52.0395 114.0789 124.8734
Call: mixmeta(formula = sbp ~ ish, S = sbp_se^2, data = hyp, method = "fixed")
Univariate fixed-effects meta-regression
Dimension: 1
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) -9.1049 0.1131 -80.5146 0.0000 -9.3266 -8.8833 ***
ish -0.4500 0.2123 -2.1195 0.0340 -0.8660 -0.0339 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Univariate Cochran Q-test for residual heterogeneity:
Q = 154.2734 (df = 8), p-value = 0.0000
I-square statistic = 94.8%
10 units, 1 outcome, 10 observations, 2 fixed and 0 random-effects parameters
logLik AIC BIC
-84.2261 172.4522 173.0574
Call: mixmeta(formula = cbind(b1, b2, b3), 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
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
Multivariate Cochran Q-test for heterogeneity:
Q = 54.6278 (df = 21), p-value = 0.0001
I-square statistic = 61.6%
8 units, 3 outcomes, 24 observations, 3 fixed and 1 random-effects parameters
Call: mixmeta(formula = cbind(PD, AL) ~ pubyear, S = berkey98[5:7],
data = berkey98, method = "vc")
Multivariate random-effects meta-regression
Dimension: 2
Estimation method: Variance components
Fixed-effects coefficients
PD :
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) -9.9362 43.8402 -0.2266 0.8207 -95.8614 75.9890
pubyear 0.0052 0.0221 0.2349 0.8143 -0.0381 0.0485
AL :
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
(Intercept) 23.3783 53.0925 0.4403 0.6597 -80.6811 127.4376
pubyear -0.0120 0.0268 -0.4468 0.6550 -0.0644 0.0405
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: General positive-definite
Std. Dev Corr
PD 0.1450 PD
AL 0.1771 0.4756
Multivariate Cochran Q-test for residual heterogeneity:
Q = 125.7557 (df = 6), p-value = 0.0000
I-square statistic = 95.2%
5 units, 2 outcomes, 10 observations, 4 fixed and 1 random-effects parameters
Call: mixmeta(formula = y, 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
Random-effects (co)variance components
Structure: General positive-definite
Std. Dev Corr
yB 0.3141 yB yC
yC 0.7498 0.9363
yD 0.7225 0.8558 0.6196
Multivariate Cochran Q-test for heterogeneity:
Q = 204.2165 (df = 28), p-value = 0.0000
I-square statistic = 86.3%
24 units, 3 outcomes, 31 observations, 3 fixed and 6 random-effects parameters
logLik AIC BIC
-50.5629 119.1259 131.1157
y.yB y.yC y.yD
1 NA 1.05129302 0.12852758
2 0.39042714 0.39167172 0.61576045
3 -0.01596494 NA NA
4 0.39350453 NA NA
5 0.70294160 NA NA
6 NA 2.20228934 NA
7 NA 0.87035364 NA
8 NA 0.41564852 NA
9 NA 2.77968383 NA
10 NA 2.70539331 NA
11 NA 2.42518735 NA
12 NA 0.44361687 NA
13 NA 0.46459091 NA
14 NA -0.15581043 NA
15 NA -0.23997016 NA
16 NA 0.03895601 NA
17 NA 0.39041227 NA
18 NA 0.10633565 NA
19 NA 0.58339828 NA
20 NA NA 3.52251673
21 1.82566094 1.67397630 NA
22 0.06559721 NA 1.10908353
23 NA 0.52324808 1.20397270
24 NA 0.56580770 0.16034257
sbp_se.sbp_se dbp_se.sbp_se dbp_se.dbp_se
[1,] 0.5184 0.151632 0.0729
[2,] 22.3729 3.065040 2.0736
[3,] 106.2961 10.766733 3.1329
[4,] 0.0900 0.023100 0.0100
[5,] 0.0196 0.004620 0.0025
[6,] 0.3364 0.051156 0.0324
[7,] 0.0900 0.040500 0.0729
[8,] 33.8724 4.650762 1.7161
[9,] 0.1681 0.020295 0.0121
[10,] 0.0400 0.004080 0.0016
Call: mixmeta(formula = cbind(y1, y2), S = cbind(V1, V2), data = p53,
control = list(Scor = 0.95))
Multivariate random-effects meta-analysis
Dimension: 2
Estimation method: REML
Fixed-effects coefficients
Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
y1 -0.2821 0.2587 -1.0905 0.2755 -0.7890 0.2249
y2 0.1036 0.3078 0.3366 0.7364 -0.4997 0.7069
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: General positive-definite
Std. Dev Corr
y1 0.4089 y1
y2 0.6195 1
Multivariate Cochran Q-test for heterogeneity:
Q = 24.1472 (df = 7), p-value = 0.0011
I-square statistic = 71.0%
6 units, 2 outcomes, 9 observations, 2 fixed and 3 random-effects parameters
logLik AIC BIC
-4.9888 19.9775 19.7071
Call: mixmeta(formula = cbind(b1, b2, b3), S = S, data = hsls, bscov = "diag")
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
b1 -0.0049 0.2239 -0.0219 0.9825 -0.4437 0.4339
b2 6.1380 0.3477 17.6551 0.0000 5.4566 6.8194 ***
b3 -0.6706 0.1597 -4.1988 0.0000 -0.9836 -0.3575 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: Diagonal
Std. Dev Corr
b1 0.3973 b1 b2
b2 0.5618 0
b3 0.0060 0 0
Multivariate Cochran Q-test for heterogeneity:
Q = 54.6278 (df = 21), p-value = 0.0001
I-square statistic = 61.6%
8 units, 3 outcomes, 24 observations, 3 fixed and 3 random-effects parameters
logLik AIC BIC
-26.7977 65.5954 71.8626
b1 b2 b3
b1 0.1578586 0.0000000 0.000000e+00
b2 0.0000000 0.3156256 0.000000e+00
b3 0.0000000 0.0000000 3.585253e-05
Call: mixmeta(formula = cbind(b1, b2, b3), S = S, data = hsls, bscov = "cs")
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
b1 -0.0275 0.1980 -0.1388 0.8896 -0.4156 0.3606
b2 6.1728 0.3011 20.4981 0.0000 5.5825 6.7630 ***
b3 -0.7089 0.2173 -3.2621 0.0011 -1.1348 -0.2829 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Random-effects (co)variance components
Structure: Compound symmetry
Std. Dev Corr
b1 0.3169 b1 b2
b2 0.3169 -0.1392
b3 0.3169 -0.1392 -0.1392
Multivariate Cochran Q-test for heterogeneity:
Q = 54.6278 (df = 21), p-value = 0.0001
I-square statistic = 61.6%
8 units, 3 outcomes, 24 observations, 3 fixed and 2 random-effects parameters
logLik AIC BIC
-27.8862 65.7724 70.9950
b1 b2 b3
b1 0.10040324 -0.01397525 -0.01397525
b2 -0.01397525 0.10040324 -0.01397525
b3 -0.01397525 -0.01397525 0.10040324
IGLS iterations:
iter 0: value 120.5032
iter 1: value 50.86766
iter 2: value 50.6475
iter 3: value 50.65019
iter 4: value 50.64327
iter 5: value 50.63971
iter 6: value 50.63825
iter 7: value 50.63765
iter 8: value 50.63739
iter 9: value 50.63727
iter 10: value 50.63722
iter 11: value 50.63719
iter 12: value 50.63718
iter 13: value 50.63717
iter 14: value 50.63717
iter 15: value 50.63716
iter 16: value 50.63716
iter 17: value 50.63716
iter 18: value 50.63716
iter 19: value 50.63716
Newton iterations:
initial value 50.637162
iter 2 value 50.614498
iter 3 value 50.597309
iter 4 value 50.577756
iter 5 value 50.572085
iter 6 value 50.565450
iter 7 value 50.563093
iter 8 value 50.562999
iter 9 value 50.562951
iter 10 value 50.562949
iter 10 value 50.562949
iter 10 value 50.562949
final value 50.562949
converged
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