qtest.mvmeta: Cochran Q Test of Heterogeneity for mvmeta Models

In mvmeta: Multivariate and Univariate Meta-Analysis and Meta-Regression

Description

This method function performs a Cochran Q test of (residual) heterogeneity on fitted univariate or multivariate meta-analytical models represented in objects of class "mvmeta".

Usage

## S3 method for class 'mvmeta'
qtest(object, ...)

## S3 method for class 'qtest.mvmeta'
print(x, digits=3, ...)

Arguments

object, x	objects of classes "mvmeta" and "qtest.mvmeta", respectively.
digits	an integer specifying the number of digits to which printed results must be rounded.
...	further arguments passed to or from other methods.

Details

In multivariate models, the test assesses the null hypothesis that the variability in the multivariate distribution of the outcomes is explained only in terms of estimation error in each study, measured by the within-study (co)variance matrices stored in the component S of mvmeta objects. This is equal to test the hypothesis that the between-study (co)variance matrix is a zero matrix, and there is no random deviation in study-specific estimates. Tests for single outcome parameters, comparable to estimates from multiple univariate meta-analysis, are also reported. This test reduces to the standard Q test in univariate models.

The function compute the statistics by actually fitting the related fixed-effects model, re-evaluating the call of the model with method changed to "fixed".

Value

A list object of class "qtest.mvmeta" with the following components:

Q	the vector of test statistics for overall and outcome-specific tests, distributed under the null hypothesis as a Chi-square with degrees of freedom df.
df	the vector of degrees of freedom of the null distribution for overall and outcome-specific tests. For the overall test, equal to the number of observations used for estimation minus the number of coefficients in the fixed part of the model. For outcome-specific test, equal to number of observed values minus the number of coefficients.
pvalue	the vector of p-values for overall and outcome-specific tests.
residual	logical switch indicating if a meta-regression model is assessed, meaning that the tested heterogeneity is residual.
k	dimensionality of the overall test, that is the number of outcome parameters in the model.

As usual, the print method function for class "qtest.mvmeta" does not return any value.

Note

Tests on single outcome parameters are performed by extracting the related estimates and variances, but they do not account for the correlation between them, which nevertheless has been considered in estimation. These tests are not therefore comparable with those performed by running a univariate model on each outcome parameter.

Author(s)

Antonio Gasparrini, [e-mail]

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].

Berkey, CS, Hoaglin DC, et al. (1998). Meta-analysis of multiple outcomes by regression with random effects. Statistics in Medicine. 17(22):2537–2550.

Ritz J, Demidenkob E, Spiegelman G (2008). Multivariate meta-analysis for data consortia, individual patient meta-analysis, and pooling projects. Journal of Statistical Planning and Inference. 139(7):1919–1933.

See Also

See qtest for the generic method function. See mvmeta-package for an overview of the package and modelling framework.

Examples

# RUN THE MODEL
model <- mvmeta(cbind(PD,AL)~1,S=berkey98[5:7],data=berkey98)

# MULTIVARIATE COCHRAN Q TEST FOR HETEROGENEITY
test <- qtest(model)
print(test,digits=2)
unclass(test)

Example output

This is mvmeta 0.4.11. For an overview type: help('mvmeta-package').
Multivariate Cochran Q-test for heterogeneity

Overall test: 
Q = 128.23 (df = 8), p-value = 0.00

Tests on single outcome parameters: 
         Q  df  p-value     
PD   14.74   4     0.01   **
AL  112.09   4     0.00  ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

$Q
     .all        PD        AL 
128.22672  14.73537 112.08979 

$df
.all   PD   AL 
   8    4    4 

$pvalue
       .all          PD          AL 
0.000000000 0.005282755 0.000000000 

$residual
[1] FALSE

$k
[1] 2

mvmeta documentation built on Dec. 10, 2019, 5:07 p.m.