Example for the mvmeta package

mvmeta_example.R

> berkey98
          trial pubyear npat   PD    AL var_PD cov_PD_AL var_AL
1 Pihlstrom1983    1983   14 0.47 -0.32 0.0075    0.0030 0.0077
2    Lindhe1982    1982   15 0.20 -0.60 0.0057    0.0009 0.0008
3   Knowles1979    1979   78 0.40 -0.12 0.0021    0.0007 0.0014
4  Ramfjord1987    1987   89 0.26 -0.31 0.0029    0.0009 0.0015
5    Becker1988    1988   16 0.56 -0.39 0.0148    0.0072 0.0304

> model <- mvmeta(cbind(PD,AL),S=berkey98[6:8],data=berkey98,lab=list(mlab=trial))

> summary(model)
MULTIVARIATE RANDOM-EFFECTS META-ANALYSIS
Dimensions: 2
Studies: 5
Estimation method: REML
Variance-covariance matrix Psi: unstructured

Fixed effects
    Estimate  StdErr        z  p-value  95%ci.lb  95%ci.ub     
PD    0.3534  0.0588   6.0057   0.0000    0.2381    0.4688  ***
AL   -0.3392  0.0879  -3.8589   0.0001   -0.5115   -0.1669  ***

Variance components: between-studies stdev and correlation matrix
    StdDev      PD      AL
PD  0.1083  1.0000       .
AL  0.1807  0.6090  1.0000

Multivariate Cochran Q-test for heterogeneity:
Q = 128.2267 (df = 8), p-value = <0.0001

10 observations, 2 fixed and 3 random parameters
logLik     AIC     BIC  
2.0823  5.8353  6.2325  

> AIC(model)
[1] 5.83534

> blup(model,pi=TRUE,aggregate="y",pi.level=0.90)
$PD
                   blup      pi.lb     pi.ub
Pihlstrom1983 0.4175761 0.27265246 0.5624997
Lindhe1982    0.2299012 0.09377627 0.3660262
Knowles1979   0.4024566 0.28408589 0.5208273
Ramfjord1987  0.2864583 0.16258938 0.4103272
Becker1988    0.4307487 0.26821197 0.5932853

$AL
                    blup      pi.lb       pi.ub
Pihlstrom1983 -0.3248929 -0.5192103 -0.13057558
Lindhe1982    -0.5912270 -0.7426969 -0.43975700
Knowles1979   -0.1283270 -0.2849441  0.02829000
Ramfjord1987  -0.3077010 -0.4650393 -0.15036267
Becker1988    -0.3439279 -0.5948634 -0.09299245

> model <- mvmeta(cbind(PD,AL)~pubyear,S=berkey98[6:8],data=berkey98,
+   lab=list(mlab=trial),method="ml")

> summary(model)
MULTIVARIATE RANDOM-EFFECTS META-ANALYSIS
Dimensions: 2
Studies: 5
Estimation method: ML
Variance-covariance matrix Psi: unstructured

Fixed effects
PD : 
         Estimate   StdErr        z  p-value  95%ci.lb  95%ci.ub   
(Int)     -1.5822  30.6137  -0.0517   0.9588  -61.5839   58.4195   
pubyear    0.0010   0.0154   0.0631   0.9497   -0.0293    0.0312   

AL : 
         Estimate   StdErr        z  p-value  95%ci.lb  95%ci.ub   
(Int)     21.1354  48.2512   0.4380   0.6614  -73.4353  115.7061   
pubyear   -0.0108   0.0243  -0.4450   0.6563   -0.0585    0.0369   

Variance components: between-studies stdev and correlation matrix
    StdDev      PD      AL
PD  0.0897  1.0000       .
AL  0.1582  0.6590  1.0000

Multivariate Cochran Q-test for residual heterogeneity:
Q = 125.7557 (df = 6), p-value = <0.0001

10 observations, 4 fixed and 3 random parameters
logLik     AIC     BIC  
6.0043  1.9914  4.1095  

> qtest(model)
Multivariate Cochran Q-test for residual heterogeneity:
Q = 125.7557 (df = 6), p-value = <0.0001

> newdata <- data.frame(pubyear=1985:1989)

> predict(model,newdata,se=TRUE)
$pred
            PD         AL
[1,] 0.3498409 -0.3567822
[2,] 0.3508143 -0.3676094
[3,] 0.3517876 -0.3784367
[4,] 0.3527610 -0.3892640
[5,] 0.3537343 -0.4000913

$se
             PD         AL
[1,] 0.05792492 0.08828305
[2,] 0.06631198 0.10185017
[3,] 0.07691408 0.11889814
[4,] 0.08894261 0.13814422
[5,] 0.10189365 0.15879116