Berkey98: Five Published Trails from Berkey et al. (1998)

Description Usage Details Source Examples

Description

The data set includes five published trials, reported by Berkey et al. (1998), comparing surgical and non-surgical treatments for medium-severity periodontal disease, one year after treatment.

Usage

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Details

The variables are:

trial

Trial number

pub_year

Publication year

no_of_patients

Number of patients

PD

Patient improvements (mm) in probing depth

AL

Patient improvements (mm) in attachment level

var_PD

Sampling variance of PD

cov_PD_AL

Sampling covariance between PD and AD

var_AL

Sampling variance of AL

Source

Berkey, C. S., Hoaglin, D. C., Antczak-Bouckoms, A., Mosteller, F, & Colditz, G. A. (1998). Meta-analysis of multiple outcomes by regression with random effects. Statistics in Medicine, 17, 2537-2550.

Examples

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data(Berkey98)

#### ML estimation method
## Multivariate meta-analysis
x <- meta(y=cbind(PD, AL), v=cbind(var_PD, cov_PD_AL, var_AL), data=Berkey98)
x <- rerun(x)
summary(x)
plot(x)

## Plot individual studies proportional to the weights
plot(x, study.weight.plot=TRUE)

## Include forest plot from the metafor package
library(metafor)
plot(x, diag.panel=TRUE, main="Multivariate meta-analysis",
     axis.label=c("PD", "AL"))
     forest( rma(yi=PD, vi=var_PD, data=Berkey98) )
     title("Forest plot of PD")
     forest( rma(yi=AL, vi=var_AL, data=Berkey98) )
     title("Forest plot of AL")

## Multivariate meta-analysis with "publication year-1979" as the predictor
summary( meta(y=cbind(PD, AL), v=cbind(var_PD, cov_PD_AL, var_AL),
              x=scale(pub_year, center=1979), data=Berkey98,
              RE.lbound=NA) )

## Multivariate meta-analysis with equality constraint on the regression coefficients
summary( meta(y=cbind(PD, AL), v=cbind(var_PD, cov_PD_AL, var_AL),
              x=scale(pub_year, center=1979), data=Berkey98,
              coef.constraints=matrix(c("0.3*Eq_slope", "0.3*Eq_slope"),
              nrow=2)) )

#### REML estimation method
## Multivariate meta-analysis
summary( reml(y=cbind(PD, AL), v=cbind(var_PD, cov_PD_AL, var_AL),
              data=Berkey98,
              model.name="Multivariate meta analysis with REML") )

## Multivariate meta-analysis with "publication year-1979" as the predictor
## Diagonal structure for the variance component
summary( reml(y=cbind(PD, AL), v=cbind(var_PD, cov_PD_AL, var_AL),
              RE.constraints=Diag(c("1e-5*Tau2_1_1", "1e-5*Tau2_2_2")),
              x=scale(pub_year, center=1979), data=Berkey98) )

Example output

Loading required package: OpenMx
To take full advantage of multiple cores, use:
  mxOption(NULL, 'Number of Threads', parallel::detectCores()) #now
  Sys.setenv(OMP_NUM_THREADS=parallel::detectCores()) #before library(OpenMx)
"SLSQP" is set as the default optimizer in OpenMx.
mxOption(NULL, "Gradient algorithm") is set at "central".
mxOption(NULL, "Optimality tolerance") is set at "6.3e-14".
mxOption(NULL, "Gradient iterations") is set at "2".

Beginning initial fit attempt

 Lowest minimum so far:  -11.6813137695501

Solution found



Solution found!  Final fit=-11.681314 (started at -11.681314)  (1 attempt(s): 1 valid, 0 errors)


Call:
meta(y = cbind(PD, AL), v = cbind(var_PD, cov_PD_AL, var_AL), 
    data = Berkey98)

95% confidence intervals: z statistic approximation
Coefficients:
             Estimate  Std.Error     lbound     ubound z value  Pr(>|z|)    
Intercept1  0.3448392  0.0536312  0.2397239  0.4499544  6.4298 1.278e-10 ***
Intercept2 -0.3379381  0.0812479 -0.4971812 -0.1786951 -4.1593 3.192e-05 ***
Tau2_1_1    0.0070020  0.0090497 -0.0107351  0.0247391  0.7737    0.4391    
Tau2_2_1    0.0094607  0.0099698 -0.0100797  0.0290010  0.9489    0.3427    
Tau2_2_2    0.0261445  0.0177409 -0.0086270  0.0609161  1.4737    0.1406    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Q statistic on the homogeneity of effect sizes: 128.2267
Degrees of freedom of the Q statistic: 8
P value of the Q statistic: 0

Heterogeneity indices (based on the estimated Tau2):
                             Estimate
Intercept1: I2 (Q statistic)   0.6021
Intercept2: I2 (Q statistic)   0.9250

Number of studies (or clusters): 5
Number of observed statistics: 10
Number of estimated parameters: 5
Degrees of freedom: 5
-2 log likelihood: -11.68131 
OpenMx status1: 0 ("0" or "1": The optimization is considered fine.
Other values may indicate problems.)
Loading required package: Matrix

Attaching package: 'Matrix'

The following objects are masked from 'package:OpenMx':

    %&%, expm

Loading 'metafor' package (version 2.0-0). For an overview 
and introduction to the package please type: help(metafor).

Call:
meta(y = cbind(PD, AL), v = cbind(var_PD, cov_PD_AL, var_AL), 
    x = scale(pub_year, center = 1979), data = Berkey98, RE.lbound = NA)

95% confidence intervals: z statistic approximation
Coefficients:
             Estimate  Std.Error     lbound     ubound z value  Pr(>|z|)    
Intercept1  0.3440001  0.0857659  0.1759020  0.5120982  4.0109 6.048e-05 ***
Intercept2 -0.2918175  0.1312797 -0.5491208 -0.0345141 -2.2229   0.02622 *  
Slope1_1    0.0063540  0.1078235 -0.2049762  0.2176842  0.0589   0.95301    
Slope2_1   -0.0705888  0.1620966 -0.3882922  0.2471147 -0.4355   0.66322    
Tau2_1_1    0.0080405  0.0101206 -0.0117955  0.0278766  0.7945   0.42692    
Tau2_2_1    0.0093413  0.0105515 -0.0113392  0.0300218  0.8853   0.37599    
Tau2_2_2    0.0250135  0.0170788 -0.0084603  0.0584873  1.4646   0.14303    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Q statistic on the homogeneity of effect sizes: 128.2267
Degrees of freedom of the Q statistic: 8
P value of the Q statistic: 0

Explained variances (R2):
                              y1     y2
Tau2 (no predictor)    0.0070020 0.0261
Tau2 (with predictors) 0.0080405 0.0250
R2                     0.0000000 0.0433

Number of studies (or clusters): 5
Number of observed statistics: 10
Number of estimated parameters: 7
Degrees of freedom: 3
-2 log likelihood: -12.00859 
OpenMx status1: 0 ("0" or "1": The optimization is considered fine.
Other values may indicate problems.)

Call:
meta(y = cbind(PD, AL), v = cbind(var_PD, cov_PD_AL, var_AL), 
    x = scale(pub_year, center = 1979), data = Berkey98, coef.constraints = matrix(c("0.3*Eq_slope", 
        "0.3*Eq_slope"), nrow = 2))

95% confidence intervals: z statistic approximation
Coefficients:
             Estimate  Std.Error     lbound     ubound z value  Pr(>|z|)    
Intercept1  0.3437612  0.0849829  0.1771978  0.5103245  4.0451 5.231e-05 ***
Intercept2 -0.3390010  0.1041006 -0.5430344 -0.1349677 -3.2565  0.001128 ** 
Eq_slope    0.0016748  0.1024443 -0.1991123  0.2024620  0.0163  0.986956    
Tau2_1_1    0.0070474  0.0094638 -0.0115013  0.0255962  0.7447  0.456471    
Tau2_2_1    0.0095165  0.0105668 -0.0111940  0.0302269  0.9006  0.367800    
Tau2_2_2    0.0261979  0.0180773 -0.0092330  0.0616288  1.4492  0.147278    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Q statistic on the homogeneity of effect sizes: 128.2267
Degrees of freedom of the Q statistic: 8
P value of the Q statistic: 0

Explained variances (R2):
                              y1     y2
Tau2 (no predictor)    0.0070020 0.0261
Tau2 (with predictors) 0.0070474 0.0262
R2                     0.0000000 0.0000

Number of studies (or clusters): 5
Number of observed statistics: 10
Number of estimated parameters: 6
Degrees of freedom: 4
-2 log likelihood: -11.68158 
OpenMx status1: 0 ("0" or "1": The optimization is considered fine.
Other values may indicate problems.)

Call:
reml(y = cbind(PD, AL), v = cbind(var_PD, cov_PD_AL, var_AL), 
    data = Berkey98, model.name = "Multivariate meta analysis with REML")

95% confidence intervals: z statistic approximation
Coefficients:
          Estimate Std.Error    lbound    ubound z value Pr(>|z|)
Tau2_1_1  0.011733  0.013645 -0.015011  0.038477  0.8599   0.3899
Tau2_2_1  0.011916  0.014416 -0.016340  0.040172  0.8266   0.4085
Tau2_2_2  0.032651  0.024402 -0.015176  0.080479  1.3380   0.1809

Number of studies (or clusters): 5
Number of observed statistics: 8
Number of estimated parameters: 3
Degrees of freedom: 5
-2 log likelihood: -18.86768 
OpenMx status1: 0 ("0" or "1": The optimization is considered fine.
Other values may indicate problems.)

Call:
reml(y = cbind(PD, AL), v = cbind(var_PD, cov_PD_AL, var_AL), 
    x = scale(pub_year, center = 1979), data = Berkey98, RE.constraints = Diag(c("1e-5*Tau2_1_1", 
        "1e-5*Tau2_2_2")))

95% confidence intervals: z statistic approximation
Coefficients:
          Estimate Std.Error    lbound    ubound z value Pr(>|z|)
Tau2_1_1  0.019041  0.021268 -0.022643  0.060725  0.8953   0.3706
Tau2_2_2  0.039450  0.033467 -0.026144  0.105045  1.1788   0.2385

Number of studies (or clusters): 5
Number of observed statistics: 6
Number of estimated parameters: 2
Degrees of freedom: 4
-2 log likelihood: -10.69275 
OpenMx status1: 0 ("0" or "1": The optimization is considered fine.
Other values may indicate problems.)

metaSEM documentation built on May 18, 2021, 1:06 a.m.