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.

1 |

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

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.

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 | ```
data(Berkey98)
#### ML estimation method
## Multivariate meta-analysis
summary( meta(y=cbind(PD, AL), v=cbind(var_PD, cov_PD_AL, var_AL),
data=Berkey98, I2=c("I2q", "I2hm", "I2am")) )
## 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
summary( reml(y=cbind(PD, AL), v=cbind(var_PD, cov_PD_AL, var_AL),
x=scale(pub_year, center=1979), data=Berkey98) )
``` |

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