berkey98: Five Published Trials on Periodontal Disease
In mvmeta: Multivariate and Univariate Meta-Analysis and Meta-Regression

Description Usage Format Source Examples

The dataset contains the results of 5 published trials comparing surgical and non-surgical treatments for medium-severity periodontal disease, one year after treatment. The 2 estimated outcomes are average improvements (surgical minus non-surgical, in mm) in probing depth (PD) and attachment level (AL).

berkey98

A data frame with 5 observations on the following 7 variables:

pubyear: publication year of the trial.
npat: number of patients included in the trial.
PD: estimated improvement of surgical versus non-surgical treatments in probing depth (mm).
AL: estimated improvement of surgical versus non-surgical treatments in attachment level (mm).
var_PD: variance of the estimated outcome for PD.
cov_PD_AL: covariance of the estimated outcomes for PD and AL.
var_AL: variance of the estimated outcome for AL.

Row names specify the author of the paper reporting the results of each trial.

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

Berkey C. S., Antczak-Bouckoms A., et al. (1995). Multiple-outcomes meta-analysis of treatments for periodontal disease. Journal of Dental Research. 74(4):1030–1039.

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].

### REPRODUCE THE RESULTS IN BERKEY ET AL. (1998)

# INSPECT THE DATA
berkey98

# FIXED-EFFECTS
year <- berkey98$pubyear - 1983
model <- mvmeta(cbind(PD,AL)~year,S=berkey98[5:7],data=berkey98,method="fixed")
print(summary(model),digits=3)

# GLS MODEL (VARIANCE COMPONENTS) 
model <- mvmeta(cbind(PD,AL)~year,S=berkey98[5:7],data=berkey98,method="vc",
  control=list(vc.adj=FALSE))
print(summary(model),digits=3)
round(model$Psi,3)

# ML MODEL
model <- mvmeta(cbind(PD,AL)~year,S=berkey98[5:7],data=berkey98,method="ml")
print(summary(model),digits=3)
round(model$Psi,3)

This is mvmeta 0.4.11. For an overview type: help('mvmeta-package').
          pubyear npat   PD    AL var_PD cov_PD_AL var_AL
Pihlstrom    1983   14 0.47 -0.32 0.0075    0.0030 0.0077
Lindhe       1982   15 0.20 -0.60 0.0057    0.0009 0.0008
Knowles      1979   78 0.40 -0.12 0.0021    0.0007 0.0014
Ramfjord     1987   89 0.26 -0.31 0.0029    0.0009 0.0015
Becker       1988   16 0.56 -0.39 0.0148    0.0072 0.0304
Call:  mvmeta(formula = cbind(PD, AL) ~ year, S = berkey98[5:7], data = berkey98, 
    method = "fixed")

Multivariate fixed-effects meta-regression
Dimension: 2

Fixed-effects coefficients
PD : 
             Estimate  Std. Error       z  Pr(>|z|)  95%ci.lb  95%ci.ub     
(Intercept)     0.305       0.029  10.627     0.000     0.249     0.361  ***
year           -0.005       0.008  -0.605     0.545    -0.021     0.011     
AL : 
             Estimate  Std. Error        z  Pr(>|z|)  95%ci.lb  95%ci.ub     
(Intercept)    -0.399       0.019  -21.133     0.000    -0.436    -0.362  ***
year           -0.010       0.006   -1.571     0.116    -0.023     0.003     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Multivariate Cochran Q-test for residual heterogeneity:
Q = 125.756 (df = 6), p-value = 0.000
I-square statistic = 95.2%

5 studies, 10 observations, 4 fixed and 0 random-effects parameters
 logLik      AIC      BIC  
-44.206   96.412   97.623  

Call:  mvmeta(formula = cbind(PD, AL) ~ year, S = berkey98[5:7], data = berkey98, 
    method = "vc", control = list(vc.adj = FALSE))

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)     0.359       0.075  4.782     0.000     0.212     0.507  ***
year            0.005       0.022  0.240     0.811    -0.038     0.049     
AL : 
             Estimate  Std. Error       z  Pr(>|z|)  95%ci.lb  95%ci.ub     
(Intercept)    -0.336       0.083  -4.040     0.000    -0.499    -0.173  ***
year           -0.011       0.026  -0.445     0.656    -0.062     0.039     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Between-study random-effects (co)variance components
Structure: General positive-definite
    Std. Dev   Corr
PD     0.147     PD
AL     0.169  0.525

Multivariate Cochran Q-test for residual heterogeneity:
Q = 125.756 (df = 6), p-value = 0.000
I-square statistic = 95.2%

5 studies, 10 observations, 4 fixed and 1 random-effects parameters

      PD    AL
PD 0.022 0.013
AL 0.013 0.028
Call:  mvmeta(formula = cbind(PD, AL) ~ year, S = berkey98[5:7], data = berkey98, 
    method = "ml")

Multivariate random-effects meta-regression
Dimension: 2
Estimation method: ML

Fixed-effects coefficients
PD : 
             Estimate  Std. Error      z  Pr(>|z|)  95%ci.lb  95%ci.ub     
(Intercept)     0.348       0.052  6.694     0.000     0.246     0.450  ***
year            0.001       0.015  0.063     0.950    -0.029     0.031     
AL : 
             Estimate  Std. Error       z  Pr(>|z|)  95%ci.lb  95%ci.ub     
(Intercept)    -0.335       0.079  -4.261     0.000    -0.489    -0.181  ***
year           -0.011       0.024  -0.445     0.656    -0.059     0.037     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Between-study random-effects (co)variance components
Structure: General positive-definite
    Std. Dev   Corr
PD     0.090     PD
AL     0.158  0.659

Multivariate Cochran Q-test for residual heterogeneity:
Q = 125.756 (df = 6), p-value = 0.000
I-square statistic = 95.2%

5 studies, 10 observations, 4 fixed and 3 random-effects parameters
logLik     AIC     BIC  
 6.004   1.991   4.110  

      PD    AL
PD 0.008 0.009
AL 0.009 0.025