Statistical Models for Overviews of Reviews

Abstract

Since the rise of evidence-based medicine movement, systematic reviews and meta-analyses have been widely used for synthesis of evidence on beneficial and/or harmful effects of different treatments. Moreover, with the advances in medical science and knowledge, many new treatments and interventions become available, and identifying how best to compare multiple treatments is an important challenge to evidence-based medicine. Although network meta-analysis is a very powerful tool for comparing multiple treatments in terms of their benefits or harms, it requires a lot of resources and a substantial amount of time for literature search, data extraction and statistical analysis. If a decision based on currently available evidence needs to be made urgently, it might not be feasible to undertake network meta-analysis within a short period of time. Nevertheless, many traditional pairwise meta-analyses of a good quality may have been published, and there are great overlaps in literature search and data extractions between those pairwise meta-analyses and a network meta-analysis. If results of traditional meta-analysis can be used for an expedient comparison of multiple treatments, this would help researchers spend less time and resources in reaching a decision within a shorter period of time. Statistical models for an umbrella review are similar to those for a network meta-analysis, as they both aim to compare multiple treatments. Both Bayesian approach and generalized least-squares approach can be used to conduct statistical analysis for an umbrella review. This will be especially useful for policy makers or busy clinicians to obtain up-to-date evidence to make an informed decision.

Appendices

Appendix 10.1: WinBUGS Code of Umbrella Review

#MODEL

model{

for (i in 1:N){

LOR[i]~dnorm(lor[comp[i],treat[i]],prec[i])

prec[i]<-1/var[i]

var[i]<-sd[i]*sd[i]

sd[i]<-(LUCI[i]-LLCI[i])/3.92

dev[i]<-(LOR[i]-lor[comp[i],treat[i]])*(LOR[i]-lor[comp[i],treat[i]])*prec[i]

}

resdev<-sum(dev[]) #summed residual deviance

d[1]<-0

for (k in 2:NT){

d[k]~dnorm(0,0.0001) #vague prior for basic parameters

}

for (k in 1:NT){

best[k]<-equals(rank(d[],k),1)

}

for (c in 1:NT-1){

for (k in (c+1):NT){

lor[c,k]<-d[k]-d[c]

or[c,k]<-exp(lor[c,k])

}

}

}

#DATA for FE

list(N=4, NT=4,

comp=c(1,2,2,3),

treat=c(2,3,4,4),

LOR=c(-1.993,0.279,1.14,0.83),

LLCI=c(-2.583,0.038,0.868,0.359),

LUCI=c(-1.402,0.521,1.412,1.3)

)

#DATA for RE

list(N=4, NT=4,

comp=c(1,2,2,3),

treat=c(2,3,4,4),

LOR=c(-2.528,0.412,1.453,1.011),

LLCI=c(-4.345,-0.166,0.58,-0.839),

LUCI=c(-0.711,0.991,2.327,2.86)

)

#INITIAL VALUES

list(

d=c(NA, 0,0,0)

)

Appendix 10.2: Stata Codes for Statistical Analysis of Umbrella Reviews

Using weighted least squares (WLS) method

vwls d t12-t14, noconstant sd(se)

Using Stata command GLLAMM

generate lns = ln(se)

* set up lns as the lower level residual variance

eq het: lns

* set constraint 1: the coefficient for lns is 1

constraint define 1 [lns1]lns=1

* generate a new variable cons which is a vector of 1

gene cons=1

* set up random intercept model for treatment effect

eq int: cons

* constrain the variance of random effects to 0, so it becomes a fixed effect analysis

constraint define 2 [stud1]_cons=0

* run the fixed effect analysis using gllamm

gllamm d t12-t14, noconstant i(study) constraint(1 2) adapt s(het) nip(5)