Meta Analysis Younghun Han

Meta Analysis

• Younghun Han

• Department of Epidemiology

• UT MD Anderson Cancer Center

Introduction

• Meta-analysis is the statistical procedure for combining the results of several studies that address a set of related research hypotheses.

• When the treatment effect (or effect size) is consistent from one study to the next, meta-analysis can be used to identify this common effect
• When the effect is varies from one study to the next, meta-analysis may be used to identify reason for the variation

• In epidemiological terms, meta-analysis provide a better estimate of effect size.

• A meta-analysis can increase power and provide standards of reporting results in genome-wide association studies (GWAS)

Terminology

• Effect size : In statistics, effect size is a measure of the strength of the relationship between two variables.

• Binary outcomes : odds ratio, relative risk, risk difference
• Continuous outcomes: difference in means, standardized difference in means, ∙ ∙ ∙

• Summary effect size

• (pooled, overall, or combined effect size)

• Weighted average = ∑i(effecti × weighti) / ∑weighti
• weight : sample size, Inverse of the variance, Quality …..

Terminology (continuous)

• Fixed effect model (assume that the studies are homogeneous)

• Mantel-Haenszel
• Peto
• Inverse Variance

• Random effect model

• DerSimonian and Laird
• When the studies are found to be homogeneous, random and fixed effects models are indistinguishable.

• Test for heterogeneity

• Cochrans’s Q statistics
• I2

Terminology (continuous)

• Forest plot

Terminology (continuous)

• Publication bias

• Publication bias is the tendency to publish research with a positive outcome more frequently than research with a negative outcome.
• Publication bias can lead to misleading results
• Check publication bias by Funnel plots

Terminology (continuous)

• Funnel plot

• Effect size vs Sample size
• Effect size vs S.E.
• Effect size vs 1/S.E. (precision)
• (a) (b)

Mantel-Haenszel methods

• Most commonly used method for meta-analysis

• Need 2×2 frequency table for Mantel-Haenszel

Mantel-Haenszel methods (continuous)

• summary effectMH

• =∑i(effecti ×weighti)/ ∑i weighti

• For OR: ORi = (ai×di)/ (bi×ci) , weighti= (bi×ci)/ni

• For RR: RRi = [ai/(ai+ci)]/[bi/(bi×di)] , weighti=(ai+ci)bi/ni

• For RD: RDi = [ai/(ai+ci)]-[bi/(bi×di)] , weighti=(ai+ci)(bi +di) /ni

• where ni = ai + bi + ci + di

Meta-Analysis using R

• Datasets : Four GWAS for Lung Cancer case-control data (US, Canada, France, and UK)

• Example1 : rs2838891

Meta-Analysis using R (continuous)

• Fixed effect meta-analysis (Mantel-Haenszel)

• > LungOR <- meta.MH(data[,1],data[,2],data[,3],data[,4],names=name)

• > # data[,1]=Number of subjects in treated/exposed group

• > # data[,2]=Number of subjects in control group

• > # data[,3]=Number of events in treated/exposed group

• > # data[,4]=Number of events in control group

• > # names = names or labels for studies

• >

• > summary(LungOR)

• Fixed effects ( Mantel-Haenszel ) meta-analysis

• Call: meta.MH(ntrt = data[, 1], nctrl = data[, 2], ptrt = data[, 3],

• pctrl = data[, 4], names = name)

• ----------------------------------------------

• OR (lower 95% upper)

• US 0.97 0.86 1.09

• Canada 1.02 0.83 1.24

• France 1.05 0.96 1.14

• UK 2.70 2.42 3.01

• ---------------------------------------------

• Mantel-Haenszel OR =1.34 95% CI ( 1.27,1.41 )

• Test for heterogeneity: X^2( 3 ) = 231.71 ( p-value 0 )

Meta-Analysis using R (continuous)

• >plot(LungOR, ylab="") # Forest Plot

Meta-Analysis using R (continuous)

• tabletext<-cbind(c("Study",NA,LungOR$names,NA,"Summary"),

• c("OR", NA, format(exp(LungOR$logOR),digits=2), NA, format(exp(LungOR$logMH),digits=3)),

• c( NA,NA,format(exp(LungOR$logOR-LungOR$selogOR*1.96),digits=2), NA, format(exp(LungOR$logMH-LungOR$selogMH*1.96), digits=3 )),

• c("(95% CI)", NA, format(exp(LungOR$logOR+LungOR$selogOR*1.96), digits=3), NA, format(exp(LungOR$logMH+LungOR$selogMH*1.96), digits=3 )))

• m<- c(NA,NA,LungOR$logOR,NA,LungOR$logMH)

• l<- m-c(NA,NA,LungOR$selogOR,NA,LungOR$selogMH)*1.96

• u<- m+c(NA,NA,LungOR$selogOR,NA,LungOR$selogMH)*1.96

• forestplot(tabletext, m, l, u, zero=0,

• is.summary=c( TRUE, rep(FALSE,6),TRUE),

• clip=c(log(0.4),log(3.5)), xlab="Odds Ratio", xlog=TRUE,

• col=meta.colors(box="royalblue",line="darkblue", summary="royalblue"))

• # xlog=TRUE : x-axis tick marks are exponentiated

Meta-Analysis using R (continuous)

Meta-Analysis using R (continuous)

• Random effect meta-analysis ( DerSimonian-Laird )

• > LungDSL <- meta.DSL(data[,1],data[,2],data[,3],data[,4],names=name)

• > summary(LungDSL)

• Random effects ( DerSimonian-Laird ) meta-analysis

• Call: meta.DSL(ntrt = data[, 1], nctrl = data[, 2], ptrt = data[, 3],

• pctrl = data[, 4], names = name)

• --------------------------------------------

• OR (lower 95% upper)

• US 0.97 0.86 1.09

• Canada 1.02 0.83 1.24

• France 1.05 0.96 1.14

• UK 2.70 2.42 3.01

• -------------------------------------------

• SummaryOR= 1.29 95% CI ( 0.77,2.16 )

• Test for heterogeneity: X^2( 3 ) = 231.58 ( p-value 0 )

• check publication bias

• >funnelplot()

Meta-Analysis using Stata

• install commands

• ssc install metan

• ssc install metafunnel

• ssc install metabias

• metan (the main meta-analysis routine) requires either two, three, four or six variables to be declared.

• Two variables : effect estimate and standard error

• Three variables: effect estimate and its lower and upper confidence interval

• Four variables: the number of events and non-events in the experimental group followed by those of the control group, and analysis of binary data is performed on the 2x2 table.

• Six variables : the data are assumed continuous sample size, mean and standard deviation of the experimental group followed by those of the control group.

• metafunnel plots funnel plots.

• metabias performs the test for publication bias

Meta-Analysis using Stata (continuous)

• Example1 : rs2838891

• . metan case_risk con_risk case_ref con_ref, or label(namevar=study) xlabel(0.5 , 3.5 ) texts(200) classic

• Study | OR [95% Conf. Interval] % Weight

• ---------------------+--------------------------------------------------------

• US | 0.969 0.860 1.091 25.08

• Canada | 1.015 0.835 1.235 8.99

• France | 1.046 0.961 1.139 46.96

• UK | 2.700 2.424 3.007 18.98

• ---------------------+--------------------------------------------------------

• M-H pooled OR | 1.338 1.266 1.413 100.00

• ---------------------+--------------------------------------------------------

• Heterogeneity chi-squared = 231.71 (d.f. = 3) p = 0.000

• I-squared (variation in OR attributable to heterogeneity) = 98.7%

• Test of OR=1 : z= 10.39 p = 0.000

Meta-Analysis using Stata (continuous)

Meta-Analysis using Stata (continuous)

• . metan case_risk con_risk case_ref con_ref, or random label(namevar=study)

• xlabel(0.5, 3.5 ) texts(200) classic

• Study | OR [95% Conf. Interval] % Weight

• ---------------------+--------------------------------------------------------

• US | 0.969 0.860 1.091 25.09

• Canada | 1.015 0.835 1.235 24.52

• France | 1.046 0.961 1.139 25.25

• UK | 2.700 2.424 3.007 25.15

• ---------------------+--------------------------------------------------------

• D+L pooled OR | 1.293 0.774 2.159 100.00

• ---------------------+--------------------------------------------------------

• Heterogeneity chi-squared = 231.71 (d.f. = 3) p = 0.000

• I-squared (variation in OR attributable to heterogeneity) = 98.7%

• Estimate of between-study variance Tau-squared = 0.2691

• Test of OR=1 : z= 0.98 p = 0.326

Meta-Analysis using Stata (continuous)

Meta-Analysis using Stata (continuous)

• Example2 : rs1051730

Meta-Analysis using Stata (continuous)

• . metan case_risk con_risk case_ref con_ref, or label(namevar=study) texts(200) classic

• Study | OR [95% Conf. Interval] % Weight

• ---------------------+---------------------------------------------------

• US | 1.313 1.163 1.481 21.08

• Canada | 1.272 1.039 1.558 7.53

• France | 1.302 1.194 1.420 40.51

• UK | 1.295 1.172 1.432 30.89

• ---------------------+---------------------------------------------------

• M-H pooled OR | 1.300 1.230 1.374 100.00

• ---------------------+---------------------------------------------------

• Heterogeneity chi-squared = 0.07 (d.f. = 3) p = 0.995

• I-squared (variation in OR attributable to heterogeneity) = 0.0%

• Test of OR=1 : z= 9.27 p = 0.000

Meta-Analysis using Stata (continuous)

Meta-Analysis using Stata (continuous)

• . metan case_risk con_risk case_ref con_ref, or random label(namevar=study) texts(200) classic

• Study | OR [95% Conf. Interval] % Weight

• ---------------------+---------------------------------------------------

• US | 1.313 1.163 1.481 21.15

• Canada | 1.272 1.039 1.558 7.49

• France | 1.302 1.194 1.420 40.70

• UK | 1.295 1.172 1.432 30.66

• ---------------------+---------------------------------------------------

• D+L pooled OR | 1.300 1.230 1.374 100.00

• ---------------------+---------------------------------------------------

• Heterogeneity chi-squared = 0.07 (d.f. = 3) p = 0.995

• I-squared (variation in OR attributable to heterogeneity) = 0.0%

• Estimate of between-study variance Tau-squared = 0.0000

• Test of OR=1 : z= 9.27 p = 0.000

Meta-Analysis using Stata (continuous)

• . gen logor=ln((case_risk*con_ref)/(case_ref*con_risk))

• . gen selogor=sqrt(1/case_risk + 1/case_ref + 1/con_risk +1/con_ref)

• . metan logor selogor, eform effect(Odds ratio) xlabel(0.5, 3.5 ) texts(200)

• classic

• Study | ES [95% Conf. Interval] % Weight

• ---------------------+-------------------------------------------------------

• 1 | 1.313 1.163 1.481 21.15

• 2 | 1.272 1.039 1.558 7.49

• 3 | 1.302 1.194 1.420 40.70

• 4 | 1.295 1.172 1.432 30.66

• ---------------------+-------------------------------------------------------

• I-V pooled ES | 1.300 1.230 1.374 100.00

• ---------------------+-------------------------------------------------------

• Heterogeneity chi-squared = 0.07 (d.f. = 3) p = 0.995

• I-squared (variation in ES attributable to heterogeneity) = 0.0%

• Test of ES=1 : z= 9.27 p = 0.000

• Thank you!!!