Meta Analysis Younghun Han


Download 451 b.
Sana02.03.2018
Hajmi451 b.


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)

  • Random effect model

  • 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



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!!!




Do'stlaringiz bilan baham:


Ma'lumotlar bazasi mualliflik huquqi bilan himoyalangan ©fayllar.org 2017
ma'muriyatiga murojaat qiling