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Lecture 8: Systematic Reviews and Meta-analysis Christopher S. Hollenbeak, PhD Jane R. Schubart, PhD The Outcomes Research Toolbox

Homework

•  Stata Example: –  stset surv_days, failure(died) –  sts test age_cat –  sts graph, by(age_cat) title("Age") xtitle("Days Since Liver Transplant") ytitle("Percent Surviving") text(.6 2300 "P = 0.0007")

–  stcox age4049 age5059 age60 female black ab1 ab2 ab3 ab4 obese rbc ssi

Homework

P = 0.0007

0.00

0.25

0.50

0.75

1.00

Perc

ent S

urvi

ving

0 500 1000 1500 2000 2500Days Since Liver Transplant

1. 18-39 2. 40-493. 50-59 4. 60+

Age

P = 0.40

0.00

0.25

0.50

0.75

1.00

Perc

ent S

urvi

ving

0 500 1000 1500 2000 2500Days Since Liver Transplant

female = 0 female = 1

Sex

P = 0.04

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0.50

0.75

1.00

Perc

ent S

urvi

ving

0 500 1000150020002500Days Since Liver Transplant

ssi = 0 ssi = 1

Surgical Site Infection

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Homework No. of subjects = 753 Number of obs = 753 No. of failures = 143 Time at risk = 1114206 LR chi2(12) = 34.43 Log likelihood = -899.46794 Prob > chi2 = 0.0006 ------------------------------------------------------------------------------ _t | Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- age4049 | 1.51421 .4065148 1.55 0.122 .8946787 2.562745 age5059 | 2.040969 .5246711 2.78 0.006 1.233157 3.37796 age60 | 2.581395 .7049597 3.47 0.001 1.511464 4.408707 female | .9352378 .1619229 -0.39 0.699 .6661144 1.313092 black | .6976266 .3597143 -0.70 0.485 .2539344 1.916569 ab1 | .2514728 .3085398 -1.13 0.261 .0227052 2.785203 ab2 | .990665 .7374977 -0.01 0.990 .2302779 4.261881 ab3 | 1.200048 .8678841 0.25 0.801 .2908057 4.952155 ab4 | .9637897 .6958632 -0.05 0.959 .2341039 3.967857 obese | .7716182 .1915267 -1.04 0.296 .4743753 1.255113 rbc | 1.04657 .0192709 2.47 0.013 1.009473 1.08503 ssi | 1.399269 .2393173 1.96 0.049 1.000737 1.956512 ------------------------------------------------------------------------------

Homework

•  R Example: –  sv2 <- Surv(dat1$surv_days, dat1$died) ~ dat1$ssi

–  survdiff(sv2) –  plot(survfit(sv2), xlab="Days since Treatment", ylab="Percent Surviving", lty=c(1,2), col=c("black","grey75"), lwd=1, cex=2, mark.time=FALSE)

–  legend(2000, 1, c("SSI","No SSI"), lty=c(1,2), col=c("black", "grey75"), bty="n")

–  text(2350, .68, "P = 0.0171”)

Homework

0 500 1000 1500 2000 2500

0.0

0.2

0.4

0.6

0.8

1.0

Age

Days since Treatment

Perc

ent S

urvi

ving

0−3940−4950−5960+

P = 0.0007

0 500 1000 1500 2000 2500

0.0

0.2

0.4

0.6

0.8

1.0

Sex

Days since Treatment

Perc

ent S

urvi

ving

MaleFemale

P = 0.39

0 500 1000 1500 2000 2500

0.0

0.2

0.4

0.6

0.8

1.0

Surgical Site Infection

Days since Treatment

Perc

ent S

urvi

ving

SSINo SSI

P = 0.04

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Homework coef exp(coef) se(coef) z Pr(>|z|) dat1$age4049 0.46468 1.59151 0.26674 1.742 0.081493 . dat1$age5059 0.74692 2.11049 0.25579 2.920 0.003500 ** dat1$age60 1.02901 2.79828 0.27009 3.810 0.000139 *** dat1$female -0.09111 0.91292 0.17189 -0.530 0.596081 dat1$black -0.30299 0.73861 0.51413 -0.589 0.555647 dat1$ab1 -1.39105 0.24881 1.22696 -1.134 0.256906 dat1$ab2 0.09354 1.09805 0.74310 0.126 0.899830 dat1$ab3 0.23941 1.27050 0.72305 0.331 0.740559 dat1$ab4 0.03385 1.03443 0.72137 0.047 0.962568 dat1$ssi 0.37948 1.46152 0.16992 2.233 0.025527 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 exp(coef) exp(-coef) lower .95 upper .95 dat1$age4049 1.5915 0.6283 0.94354 2.684 dat1$age5059 2.1105 0.4738 1.27836 3.484 dat1$age60 2.7983 0.3574 1.64813 4.751 dat1$female 0.9129 1.0954 0.65181 1.279 dat1$black 0.7386 1.3539 0.26964 2.023 dat1$ab1 0.2488 4.0191 0.02246 2.756 dat1$ab2 1.0981 0.9107 0.25591 4.711 dat1$ab3 1.2705 0.7871 0.30797 5.241 dat1$ab4 1.0344 0.9667 0.25158 4.253 dat1$ssi 1.4615 0.6842 1.04754 2.039 Concordance= 0.62 (se = 0.025 ) Rsquare= 0.037 (max possible= 0.912 ) Likelihood ratio test= 28.52 on 10 df, p=0.00149 Wald test = 25.47 on 10 df, p=0.004522 Score (logrank) test = 26.92 on 10 df, p=0.002683

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Introduction

•  A systematic review identifies previous studies of a research question and attempts to arrive at an overall conclusion about the body of evidence

•  The statistical methods used in a systematic review are called meta-analysis

•  Cornerstone of evidence based medicine and comparative effectiveness

Example

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Bahekar et al., Am Heart J 2007;154:830-7

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Overview

•  There are four elements of a well-executed meta-analysis

1.  Identify studies with potentially relevant data 2.  Impose eligibility restrictions on the studies 3.  Abstract the data 4.  Analyze and summarize the data

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Identify Relevant Studies

•  The most important part of the meta-analysis is the way that potential studies are identified

•  The method must be systematic and explicit

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Example

•  DuPont and Page (1991) •  Interested in the relationship between menopausal

estrogen replacement therapy and breast cancer •  Used MEDLINE to identify 556 articles

–  35 of these publications provided an estimate of breast cancer risk in women who took estrogen replacement therapy

–  The reference lists of these 35 publications and those in a review article led to identification of 15 more publications

•  50 articles were included in the study

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Search Algorithm

•  Search personal files •  Computerized search of databases

–  Eliminate from information in titles and abstracts –  Review remaining articles

•  Review bibliographies of articles and review articles

•  Consult experts in the field

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Publication Bias

•  Publication bias is the phenomenon that statistically significant results tend to be published

•  Funnel Plot is a visual tool for detecting publication bias

Funnel Plots

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0.0 0.5 1.0 1.5 2.0 2.5 3.0

05

1015

2025

Odds Ratio

Sam

ple

Size

0.0 0.5 1.0 1.5 2.0 2.5 3.0

05

1015

2025

Odds Ratio

Sam

ple

Size

This area is relatively empty, suggesting publication bias for small trials

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Publication Bias – What to do?

•  Try to get data from unpublished studies –  Abstracts from conference presentations

•  There are statistical methods to deal with publication bias but they are beyond the realm of this course

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Restricting the Literature

•  Not all studies should be included in the analysis •  Eligibility criteria should be explicitly defined prior

to the literature search •  Criteria should be based on sound reasoning, not

convenience

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Eligibility Considerations

1.  Study designs 2.  Years of publication 3.  Languages 4.  Choice among multiple publications 5.  Sample size 6.  Follow-up time 7.  Similarity of treatment or exposure 8.  Completeness of information

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Example

•  Yusuf et al. (1985) studied beta blockers after AMI –  Included all beta blockers –  Odds ratio for death was 0.77 (CI: 0.70-0.85)

•  OR for beta blockers with intrinsic sympathomimetic activity was 0.90 (CI: 0.77-1.05)

•  OR for beta blockers without intrinsic sympathomimetic activity was 0.69 (CI: 0.61-0.79)

–  Choice to include all studies biased the result toward the null

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Abstracting Data

•  Develop abstraction forms prior to starting the study

•  Develop a written protocol for abstraction •  Provide training to abstractors •  Assess inter-abstractor reliability •  Revise forms and protocol

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Statistical Methods

•  Goal is to –  Compute an overall measure of effect

•  Ratio measures (Odds, risk, rate ratios) •  Continuous measures

–  Then assess the variability of the overall effect •  Usually a 95% confidence interval

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Statistical Models

•  First choose a statistical model –  Fixed Effects model –  Random Effects model

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Fixed Effects Model

•  The fixed effect model assumes all studies are independently drawn from the same population

•  Only source of variation in between studies

yi = ✓ + ✏i

✏i ⇠ N(0,�2)

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Fixed Effects Model

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Random Effects Model •  The random effects model assumes each study is

drawn from its own distribution, with its own mean and variance

•  Captures both within and between study variation

yi = ✓i + ✏i

✓i ⇠ N(✓, ⌧2)

✏i ⇠ N(0,�2)

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Random Effects Model

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Dichotomous Effects

•  Data must be 2x2 table data •  Fixed effects

–  Mantel-Haenszel – Any risk measure: odds ratio, risk ratio, risk difference

–  Peto – Odds ratio only, events must be common

•  Random effects –  DerSimonian-Laird

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Continuous Effects

•  Fixed effects –  General Variance Based Method

•  Random effects –  Random Effects Model

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Fixed or Random Effects

•  Methods based on both fixed and random effects are available for both types of effects measure

•  The choice can have a significant effect on the results

•  In most cases, the random effects model is more conservative and is preferred –  Tradeoff is that these methods are more difficult to

implement

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Fixed or Random Effects

•  If the “true” model is fixed effects, then fixed and random give the correct answer

•  If the “true” model is random effects then only the random effects model is correct

•  Always safer to go with random effects

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Heterogeneity

•  The choice between fixed and random effects models is based on a statistical test for heterogeneity –  If the variance differs between studies, then there is

heterogeneity •  Stata and R both provide a Woolf test for

heterogeneity •  If heterogeneity is insignificant…fixed effects model •  If heterogeneity is significant…random effects

model

Inverse Variance Weighting

•  The overall effect estimated by either the fixed or random effects model is a weighted average of the individual effects

•  Weight is simply the inverse of the variance •  Variance term differs for fixed and random effects

models

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Example

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Graphical Presentation

•  A Forest Plot is the standard display for meta-analysis results

•  The goal is to convey an impression of the overall body of evidence

•  Important features –  Effect size is shown –  95% confidence intervals are shown –  Overall effect estimate is shown –  Reference to the null or overall effect is shown

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02

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Odds Ratio

Stud

y

Pooled

Study 9

Study 8

Study 7

Study 6

Study 5

Study 4

Study 3

Study 2

Study 1Favors Treatment Favors Control

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Problems

•  Larger error bars draw visual attention –  Larger error bars suggest weaker information

•  Could modify the symbols to reflect the amount of information –  Sized proportional to their weights

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Study 9

Study 8

Study 7

Study 6

Study 5

Study 4

Study 3

Study 2

Study 1Favors Treatment Favors Control

Conventional and cumulative meta-analysis of 33 trials of intravenous streptokinase for acute myocardial infarction.

Mulrow C D BMJ 1994;309:597-599 ©1994 by British Medical Journal Publishing Group

Stata Code

•  We use a user written package called “metan” to do meta-analysis

•  net search metan –  Look for sbe24_3 –  Click Install Package

•  Syntax is: –  2x2 table: metan a b c d, options –  Other: metan effect se_effect, options –  Important options: or rr fixed random peto

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Stata Example

•  Consider the BCG meta-analysis •  Meta-analysis of clinical trials for a vaccine for

tuberculosis •  Studies included randomized trials that reported

2x2 table data

Stata Example

•  Perform a Mantel-Haenzel meta-analysis of the trials –  metan treat_disease treat_no_disease control_disease control_no_disease

Stata Example Study | RR [95% Conf. Interval] % Weight ---------------------+--------------------------------------------------- 1 | 0.411 0.134 1.257 0.66 2 | 0.205 0.086 0.486 1.85 3 | 0.260 0.073 0.919 0.72 4 | 0.237 0.179 0.312 16.19 5 | 0.804 0.516 1.254 2.78 6 | 0.456 0.387 0.536 24.35 7 | 0.198 0.078 0.499 1.02 8 | 1.012 0.895 1.145 31.71 9 | 0.625 0.393 0.996 2.90 10 | 0.254 0.149 0.431 4.19 11 | 0.712 0.573 0.886 11.64 12 | 1.562 0.374 6.528 0.20 13 | 0.983 0.582 1.659 1.79 ---------------------+--------------------------------------------------- M-H pooled RR | 0.635 0.588 0.686 100.00 ---------------------+--------------------------------------------------- Heterogeneity chi-squared = 152.57 (d.f. = 12) p = 0.000 I-squared (variation in RR attributable to heterogeneity) = 92.1% Test of RR=1 : z= 11.53 p = 0.000

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Stata Example

Overall (I-squared = 92.1%, p = 0.000)

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9

6

8

2

Study

7

ID

12

5

4

10

11

1

3

0.64 (0.59, 0.69)

0.98 (0.58, 1.66)

0.63 (0.39, 1.00)

0.46 (0.39, 0.54)

1.01 (0.89, 1.14)

0.20 (0.09, 0.49)

0.20 (0.08, 0.50)

RR (95% CI)

1.56 (0.37, 6.53)

0.80 (0.52, 1.25)

0.24 (0.18, 0.31)

0.25 (0.15, 0.43)

0.71 (0.57, 0.89)

0.41 (0.13, 1.26)

0.26 (0.07, 0.92)

100.00

1.79

2.90

24.35

31.71

1.85

%

1.02

Weight

0.20

2.78

16.19

4.19

11.64

0.66

0.72

0.64 (0.59, 0.69)

0.98 (0.58, 1.66)

0.63 (0.39, 1.00)

0.46 (0.39, 0.54)

1.01 (0.89, 1.14)

0.20 (0.09, 0.49)

0.20 (0.08, 0.50)

RR (95% CI)

1.56 (0.37, 6.53)

0.80 (0.52, 1.25)

0.24 (0.18, 0.31)

0.25 (0.15, 0.43)

0.71 (0.57, 0.89)

0.41 (0.13, 1.26)

0.26 (0.07, 0.92)

100.00

1.79

2.90

24.35

31.71

1.85

%

1.02

Weight

0.20

2.78

16.19

4.19

11.64

0.66

0.72

1.0734 1 13.6

Stata Example

•  Is there significant heterogeneity? •  Solution: Use random effects model instead •  Also, report Odds Ratios instead of Risk Ratios •  metan treat_disease treat_no_disease control_disease control_no_disease, random or

Stata Example Study | OR [95% Conf. Interval] % Weight ---------------------+--------------------------------------------------- 1 | 0.391 0.121 1.262 5.12 2 | 0.189 0.077 0.462 6.44 3 | 0.250 0.069 0.908 4.63 4 | 0.233 0.176 0.308 9.55 5 | 0.803 0.514 1.256 8.83 6 | 0.384 0.316 0.466 9.82 7 | 0.195 0.077 0.497 6.24 8 | 1.012 0.894 1.146 9.97 9 | 0.624 0.391 0.996 8.73 10 | 0.246 0.144 0.422 8.37 11 | 0.711 0.571 0.886 9.75 12 | 1.563 0.373 6.548 4.11 13 | 0.983 0.582 1.661 8.44 ---------------------+--------------------------------------------------- D+L pooled OR | 0.474 0.325 0.691 100.00 ---------------------+--------------------------------------------------- Heterogeneity chi-squared = 163.94 (d.f. = 12) p = 0.000 I-squared (variation in OR attributable to heterogeneity) = 92.7% Estimate of between-study variance Tau-squared = 0.3682 Test of OR=1 : z= 3.88 p = 0.000

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Stata Example

NOTE: Weights are from random effects analysis

Overall (I-squared = 92.7%, p = 0.000)

4

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ID

2

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8

Study

1

3

0.47 (0.32, 0.69)

0.23 (0.18, 0.31)

0.25 (0.14, 0.42)

1.56 (0.37, 6.55)

0.80 (0.51, 1.26)

0.62 (0.39, 1.00)

0.20 (0.08, 0.50)

OR (95% CI)

0.19 (0.08, 0.46)

0.98 (0.58, 1.66)

0.38 (0.32, 0.47)

0.71 (0.57, 0.89)

1.01 (0.89, 1.15)

0.39 (0.12, 1.26)

0.25 (0.07, 0.91)

100.00

9.55

8.37

4.11

8.83

8.73

6.24

Weight

6.44

8.44

9.82

9.75

9.97

%

5.12

4.63

0.47 (0.32, 0.69)

0.23 (0.18, 0.31)

0.25 (0.14, 0.42)

1.56 (0.37, 6.55)

0.80 (0.51, 1.26)

0.62 (0.39, 1.00)

0.20 (0.08, 0.50)

OR (95% CI)

0.19 (0.08, 0.46)

0.98 (0.58, 1.66)

0.38 (0.32, 0.47)

0.71 (0.57, 0.89)

1.01 (0.89, 1.15)

0.39 (0.12, 1.26)

0.25 (0.07, 0.91)

100.00

9.55

8.37

4.11

8.83

8.73

6.24

Weight

6.44

8.44

9.82

9.75

9.97

%

5.12

4.63

1.0688 1 14.5

R Code

•  To perform meta-analysis in R we use a package called “rmeta” –  install.packages(“rmeta”) –  library(rmeta)

•  IMPORTANT: rmeta wants the data in a different format than Stata! –  Stata wants cell counts –  rmeta wants event counts and totals

•  metan format •  rmeta format

R Code

Create new variables:

ma$treat_tot <- ma$treat_disease + ma$treat_no_disease ma$control_tot <- ma$control_disease + ma$control_no_diseas

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R Code

•  Three steps: –  Step 1: Create a meta-analysis object, meta.MH() or meta.DSL()

–  Step 2: Summarize the object, summary() –  Step 3: Plot the object, plot()

•  Step 1: Syntax is –  Fixed Effects: meta.MH(n.trt, n.ctrl, col.trt,

col.ctrl, names=studyname, statistic=[“OR” or “RR”])

–  Random Effects: meta.DSL(n.trt, n.ctrl, col.trt, col.ctrl, names=studyname, statistic=[“OR” or “RR”])

R Results ma1 <- meta.MH(ma$treat_tot, ma$control_tot, ma$treat_disease,

ma$control_disease, names=ma$study, statistic="OR") summary(ma1) Fixed effects ( Mantel-Haenszel ) meta-analysis ------------------------------------ OR (lower 95% upper) 1 0.39 0.12 1.26 2 0.19 0.08 0.46 3 0.25 0.07 0.91 4 0.23 0.18 0.31 5 0.80 0.51 1.26 6 0.38 0.32 0.47 7 0.20 0.08 0.50 8 1.01 0.89 1.15 9 0.62 0.39 1.00 10 0.25 0.14 0.42 11 0.71 0.57 0.89 12 1.56 0.37 6.55 13 0.98 0.58 1.66 ------------------------------------ Mantel-Haenszel OR =0.62 95% CI ( 0.57,0.68 ) Test for heterogeneity: X^2( 12 ) = 163.94 ( p-value 0 )

R Code

plot(ma1)

Odds Ratio

Stud

y R

efer

ence

0.10 0.25 0.63 1.58 3.98

12345678910111213

Summary

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R Results ma2 <- meta.DSL(ma$treat_tot, ma$control_tot, ma$treat_disease,

ma$control_disease, names=ma$study, statistic=“OR") summary(ma2) Random effects ( DerSimonian-Laird ) meta-analysis ------------------------------------ OR (lower 95% upper) 1 0.39 0.12 1.26 2 0.19 0.08 0.46 3 0.25 0.07 0.91 4 0.23 0.18 0.31 5 0.80 0.51 1.26 6 0.38 0.32 0.47 7 0.20 0.08 0.50 8 1.01 0.89 1.15 9 0.62 0.39 1.00 10 0.25 0.14 0.42 11 0.71 0.57 0.89 12 1.56 0.37 6.55 13 0.98 0.58 1.66 ------------------------------------ SummaryOR= 0.47 95% CI ( 0.32,0.69 ) Test for heterogeneity: X^2( 12 ) = 163.16 ( p-value 0 ) Estimated random effects variance: 0.37

R Code

plot(ma2)

Odds Ratio

Stud

y R

efer

ence

0.10 0.25 0.63 1.58 3.98

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Summary

Forest Plot Options

•  The forest plot can be customized using the meta.colors() options –  Summary symbol color: summary="color" –  95% CI line color: lines="color" –  Study outcome symbol color: box="black" –  Null hypothesis line color: zero="red" –  Color of text: text="white" –  Background color of graph: background="gray80" –  Color of axes: axes="white"

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Forest Plot Options plot(ma1, colors=meta.colors(summary="gray50", lines="gray50",

box="black", zero="red", text="white", background="thistle”, axes="white"))

Odds Ratio

Stud

y R

efer

ence

0.10 0.25 0.63 1.58 3.98

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Summary

PRISMA Guidelines

•  PRISMA: Preferred Reporting Items for Systematic Reviews and Meta-Analyses

•  An evidence-based standard for reporting in systematic reviews and meta-analyses

•  PRISMA consists of: –  A 27-item checklist of items to include in your write-up –  A four-phase flow diagram to include as a figure in your write-

up •  The standard change periodically so consult the

website: –  http://www.prisma-statement.org/

PRISMA Checklist

•  The PRISMA Checklist contains 27 issues to specifically address in your write-up

•  Many are not specific to systematic reviews –  “Describe the rationale for the review in the context of

what is already known.” Duh. •  Also suggests the level of detail needed in

identifying information sources and conducting searches

•  Highly recommended that you follow these guidelines

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PRISMA Flow Di agram

•  Four stages: –  Identification –  Screening –  Eligibility –  Inclusion

•  You should create this diagram for your study and include it in your paper

•  Reviewers are becoming savvy to PRISMA and will make you do it

PRISMA Flow Diagram

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Includ

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Eligibility�

PRISMA�2009�Flow�Diagram

From: Moher D, Liberati A, Tetzlaff J, Altman DG, The PRISMA Group (2009). Preferred Reporting Items for Systematic Reviews and Meta-Analyses: The PRISMA Statement. PLoS Med 6(6): e1000097. doi:10.1371/journal.pmed1000097

For�more�information,�visit�www.prismaͲstatement.org.�

Iden

tification�

#�of�additional�records�identified�through�other�sources�

#�of�records�after�duplicates�removed�

#�of�records�screened� #�of�records�excluded�

#�of�fullͲtext�articles�assessed�for�eligibility�

#�of�fullͲtext�articles�excluded,�with�reasons�

#�of�studies�included�in�qualitative�synthesis�

#�of�studies�included�in�quantitative�synthesis�

(metaͲanalysis)�

Conclusions

•  Systematic reviews are an important part of the comparative effectiveness toolkit –  Summarize what is known about the effectiveness of

interventions –  Provide inputs in into decision analysis models and cost-

effectiveness models •  Meta-analysis is the set of statistical methods used

to conduct a systematic review •  Goal is to summarize the body of knowledge

surrounding a clinical question •  Not a shortcut to research

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Homework

•  There is a data set on the website (blockers.csv) •  22 clinical trials of beta blockers after AMI •  Four variables:

–  rt: number of patients who in the treatment group who died –  nt: total number of patients in the treatment group –  rc: number of patients in the control group who died –  nc: total number of patients in the control group

•  1. Perform a Mantel-Haenzel meta-analysis –  What is the pooled odds ratio? Is it significant? –  What is the pooled risk ratio? Is it significant?

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Homework

•  2. Produce forest plots for both the odds ratio and the risk ratio

•  3. Is there significant heterogeneity? •  4. Perform a Dersimonian-Laird random effects

meta-analysis for the odds ratio –  How does the pooled odds ratio compare to the fixed

effects model?

•  5. If you are using Stata, perform a Peto analysis