meta-analysis 統合分析
蔡崇弘
EBM ( evidence based medicine)
 Ask
 Acquire
 Appraising
 Apply
 Audit
FIRE
Formulate an answerable question
 Information search
 Review of information and clinical appraisal
 Employ the result in clinical practice

question
Intervention
 Frequency or rate
 Diagnostic accuracy
 Risk or etiology
 Prediction and prognosis

Finding relevant studies
Existing systematic reviews
 Published primary studies
 Breaking down study question into
components
 Synonyms
 Snowballing
 Handsearching
 Methodological terms
 Methodological filters

Finding relevant studies
Different databases
 Unpublished primary studies
search relevant databases
writing to experts

Appraising and selecting studies
VIP
 Jadad score

review
Narrative reviews
 Systematic review

paper
One question, one paper
 One question, more papers
 More papers to get one conclusion.
 Different paper, different effect
 7 ( 4 effect 3 non-effect)
 Conclusion!

Vote counting
P value ( P>0.05, P<0.05)
 Is it good for you?

Meta-analysis
Systematic review and meta-analysis
 Meta-analysis is used in many fields of
research
 Meta-analysis as part of the research
process

Four stages of research synthesis
Problem collection
 Data collection
 Data evaluation
 Data analysis and interpretation

Simpson’s paradox

法學院：報名人數 錄取人數 錄取率 商學院：報名人數 錄取人數 錄取率

男生 ： 53
女生 ： 152
總和 ： 205





8
51
59
15.1% 男生 ： 251
33.6% 女生 ： 101
28.8% 總和 ： 352
201
92
293
總報名人數 總錄取人數 總錄取率
男生：
女生：
304
253
209
143
68.8%
56.5%
80.1%
91.1%
83.3%
What does a meta-analysis entail?
Which comparisons should be made?
 Which study results should be used in each
comparison?
 What is the best summary of effect for each
comparison?
 Are the results of studies similar within each
comparison?
 How reliable are those summaries?

Types of data and effect measures

Dichototomous outcomes
OR, RD, NNT.
Continuous outcomes
mean difference, standardised mean
difference,
Ordinal outcomes
Counts and rates
Time-to-event outcomes
Log scales
How a meta-analysis work
Individual studies
 Effect size
 Precision
 Study weights
 P-values
 The summary effect
 Heterogeneity of effect sizes

software
Comprehensive meta-analysis
 Reman
 Stata macro with stata
 SAS
R

Why perform a meta-analysis
Statistical significance
 Clinical importance of the effect
 Consistency of effects

Doing arithmetic with words
 The words are based on p-values the words
are the wrong words.

Effect size and precision
Treatment effects and effect sizes
 How to choose an effect size
 Parameters and estimates
 Outline of effects size computations

Factors that affect precision
Variance, standard error, and confidence
intervals
 Factors that affect precision
 Sample size
 Study design
 Concluding remarks

Fixed-effect model
A single true value
 Weighs are 1/d2 (d2 variance of studies )

Random-effect model
True value varies
 Weighs are 1/(d2 + Tau2 )
 Tau= study- to study variation

If between study variance is small then fixed
and random effects models are similar.
 If the between study variance is large, the
weighs for each study become almost equal.
 Minimal between study variation- the choice
doesn’t matter.
 Considerable between study variation then
an explanation should be sought.

Identifying and quantifying
heterogeneity
Isolating the varivation in true effects
 Computing Q
 The expected value of Q based on withinstudy error
 The excess variation
 Ratio of observed to expected variation
 Testing the assumption of homogeneity in
effects
 Concluding remarks about Q and p-value

Estimating
 Concluding remarks about T
 Tau
 Concluding remark about T
 The I statising
 Comparing the measures of heterogeneity
 Confidence interval for

Prediction intervals
Prediction intervals in primary studies
 Prediction intervals in meta-analysis
 Confidence intervals and prediction intervals
 Comparing the confidence interval with the
prediction interval

Subgroup analysis
Fixed-effect model within subgroups
 Computing the summary effects
 Computation for A studies
 Computation for B studies
 Computations for all ten studies
 Comparing the effect

Meta-regression
Fixed-effect model
 Assessing the impact of the slope
 The Z-test and Q-test
 Quantify the magnitude of the relationship
 Fixed or random effects for unexplained
heterogeneity
 The proportion of variance explained

Publication bias
The problem of missing studies
 Studies with significant results are more
likely to be published
 Published studies are more likely to be
included in a meta-analysis
 Other sources of bias
 Methods for addressing bias.

Generally of the basic inversevariance method
Other effect sizes
 Simple descriptive statistics
 Physical contents
 Two-group studies with other types of data
 Three-group studies
 Regression coefficients

Further methods for dichotomous
data
Mantel-Haenszel method
 Peto odds ratio method
 Dersimonnian and Laird random effects
method

When does it make sense to perform
a meta-analysis?
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Are the studies similar enough to combine?
Can I combine studies with different designs?
Randomized trials versus observational studies
Studies that used independent groups, paired
groups, clustered groups
Can I combine studies that report results in
different ways?
How many studies are enough to carry out a metaanalysis?
Reporting the results of a metaanalysis
Are the effects consistent?
 The computational model
 Forest plots
 Sensitivity analysis

Cumulative meta-analysis
Why perform a cumulative meta-analysis?
 Cumulative meta-analysis as an educational
tool
 To identify patterns in the data c
 Display, not analysis
 Using a cumulative analysis prospectively

Criticisms of meta-analysis
One number cannot summarize a research
field
 The file drawer problem invalidates metaanalysis
 Mixing apples and oranges
 Garbage in, garbage out
 Important studies are ignored
 Meta-analysis can disagree with randomized
trials
 Meta-analyses are performed poorly
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