SlideShare ist ein Scribd-Unternehmen logo
1 von 50
Downloaden Sie, um offline zu lesen
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Fixed-effect vs. Random-effects
models in meta-analysis
Dr. S. A. Rizwan M.D.,
Public Health Specialist & Lecturer,
Saudi Board of Preventive Medicine – Riyadh,
Ministry of Health, KSA
25.11.2019 1
With thanks to Michael Borenstein
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Outline
• Provide a description of fixed and of random effects models
• Outline the underlying assumptions of these two models in order to
clarify the choices a reviewer has in a meta-analysis
• Discuss how to estimate key parameters in the model
25.11.2019 2
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Our choice between the two depends on
• Our assumption about how the effect sizes vary in our meta-analysis
• The two models are based on different assumptions about the nature
of the variation among effect sizes in our research synthesis
25.11.2019 3
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Sampling assumptions
• Fixed-effect
• Sampling takes place at one level only
• Any between-study variance will be ignored when assigning weights
• Random-effects
• Sampling takes place at two levels
• Any between-study variance will be used when assigning weights
25.11.2019 4
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Fixed-effect
• When there is reason to believe that all the studies are functionally identical
• When our goal is to compute the common effect size, for the studies in the
analysis
• Example of drug company has run five studies to assess the effect of a drug
• Note that the effect size from each study estimate a single common mean –
the fixed-effect
• We know that each study will give us a different effect size, but each effect
size is an estimate of a common mean, designated in the prior picture as θ
25.11.2019 5
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 6
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Random-effects
• We assume two components of variation:
• – Sampling variation as in our fixed-effect model assumption
• – Random variation because the effect sizes themselves are sampled from
population of effect sizes
• In a random effects model, we know that our effect sizes will differ
because they are sampled from an unknown distribution
• Our goal in the analysis will be to estimate the mean and variance of
the underlying population of effect sizes
• All the studies are functionally equivalent
• Example of studies culled from publications
25.11.2019 7
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Random-effects
• We see in the picture that each distribution has its own mean that is
sampled from the underlying population distribution of effect sizes
• That underlying population distribution also has its own variance, τ2,
commonly called the variance component
• Thus, each effect size has two components of variation, one due to
sampling error, and one from the underlying distribution
25.11.2019 8
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 9
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Definition of combined effect
• Fixed effect model
• There is one true effect
• Summary effect is estimate of this value
• Random effects model
• There is a distribution of effects
• Summary effect is mean of distribution
25.11.2019 10
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
How weights are assigned?
25.11.2019 11
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
W = 1/ (V1)
Fixed-effects model
25.11.2019 12
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Random-effects model
25.11.2019 13
1W = 1/ (V +T 2
)
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
190
How weights shift?
• If within-study variance only, W=1/V
• If between-study variance only, W=1/T2
• If both, W=1/(V+T2)
25.11.2019 14
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 15
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 16
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Random vs. Fixed
25.11.2019 17
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Random vs. Fixed
25.11.2019 18
RE weights are more balanced
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Random vs. Fixed
25.11.2019 19
RE confidence interval is wider
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Large study has less impact under RE
25.11.2019 20
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Small study has more impact under RE
25.11.2019 21
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
FE
25.11.2019 22
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Summary effect in Fixed model
25.11.2019 23
244.215
101.171
= 0.414FE
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Variance of summary effect in fixed model
25.11.2019 24
1
244.215
= 0.004FE
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
RE
25.11.2019 25
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Summary effect in random model
25.11.2019 26
90.284
32.342
= 0.358RE
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Variance of summary effect in random model
25.11.2019 27
1
90.284
= 0.011RE
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Why does it matter?
• One matches the sampling
• One does not match the sampling
• Wrong model yields incorrect weights
• Estimate of mean is wrong
• Estimate of CI is wrong
• MUST choose based on sampling model
• The meaning of the ES is different
• Relative weights are closer under RE (effect size will shift)
• Absolute weights are smaller under RE (CI will become wider)
• p-value will change (less significant in long run but can go either way)
25.11.2019 28
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Test of null
25.11.2019 29
M
M
Z =
SE
M*
M*
Z* =
SE
Fixed
Random
Two
sources
of error
One
source
of error
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Implications of the choice
• If you expect that the effect size from each study arises from a different
population then use random effects
• Random effects model is more likely to give non-significant estimates
• Recall that all our analyses in a meta-analysis are weighted by the inverse of
the variance of the effect size, i.e., by the precision of the effect size estimate
• Because we have more variation assumed in a random effects model, our
weights for each study will be more equal to one another
• In other words, in a fixed effect model, we will more heavily weight larger
studies. In a random effects model, the larger studies will not be weighted as
heavily
25.11.2019 30
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Question!
• Suppose we had four studies, each with
• N =1,000,000, and a true (mean) effect size of 50.
• Under the two models,
• What would the forest plot look like?
• What would the diamond look like?
25.11.2019 31
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 32
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 33
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Which model should we use?
• Base decision on the model that matched the way the data were
collected
• Not on test of homogeneity
25.11.2019 34
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
What you may hear
• Fixed-effect is simple model
• Random-effects is more complicated
25.11.2019 35
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Actually
• Fixed-effect is more restricted model
• Random-effects makes less assumptions
25.11.2019 36
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
An alternate view
• Random-effects model only makes sense if we have a clear picture of
the sampling frame
• Otherwise, we should report the mean and CI for the studies in our
sample without attempt to generalize to a larger universe
25.11.2019 37
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Goals in a fixed effect model
• In a fixed effect model, we will be most interested in estimating our
common effect, θ, and its standard error
• We will also want to know if there is heterogeneity present by
computing Q
• HOWEVER, WE WILL NOT decide on the basis of a significant Q that
we should really do a random effects model
• WE WILL make a decision about fixed effect versus random effects
models because of our substantive knowledge of the area of the
systematic review
25.11.2019 38
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Goals in a random effects model
• We also want to estimate a mean effect size, but now this is the mean
effect size from the underlying population, μ
• We also want to estimate the variance of the underlying effect size, τ2
• We will test heterogeneity by testing whether τ2 is different from 0.
• Biggest difficulty: how to estimate τ2
25.11.2019 39
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Estimating the variance component, τ2
• There are two main methods for computing τ2
• Variously called the method of moments, the DerSimonian/Laird estimate
• Restricted maximum likelihood
• The method of moments estimator is easy to compute and is based
on the value of Q, the homogeneity statistic
• Restricted maximum likelihood requires an iterative solution
25.11.2019 40
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Method of moments estimator
25.11.2019 41
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Restricted maximum likelihood estimator
• Many statisticians do not like the method of moments estimator
• Can estimate τ2 using HLM, SAS Proc Mixed, or R
25.11.2019 42
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Differences between the two
models
25.11.2019 43
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
ES assumptions
Fixed effect model
• We assume that the treatment
effect is the same in all trials.
• We use only the sampling
variation within the trials.
Random effects model
• We assume that the treatment
effect is the not same in all trials.
• The trials are a sample from a
population of possible of trials
where the treatment effect varies.
• We use the sampling variation
within the trials and the sampling
variation between trials.
25.11.2019 44
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Sampling assumptions
Fixed effect model
• If the treatment effect is the
same in all trials, it is more
powerful and easier.
• No assumption about
representativeness.
Random effects model
• Less powerful because P values are
larger and confidence intervals are
wider.
• The trials are a sample from a
population of possible of trials
where the treatment effect varies.
• They must be a representative or
random sample.
• Very strong assumption.
25.11.2019 45
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Variance
Fixed effect model
• Variance of treatment effect in
trial = standard error squared.
• Weight = 1/variance = 1/SE2
Random effects model
• Variance of treatment effect in trial
= standard error squared plus inter-
trial variance
• Weight = 1/variance.
• 1
= --------------------------------
SE2 + inter-trial variance
• Inter-trial variance has degrees of
freedom given by number of trials
minus one.
• Typically small.
25.11.2019 46
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
When heterogeneity exists
Fixed effect model
• When heterogeneity exists we
get:
• a pooled estimate which may give
too much weight to large studies,
• a confidence interval which is too
narrow,
• a P-value which is too small.
Random effects model
• When heterogeneity exists we
get:
• possibly a different pooled
estimate with a different
interpretation,
• a wider confidence interval,
• a larger P-value.
25.11.2019 47
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
When heterogeneity doesn’t exist
Fixed effect model
• When heterogeneity does not
exists:
• a pooled estimate which is
correct,
• a confidence interval which is
correct,
• a P-value which is correct.
Random effects model
• When heterogeneity does not
exist:
• a pooled estimate which is
correct,
• a confidence interval which is too
wide,
• a P-value which is too large.
25.11.2019 48
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 49
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Thank you
Kindly email your queries to sarizwan1986@outlook.com
25.11.2019 50

Weitere ähnliche Inhalte

Was ist angesagt?

Categorical data analysis
Categorical data analysisCategorical data analysis
Categorical data analysisSumit Das
 
Various statistical software's in data analysis.
Various statistical software's in data analysis.Various statistical software's in data analysis.
Various statistical software's in data analysis.SelvaMani69
 
Effect sizes in meta-analysis
Effect sizes in meta-analysisEffect sizes in meta-analysis
Effect sizes in meta-analysisRizwan S A
 
Meta-analysis and systematic reviews
Meta-analysis and systematic reviews Meta-analysis and systematic reviews
Meta-analysis and systematic reviews coolboy101pk
 
Analysis of variance
Analysis of varianceAnalysis of variance
Analysis of varianceAndi Koentary
 
Survival analysis
Survival analysisSurvival analysis
Survival analysisHar Jindal
 
Basics of Regression analysis
 Basics of Regression analysis Basics of Regression analysis
Basics of Regression analysisMahak Vijayvargiya
 
Lec. biostatistics introduction
Lec. biostatistics  introductionLec. biostatistics  introduction
Lec. biostatistics introductionRiaz101
 
Solving stepwise regression problems
Solving stepwise regression problemsSolving stepwise regression problems
Solving stepwise regression problemsSoma Sinha Roy
 
Multinomial Logistic Regression Analysis
Multinomial Logistic Regression AnalysisMultinomial Logistic Regression Analysis
Multinomial Logistic Regression AnalysisHARISH Kumar H R
 
Sample size estimation
Sample size estimationSample size estimation
Sample size estimationHanaaBayomy
 
Chi square Test Using SPSS
Chi square Test Using SPSSChi square Test Using SPSS
Chi square Test Using SPSSDr Athar Khan
 
Checking for normality (Normal distribution)
Checking for normality (Normal distribution)Checking for normality (Normal distribution)
Checking for normality (Normal distribution)Rizwan S A
 
Moderator analysis in meta-analysis
Moderator analysis in meta-analysisModerator analysis in meta-analysis
Moderator analysis in meta-analysisRizwan S A
 

Was ist angesagt? (20)

Meta analysis
Meta analysisMeta analysis
Meta analysis
 
Survival analysis
Survival analysisSurvival analysis
Survival analysis
 
Categorical data analysis
Categorical data analysisCategorical data analysis
Categorical data analysis
 
Various statistical software's in data analysis.
Various statistical software's in data analysis.Various statistical software's in data analysis.
Various statistical software's in data analysis.
 
Effect sizes in meta-analysis
Effect sizes in meta-analysisEffect sizes in meta-analysis
Effect sizes in meta-analysis
 
Meta-analysis and systematic reviews
Meta-analysis and systematic reviews Meta-analysis and systematic reviews
Meta-analysis and systematic reviews
 
Fishers test
Fishers testFishers test
Fishers test
 
Analysis of variance
Analysis of varianceAnalysis of variance
Analysis of variance
 
Survival analysis
Survival analysisSurvival analysis
Survival analysis
 
Basics of Regression analysis
 Basics of Regression analysis Basics of Regression analysis
Basics of Regression analysis
 
Lec. biostatistics introduction
Lec. biostatistics  introductionLec. biostatistics  introduction
Lec. biostatistics introduction
 
Solving stepwise regression problems
Solving stepwise regression problemsSolving stepwise regression problems
Solving stepwise regression problems
 
Multinomial Logistic Regression Analysis
Multinomial Logistic Regression AnalysisMultinomial Logistic Regression Analysis
Multinomial Logistic Regression Analysis
 
Sample size estimation
Sample size estimationSample size estimation
Sample size estimation
 
Statistical Power
Statistical PowerStatistical Power
Statistical Power
 
Chi square Test Using SPSS
Chi square Test Using SPSSChi square Test Using SPSS
Chi square Test Using SPSS
 
Checking for normality (Normal distribution)
Checking for normality (Normal distribution)Checking for normality (Normal distribution)
Checking for normality (Normal distribution)
 
Moderator analysis in meta-analysis
Moderator analysis in meta-analysisModerator analysis in meta-analysis
Moderator analysis in meta-analysis
 
Experimental Studies
Experimental StudiesExperimental Studies
Experimental Studies
 
{ANOVA} PPT-1.pptx
{ANOVA} PPT-1.pptx{ANOVA} PPT-1.pptx
{ANOVA} PPT-1.pptx
 

Ähnlich wie Fixed-effect and random-effects models in meta-analysis

Inverse variance method of meta-analysis and Cochran's Q
Inverse variance method of meta-analysis and Cochran's QInverse variance method of meta-analysis and Cochran's Q
Inverse variance method of meta-analysis and Cochran's QRizwan S A
 
Introduction & rationale for meta-analysis
Introduction & rationale for meta-analysisIntroduction & rationale for meta-analysis
Introduction & rationale for meta-analysisRizwan S A
 
Biases in meta-analysis
Biases in meta-analysisBiases in meta-analysis
Biases in meta-analysisRizwan S A
 
Overview of the systematic review process
Overview of the systematic review processOverview of the systematic review process
Overview of the systematic review processRizwan S A
 
Types of correlation coefficients
Types of correlation coefficientsTypes of correlation coefficients
Types of correlation coefficientsRizwan S A
 
A introduction to non-parametric tests
A introduction to non-parametric testsA introduction to non-parametric tests
A introduction to non-parametric testsRizwan S A
 
Analysis of small datasets
Analysis of small datasetsAnalysis of small datasets
Analysis of small datasetsRizwan S A
 
Bioinformatics practice questions Protein fragment PNLPDCDMES WLNA
Bioinformatics practice questions Protein fragment PNLPDCDMES WLNABioinformatics practice questions Protein fragment PNLPDCDMES WLNA
Bioinformatics practice questions Protein fragment PNLPDCDMES WLNAChantellPantoja184
 
mHealth Israel_Dr Dana Safran_Payment Reform Successes and Challenges_Nov 25,...
mHealth Israel_Dr Dana Safran_Payment Reform Successes and Challenges_Nov 25,...mHealth Israel_Dr Dana Safran_Payment Reform Successes and Challenges_Nov 25,...
mHealth Israel_Dr Dana Safran_Payment Reform Successes and Challenges_Nov 25,...Levi Shapiro
 
Problems Affecting Work Performance of Healthcare Practitioners in Jazan, Kin...
Problems Affecting Work Performance of Healthcare Practitioners in Jazan, Kin...Problems Affecting Work Performance of Healthcare Practitioners in Jazan, Kin...
Problems Affecting Work Performance of Healthcare Practitioners in Jazan, Kin...iosrjce
 
Statistic in Health Care Management Assignment Week 3Case Study.docx
Statistic in Health Care Management Assignment Week 3Case Study.docxStatistic in Health Care Management Assignment Week 3Case Study.docx
Statistic in Health Care Management Assignment Week 3Case Study.docxrafaelaj1
 
CEA_Next_Generation_CVD_Test_-_JME2013
CEA_Next_Generation_CVD_Test_-_JME2013CEA_Next_Generation_CVD_Test_-_JME2013
CEA_Next_Generation_CVD_Test_-_JME2013Jean-Ezra Yeung
 
13Econ Principles Milestone 1Precious Teasle
13Econ Principles Milestone 1Precious Teasle13Econ Principles Milestone 1Precious Teasle
13Econ Principles Milestone 1Precious TeasleChantellPantoja184
 
13Econ Principles Milestone 1Precious Teasle
13Econ Principles Milestone 1Precious Teasle13Econ Principles Milestone 1Precious Teasle
13Econ Principles Milestone 1Precious TeasleTaunyaCoffman887
 
NELC-A1C20120930a
NELC-A1C20120930aNELC-A1C20120930a
NELC-A1C20120930aMark Gusack
 
· Psychiatric Mental Health Nursing. Scope and Standards of Practi.docx
· Psychiatric Mental Health Nursing. Scope and Standards of Practi.docx· Psychiatric Mental Health Nursing. Scope and Standards of Practi.docx
· Psychiatric Mental Health Nursing. Scope and Standards of Practi.docxoswald1horne84988
 
Statistical tests for data involving quantitative data
Statistical tests for data involving quantitative dataStatistical tests for data involving quantitative data
Statistical tests for data involving quantitative dataRizwan S A
 
WHEN AND HOW DOES VALUE BASED PURCHASING IMPACT HOSPITAL PERFORMANCE?
WHEN AND HOW DOES VALUE BASED PURCHASING IMPACT HOSPITAL PERFORMANCE?WHEN AND HOW DOES VALUE BASED PURCHASING IMPACT HOSPITAL PERFORMANCE?
WHEN AND HOW DOES VALUE BASED PURCHASING IMPACT HOSPITAL PERFORMANCE?Kirsty Macauldy, MBA
 

Ähnlich wie Fixed-effect and random-effects models in meta-analysis (20)

Inverse variance method of meta-analysis and Cochran's Q
Inverse variance method of meta-analysis and Cochran's QInverse variance method of meta-analysis and Cochran's Q
Inverse variance method of meta-analysis and Cochran's Q
 
Introduction & rationale for meta-analysis
Introduction & rationale for meta-analysisIntroduction & rationale for meta-analysis
Introduction & rationale for meta-analysis
 
Biases in meta-analysis
Biases in meta-analysisBiases in meta-analysis
Biases in meta-analysis
 
Overview of the systematic review process
Overview of the systematic review processOverview of the systematic review process
Overview of the systematic review process
 
Types of correlation coefficients
Types of correlation coefficientsTypes of correlation coefficients
Types of correlation coefficients
 
A introduction to non-parametric tests
A introduction to non-parametric testsA introduction to non-parametric tests
A introduction to non-parametric tests
 
Analysis of small datasets
Analysis of small datasetsAnalysis of small datasets
Analysis of small datasets
 
Bioinformatics practice questions Protein fragment PNLPDCDMES WLNA
Bioinformatics practice questions Protein fragment PNLPDCDMES WLNABioinformatics practice questions Protein fragment PNLPDCDMES WLNA
Bioinformatics practice questions Protein fragment PNLPDCDMES WLNA
 
mHealth Israel_Dr Dana Safran_Payment Reform Successes and Challenges_Nov 25,...
mHealth Israel_Dr Dana Safran_Payment Reform Successes and Challenges_Nov 25,...mHealth Israel_Dr Dana Safran_Payment Reform Successes and Challenges_Nov 25,...
mHealth Israel_Dr Dana Safran_Payment Reform Successes and Challenges_Nov 25,...
 
Problems Affecting Work Performance of Healthcare Practitioners in Jazan, Kin...
Problems Affecting Work Performance of Healthcare Practitioners in Jazan, Kin...Problems Affecting Work Performance of Healthcare Practitioners in Jazan, Kin...
Problems Affecting Work Performance of Healthcare Practitioners in Jazan, Kin...
 
Statistic in Health Care Management Assignment Week 3Case Study.docx
Statistic in Health Care Management Assignment Week 3Case Study.docxStatistic in Health Care Management Assignment Week 3Case Study.docx
Statistic in Health Care Management Assignment Week 3Case Study.docx
 
Clinical prediction models
Clinical prediction modelsClinical prediction models
Clinical prediction models
 
CEA_Next_Generation_CVD_Test_-_JME2013
CEA_Next_Generation_CVD_Test_-_JME2013CEA_Next_Generation_CVD_Test_-_JME2013
CEA_Next_Generation_CVD_Test_-_JME2013
 
13Econ Principles Milestone 1Precious Teasle
13Econ Principles Milestone 1Precious Teasle13Econ Principles Milestone 1Precious Teasle
13Econ Principles Milestone 1Precious Teasle
 
13Econ Principles Milestone 1Precious Teasle
13Econ Principles Milestone 1Precious Teasle13Econ Principles Milestone 1Precious Teasle
13Econ Principles Milestone 1Precious Teasle
 
NELC-A1C20120930a
NELC-A1C20120930aNELC-A1C20120930a
NELC-A1C20120930a
 
· Psychiatric Mental Health Nursing. Scope and Standards of Practi.docx
· Psychiatric Mental Health Nursing. Scope and Standards of Practi.docx· Psychiatric Mental Health Nursing. Scope and Standards of Practi.docx
· Psychiatric Mental Health Nursing. Scope and Standards of Practi.docx
 
Statistical tests for data involving quantitative data
Statistical tests for data involving quantitative dataStatistical tests for data involving quantitative data
Statistical tests for data involving quantitative data
 
WHEN AND HOW DOES VALUE BASED PURCHASING IMPACT HOSPITAL PERFORMANCE?
WHEN AND HOW DOES VALUE BASED PURCHASING IMPACT HOSPITAL PERFORMANCE?WHEN AND HOW DOES VALUE BASED PURCHASING IMPACT HOSPITAL PERFORMANCE?
WHEN AND HOW DOES VALUE BASED PURCHASING IMPACT HOSPITAL PERFORMANCE?
 
Mab vax presentation_april 2017
Mab vax  presentation_april 2017 Mab vax  presentation_april 2017
Mab vax presentation_april 2017
 

Mehr von Rizwan S A

Introduction to scoping reviews
Introduction to scoping reviewsIntroduction to scoping reviews
Introduction to scoping reviewsRizwan S A
 
Sources of demographic data 2019
Sources of demographic data 2019Sources of demographic data 2019
Sources of demographic data 2019Rizwan S A
 
Kruskal Wallis test, Friedman test, Spearman Correlation
Kruskal Wallis test, Friedman test, Spearman CorrelationKruskal Wallis test, Friedman test, Spearman Correlation
Kruskal Wallis test, Friedman test, Spearman CorrelationRizwan S A
 
Mantel Haenszel methods in epidemiology (Stratification)
Mantel Haenszel methods in epidemiology (Stratification) Mantel Haenszel methods in epidemiology (Stratification)
Mantel Haenszel methods in epidemiology (Stratification) Rizwan S A
 
Use of checklists in critical appraisal of health literature
Use of checklists in critical appraisal of health literatureUse of checklists in critical appraisal of health literature
Use of checklists in critical appraisal of health literatureRizwan S A
 
Critical Appraisal of health literature
Critical Appraisal of health literatureCritical Appraisal of health literature
Critical Appraisal of health literatureRizwan S A
 
Critical Appraisal of health literature
Critical Appraisal of health literatureCritical Appraisal of health literature
Critical Appraisal of health literatureRizwan S A
 
Critical Appraisal of health literature - an overview
Critical Appraisal of health literature - an overviewCritical Appraisal of health literature - an overview
Critical Appraisal of health literature - an overviewRizwan S A
 
Evidence based medicine or health practice
Evidence based medicine or health practiceEvidence based medicine or health practice
Evidence based medicine or health practiceRizwan S A
 
Epidemiology: Standardisation of rates
Epidemiology: Standardisation of ratesEpidemiology: Standardisation of rates
Epidemiology: Standardisation of ratesRizwan S A
 
Statistical tests for categorical data
Statistical tests for categorical dataStatistical tests for categorical data
Statistical tests for categorical dataRizwan S A
 
Confidence intervals: Types and calculations
Confidence intervals: Types and calculationsConfidence intervals: Types and calculations
Confidence intervals: Types and calculationsRizwan S A
 
Confidence Intervals: Basic concepts and overview
Confidence Intervals: Basic concepts and overviewConfidence Intervals: Basic concepts and overview
Confidence Intervals: Basic concepts and overviewRizwan S A
 
Chi square test and its types
Chi square test and its typesChi square test and its types
Chi square test and its typesRizwan S A
 
Student's t test and variations
Student's t test and variationsStudent's t test and variations
Student's t test and variationsRizwan S A
 

Mehr von Rizwan S A (15)

Introduction to scoping reviews
Introduction to scoping reviewsIntroduction to scoping reviews
Introduction to scoping reviews
 
Sources of demographic data 2019
Sources of demographic data 2019Sources of demographic data 2019
Sources of demographic data 2019
 
Kruskal Wallis test, Friedman test, Spearman Correlation
Kruskal Wallis test, Friedman test, Spearman CorrelationKruskal Wallis test, Friedman test, Spearman Correlation
Kruskal Wallis test, Friedman test, Spearman Correlation
 
Mantel Haenszel methods in epidemiology (Stratification)
Mantel Haenszel methods in epidemiology (Stratification) Mantel Haenszel methods in epidemiology (Stratification)
Mantel Haenszel methods in epidemiology (Stratification)
 
Use of checklists in critical appraisal of health literature
Use of checklists in critical appraisal of health literatureUse of checklists in critical appraisal of health literature
Use of checklists in critical appraisal of health literature
 
Critical Appraisal of health literature
Critical Appraisal of health literatureCritical Appraisal of health literature
Critical Appraisal of health literature
 
Critical Appraisal of health literature
Critical Appraisal of health literatureCritical Appraisal of health literature
Critical Appraisal of health literature
 
Critical Appraisal of health literature - an overview
Critical Appraisal of health literature - an overviewCritical Appraisal of health literature - an overview
Critical Appraisal of health literature - an overview
 
Evidence based medicine or health practice
Evidence based medicine or health practiceEvidence based medicine or health practice
Evidence based medicine or health practice
 
Epidemiology: Standardisation of rates
Epidemiology: Standardisation of ratesEpidemiology: Standardisation of rates
Epidemiology: Standardisation of rates
 
Statistical tests for categorical data
Statistical tests for categorical dataStatistical tests for categorical data
Statistical tests for categorical data
 
Confidence intervals: Types and calculations
Confidence intervals: Types and calculationsConfidence intervals: Types and calculations
Confidence intervals: Types and calculations
 
Confidence Intervals: Basic concepts and overview
Confidence Intervals: Basic concepts and overviewConfidence Intervals: Basic concepts and overview
Confidence Intervals: Basic concepts and overview
 
Chi square test and its types
Chi square test and its typesChi square test and its types
Chi square test and its types
 
Student's t test and variations
Student's t test and variationsStudent's t test and variations
Student's t test and variations
 

Kürzlich hochgeladen

EXERCISE PERFORMANCE.pptx, Lung function
EXERCISE PERFORMANCE.pptx, Lung functionEXERCISE PERFORMANCE.pptx, Lung function
EXERCISE PERFORMANCE.pptx, Lung functionkrishnareddy157915
 
Trustworthiness of AI based predictions Aachen 2024
Trustworthiness of AI based predictions Aachen 2024Trustworthiness of AI based predictions Aachen 2024
Trustworthiness of AI based predictions Aachen 2024EwoutSteyerberg1
 
CONNECTIVE TISSUE (ANATOMY AND PHYSIOLOGY).pdf
CONNECTIVE TISSUE (ANATOMY AND PHYSIOLOGY).pdfCONNECTIVE TISSUE (ANATOMY AND PHYSIOLOGY).pdf
CONNECTIVE TISSUE (ANATOMY AND PHYSIOLOGY).pdfDolisha Warbi
 
QUESTIONS & ANSWERS FOR QUALITY ASSURANCE, RADIATIONBIOLOGY& RADIATION HAZARD...
QUESTIONS & ANSWERS FOR QUALITY ASSURANCE, RADIATIONBIOLOGY& RADIATION HAZARD...QUESTIONS & ANSWERS FOR QUALITY ASSURANCE, RADIATIONBIOLOGY& RADIATION HAZARD...
QUESTIONS & ANSWERS FOR QUALITY ASSURANCE, RADIATIONBIOLOGY& RADIATION HAZARD...Ganesan Yogananthem
 
Pregnacny, Parturition, and Lactation.pdf
Pregnacny, Parturition, and Lactation.pdfPregnacny, Parturition, and Lactation.pdf
Pregnacny, Parturition, and Lactation.pdfMedicoseAcademics
 
Physiotherapy Management of Rheumatoid Arthritis
Physiotherapy Management of Rheumatoid ArthritisPhysiotherapy Management of Rheumatoid Arthritis
Physiotherapy Management of Rheumatoid ArthritisNilofarRasheed1
 
Bulimia nervosa ( Eating Disorders) Mental Health Nursing.
Bulimia nervosa ( Eating Disorders) Mental Health Nursing.Bulimia nervosa ( Eating Disorders) Mental Health Nursing.
Bulimia nervosa ( Eating Disorders) Mental Health Nursing.aarjukhadka22
 
Male Infertility Panel Discussion by Dr Sujoy Dasgupta
Male Infertility Panel Discussion by Dr Sujoy DasguptaMale Infertility Panel Discussion by Dr Sujoy Dasgupta
Male Infertility Panel Discussion by Dr Sujoy DasguptaSujoy Dasgupta
 
CPR.nursingoutlook.pdf , Bsc nursing student
CPR.nursingoutlook.pdf , Bsc nursing studentCPR.nursingoutlook.pdf , Bsc nursing student
CPR.nursingoutlook.pdf , Bsc nursing studentsaileshpanda05
 
Red Blood Cells_anemia & polycythemia.pdf
Red Blood Cells_anemia & polycythemia.pdfRed Blood Cells_anemia & polycythemia.pdf
Red Blood Cells_anemia & polycythemia.pdfMedicoseAcademics
 
SGK RỐI LOẠN KALI MÁU CỰC KỲ QUAN TRỌNG.pdf
SGK RỐI LOẠN KALI MÁU CỰC KỲ QUAN TRỌNG.pdfSGK RỐI LOẠN KALI MÁU CỰC KỲ QUAN TRỌNG.pdf
SGK RỐI LOẠN KALI MÁU CỰC KỲ QUAN TRỌNG.pdfHongBiThi1
 
Neurological history taking (2024) .
Neurological  history  taking  (2024)  .Neurological  history  taking  (2024)  .
Neurological history taking (2024) .Mohamed Rizk Khodair
 
Moving Forward After Uterine Cancer Treatment: Surveillance Strategies, Testi...
Moving Forward After Uterine Cancer Treatment: Surveillance Strategies, Testi...Moving Forward After Uterine Cancer Treatment: Surveillance Strategies, Testi...
Moving Forward After Uterine Cancer Treatment: Surveillance Strategies, Testi...bkling
 
BENIGN BREAST DISEASE
BENIGN BREAST DISEASE BENIGN BREAST DISEASE
BENIGN BREAST DISEASE Mamatha Lakka
 
FDMA FLAP - The first dorsal metacarpal artery (FDMA) flap is used mainly for...
FDMA FLAP - The first dorsal metacarpal artery (FDMA) flap is used mainly for...FDMA FLAP - The first dorsal metacarpal artery (FDMA) flap is used mainly for...
FDMA FLAP - The first dorsal metacarpal artery (FDMA) flap is used mainly for...Shubhanshu Gaurav
 
How to cure cirrhosis and chronic hepatitis naturally
How to cure cirrhosis and chronic hepatitis naturallyHow to cure cirrhosis and chronic hepatitis naturally
How to cure cirrhosis and chronic hepatitis naturallyZurück zum Ursprung
 
Adenomyosis or Fibroid- making right diagnosis
Adenomyosis or Fibroid- making right diagnosisAdenomyosis or Fibroid- making right diagnosis
Adenomyosis or Fibroid- making right diagnosisSujoy Dasgupta
 
historyofpsychiatryinindia. Senthil Thirusangu
historyofpsychiatryinindia. Senthil Thirusanguhistoryofpsychiatryinindia. Senthil Thirusangu
historyofpsychiatryinindia. Senthil Thirusangu Medical University
 
Breast cancer -ONCO IN MEDICAL AND SURGICAL NURSING.pptx
Breast cancer -ONCO IN MEDICAL AND SURGICAL NURSING.pptxBreast cancer -ONCO IN MEDICAL AND SURGICAL NURSING.pptx
Breast cancer -ONCO IN MEDICAL AND SURGICAL NURSING.pptxNaveenkumar267201
 

Kürzlich hochgeladen (20)

EXERCISE PERFORMANCE.pptx, Lung function
EXERCISE PERFORMANCE.pptx, Lung functionEXERCISE PERFORMANCE.pptx, Lung function
EXERCISE PERFORMANCE.pptx, Lung function
 
Trustworthiness of AI based predictions Aachen 2024
Trustworthiness of AI based predictions Aachen 2024Trustworthiness of AI based predictions Aachen 2024
Trustworthiness of AI based predictions Aachen 2024
 
CONNECTIVE TISSUE (ANATOMY AND PHYSIOLOGY).pdf
CONNECTIVE TISSUE (ANATOMY AND PHYSIOLOGY).pdfCONNECTIVE TISSUE (ANATOMY AND PHYSIOLOGY).pdf
CONNECTIVE TISSUE (ANATOMY AND PHYSIOLOGY).pdf
 
QUESTIONS & ANSWERS FOR QUALITY ASSURANCE, RADIATIONBIOLOGY& RADIATION HAZARD...
QUESTIONS & ANSWERS FOR QUALITY ASSURANCE, RADIATIONBIOLOGY& RADIATION HAZARD...QUESTIONS & ANSWERS FOR QUALITY ASSURANCE, RADIATIONBIOLOGY& RADIATION HAZARD...
QUESTIONS & ANSWERS FOR QUALITY ASSURANCE, RADIATIONBIOLOGY& RADIATION HAZARD...
 
Pregnacny, Parturition, and Lactation.pdf
Pregnacny, Parturition, and Lactation.pdfPregnacny, Parturition, and Lactation.pdf
Pregnacny, Parturition, and Lactation.pdf
 
Physiotherapy Management of Rheumatoid Arthritis
Physiotherapy Management of Rheumatoid ArthritisPhysiotherapy Management of Rheumatoid Arthritis
Physiotherapy Management of Rheumatoid Arthritis
 
Cone beam CT: concepts and applications.pptx
Cone beam CT: concepts and applications.pptxCone beam CT: concepts and applications.pptx
Cone beam CT: concepts and applications.pptx
 
Bulimia nervosa ( Eating Disorders) Mental Health Nursing.
Bulimia nervosa ( Eating Disorders) Mental Health Nursing.Bulimia nervosa ( Eating Disorders) Mental Health Nursing.
Bulimia nervosa ( Eating Disorders) Mental Health Nursing.
 
Male Infertility Panel Discussion by Dr Sujoy Dasgupta
Male Infertility Panel Discussion by Dr Sujoy DasguptaMale Infertility Panel Discussion by Dr Sujoy Dasgupta
Male Infertility Panel Discussion by Dr Sujoy Dasgupta
 
CPR.nursingoutlook.pdf , Bsc nursing student
CPR.nursingoutlook.pdf , Bsc nursing studentCPR.nursingoutlook.pdf , Bsc nursing student
CPR.nursingoutlook.pdf , Bsc nursing student
 
Red Blood Cells_anemia & polycythemia.pdf
Red Blood Cells_anemia & polycythemia.pdfRed Blood Cells_anemia & polycythemia.pdf
Red Blood Cells_anemia & polycythemia.pdf
 
SGK RỐI LOẠN KALI MÁU CỰC KỲ QUAN TRỌNG.pdf
SGK RỐI LOẠN KALI MÁU CỰC KỲ QUAN TRỌNG.pdfSGK RỐI LOẠN KALI MÁU CỰC KỲ QUAN TRỌNG.pdf
SGK RỐI LOẠN KALI MÁU CỰC KỲ QUAN TRỌNG.pdf
 
Neurological history taking (2024) .
Neurological  history  taking  (2024)  .Neurological  history  taking  (2024)  .
Neurological history taking (2024) .
 
Moving Forward After Uterine Cancer Treatment: Surveillance Strategies, Testi...
Moving Forward After Uterine Cancer Treatment: Surveillance Strategies, Testi...Moving Forward After Uterine Cancer Treatment: Surveillance Strategies, Testi...
Moving Forward After Uterine Cancer Treatment: Surveillance Strategies, Testi...
 
BENIGN BREAST DISEASE
BENIGN BREAST DISEASE BENIGN BREAST DISEASE
BENIGN BREAST DISEASE
 
FDMA FLAP - The first dorsal metacarpal artery (FDMA) flap is used mainly for...
FDMA FLAP - The first dorsal metacarpal artery (FDMA) flap is used mainly for...FDMA FLAP - The first dorsal metacarpal artery (FDMA) flap is used mainly for...
FDMA FLAP - The first dorsal metacarpal artery (FDMA) flap is used mainly for...
 
How to cure cirrhosis and chronic hepatitis naturally
How to cure cirrhosis and chronic hepatitis naturallyHow to cure cirrhosis and chronic hepatitis naturally
How to cure cirrhosis and chronic hepatitis naturally
 
Adenomyosis or Fibroid- making right diagnosis
Adenomyosis or Fibroid- making right diagnosisAdenomyosis or Fibroid- making right diagnosis
Adenomyosis or Fibroid- making right diagnosis
 
historyofpsychiatryinindia. Senthil Thirusangu
historyofpsychiatryinindia. Senthil Thirusanguhistoryofpsychiatryinindia. Senthil Thirusangu
historyofpsychiatryinindia. Senthil Thirusangu
 
Breast cancer -ONCO IN MEDICAL AND SURGICAL NURSING.pptx
Breast cancer -ONCO IN MEDICAL AND SURGICAL NURSING.pptxBreast cancer -ONCO IN MEDICAL AND SURGICAL NURSING.pptx
Breast cancer -ONCO IN MEDICAL AND SURGICAL NURSING.pptx
 

Fixed-effect and random-effects models in meta-analysis

  • 1. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Fixed-effect vs. Random-effects models in meta-analysis Dr. S. A. Rizwan M.D., Public Health Specialist & Lecturer, Saudi Board of Preventive Medicine – Riyadh, Ministry of Health, KSA 25.11.2019 1 With thanks to Michael Borenstein
  • 2. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Outline • Provide a description of fixed and of random effects models • Outline the underlying assumptions of these two models in order to clarify the choices a reviewer has in a meta-analysis • Discuss how to estimate key parameters in the model 25.11.2019 2
  • 3. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Our choice between the two depends on • Our assumption about how the effect sizes vary in our meta-analysis • The two models are based on different assumptions about the nature of the variation among effect sizes in our research synthesis 25.11.2019 3
  • 4. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Sampling assumptions • Fixed-effect • Sampling takes place at one level only • Any between-study variance will be ignored when assigning weights • Random-effects • Sampling takes place at two levels • Any between-study variance will be used when assigning weights 25.11.2019 4
  • 5. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Fixed-effect • When there is reason to believe that all the studies are functionally identical • When our goal is to compute the common effect size, for the studies in the analysis • Example of drug company has run five studies to assess the effect of a drug • Note that the effect size from each study estimate a single common mean – the fixed-effect • We know that each study will give us a different effect size, but each effect size is an estimate of a common mean, designated in the prior picture as θ 25.11.2019 5
  • 6. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 6
  • 7. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Random-effects • We assume two components of variation: • – Sampling variation as in our fixed-effect model assumption • – Random variation because the effect sizes themselves are sampled from population of effect sizes • In a random effects model, we know that our effect sizes will differ because they are sampled from an unknown distribution • Our goal in the analysis will be to estimate the mean and variance of the underlying population of effect sizes • All the studies are functionally equivalent • Example of studies culled from publications 25.11.2019 7
  • 8. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Random-effects • We see in the picture that each distribution has its own mean that is sampled from the underlying population distribution of effect sizes • That underlying population distribution also has its own variance, τ2, commonly called the variance component • Thus, each effect size has two components of variation, one due to sampling error, and one from the underlying distribution 25.11.2019 8
  • 9. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 9
  • 10. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Definition of combined effect • Fixed effect model • There is one true effect • Summary effect is estimate of this value • Random effects model • There is a distribution of effects • Summary effect is mean of distribution 25.11.2019 10
  • 11. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course How weights are assigned? 25.11.2019 11
  • 12. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course W = 1/ (V1) Fixed-effects model 25.11.2019 12
  • 13. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Random-effects model 25.11.2019 13 1W = 1/ (V +T 2 )
  • 14. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 190 How weights shift? • If within-study variance only, W=1/V • If between-study variance only, W=1/T2 • If both, W=1/(V+T2) 25.11.2019 14
  • 15. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 15
  • 16. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 16
  • 17. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Random vs. Fixed 25.11.2019 17
  • 18. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Random vs. Fixed 25.11.2019 18 RE weights are more balanced
  • 19. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Random vs. Fixed 25.11.2019 19 RE confidence interval is wider
  • 20. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Large study has less impact under RE 25.11.2019 20
  • 21. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Small study has more impact under RE 25.11.2019 21
  • 22. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course FE 25.11.2019 22
  • 23. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Summary effect in Fixed model 25.11.2019 23 244.215 101.171 = 0.414FE
  • 24. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Variance of summary effect in fixed model 25.11.2019 24 1 244.215 = 0.004FE
  • 25. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course RE 25.11.2019 25
  • 26. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Summary effect in random model 25.11.2019 26 90.284 32.342 = 0.358RE
  • 27. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Variance of summary effect in random model 25.11.2019 27 1 90.284 = 0.011RE
  • 28. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Why does it matter? • One matches the sampling • One does not match the sampling • Wrong model yields incorrect weights • Estimate of mean is wrong • Estimate of CI is wrong • MUST choose based on sampling model • The meaning of the ES is different • Relative weights are closer under RE (effect size will shift) • Absolute weights are smaller under RE (CI will become wider) • p-value will change (less significant in long run but can go either way) 25.11.2019 28
  • 29. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Test of null 25.11.2019 29 M M Z = SE M* M* Z* = SE Fixed Random Two sources of error One source of error
  • 30. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Implications of the choice • If you expect that the effect size from each study arises from a different population then use random effects • Random effects model is more likely to give non-significant estimates • Recall that all our analyses in a meta-analysis are weighted by the inverse of the variance of the effect size, i.e., by the precision of the effect size estimate • Because we have more variation assumed in a random effects model, our weights for each study will be more equal to one another • In other words, in a fixed effect model, we will more heavily weight larger studies. In a random effects model, the larger studies will not be weighted as heavily 25.11.2019 30
  • 31. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Question! • Suppose we had four studies, each with • N =1,000,000, and a true (mean) effect size of 50. • Under the two models, • What would the forest plot look like? • What would the diamond look like? 25.11.2019 31
  • 32. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 32
  • 33. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 33
  • 34. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Which model should we use? • Base decision on the model that matched the way the data were collected • Not on test of homogeneity 25.11.2019 34
  • 35. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What you may hear • Fixed-effect is simple model • Random-effects is more complicated 25.11.2019 35
  • 36. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Actually • Fixed-effect is more restricted model • Random-effects makes less assumptions 25.11.2019 36
  • 37. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course An alternate view • Random-effects model only makes sense if we have a clear picture of the sampling frame • Otherwise, we should report the mean and CI for the studies in our sample without attempt to generalize to a larger universe 25.11.2019 37
  • 38. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Goals in a fixed effect model • In a fixed effect model, we will be most interested in estimating our common effect, θ, and its standard error • We will also want to know if there is heterogeneity present by computing Q • HOWEVER, WE WILL NOT decide on the basis of a significant Q that we should really do a random effects model • WE WILL make a decision about fixed effect versus random effects models because of our substantive knowledge of the area of the systematic review 25.11.2019 38
  • 39. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Goals in a random effects model • We also want to estimate a mean effect size, but now this is the mean effect size from the underlying population, μ • We also want to estimate the variance of the underlying effect size, τ2 • We will test heterogeneity by testing whether τ2 is different from 0. • Biggest difficulty: how to estimate τ2 25.11.2019 39
  • 40. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Estimating the variance component, τ2 • There are two main methods for computing τ2 • Variously called the method of moments, the DerSimonian/Laird estimate • Restricted maximum likelihood • The method of moments estimator is easy to compute and is based on the value of Q, the homogeneity statistic • Restricted maximum likelihood requires an iterative solution 25.11.2019 40
  • 41. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Method of moments estimator 25.11.2019 41
  • 42. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Restricted maximum likelihood estimator • Many statisticians do not like the method of moments estimator • Can estimate τ2 using HLM, SAS Proc Mixed, or R 25.11.2019 42
  • 43. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Differences between the two models 25.11.2019 43
  • 44. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course ES assumptions Fixed effect model • We assume that the treatment effect is the same in all trials. • We use only the sampling variation within the trials. Random effects model • We assume that the treatment effect is the not same in all trials. • The trials are a sample from a population of possible of trials where the treatment effect varies. • We use the sampling variation within the trials and the sampling variation between trials. 25.11.2019 44
  • 45. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Sampling assumptions Fixed effect model • If the treatment effect is the same in all trials, it is more powerful and easier. • No assumption about representativeness. Random effects model • Less powerful because P values are larger and confidence intervals are wider. • The trials are a sample from a population of possible of trials where the treatment effect varies. • They must be a representative or random sample. • Very strong assumption. 25.11.2019 45
  • 46. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Variance Fixed effect model • Variance of treatment effect in trial = standard error squared. • Weight = 1/variance = 1/SE2 Random effects model • Variance of treatment effect in trial = standard error squared plus inter- trial variance • Weight = 1/variance. • 1 = -------------------------------- SE2 + inter-trial variance • Inter-trial variance has degrees of freedom given by number of trials minus one. • Typically small. 25.11.2019 46
  • 47. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course When heterogeneity exists Fixed effect model • When heterogeneity exists we get: • a pooled estimate which may give too much weight to large studies, • a confidence interval which is too narrow, • a P-value which is too small. Random effects model • When heterogeneity exists we get: • possibly a different pooled estimate with a different interpretation, • a wider confidence interval, • a larger P-value. 25.11.2019 47
  • 48. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course When heterogeneity doesn’t exist Fixed effect model • When heterogeneity does not exists: • a pooled estimate which is correct, • a confidence interval which is correct, • a P-value which is correct. Random effects model • When heterogeneity does not exist: • a pooled estimate which is correct, • a confidence interval which is too wide, • a P-value which is too large. 25.11.2019 48
  • 49. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 49
  • 50. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 06/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Thank you Kindly email your queries to sarizwan1986@outlook.com 25.11.2019 50