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Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Presenting the results of
meta-analysis
Dr. S. A. Rizwan M.D.,
Public Health Specialist & Lecturer,
Saudi Board of Preventive Medicine – Riyadh,
Ministry of Health, KSA
26.11.2019 1
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Outline
• Panels
• Charts
• Tables
• Graphs
26.11.2019 2
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Panels
26.11.2019 3
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Panel
26.11.2019 4
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Panel
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Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Panel
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Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Panel
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Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Charts
26.11.2019 8
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Flowchart
Study selection
process
26.11.2019 9
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Flowchart
Study selection
process
26.11.2019 10
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Other charts
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Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Other charts
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Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Tables
26.11.2019 13
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Types of analyses and tables
• Main or primary analysis
• The main objective of the paper
• Pooled estimate of effect size
• Secondary analysis
• Subgroup analysis
• To see if effects are different across interest groups
• Need to have sufficient sample
• Sensitivity analysis
• To see if estimates change by changing some parameters like excluding low quality studies
• Meta-regression
• Publication bias analysis
26.11.2019 14
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Description of
study features
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Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Primary analyses table
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Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Subgroup
analyses table
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Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Subgroup
analyses table
26.11.2019 18
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Sensitivity analyses table
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Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Meta-regression table
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Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Graphs
26.11.2019 21
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Graphs
• Graphs are an essential tool for conveying the results of a meta-
analysis to readers
• But if poorly constructed, graphs can be misleading and/or confuse
readers
• Graphs should strive for accuracy, simplicity, clarity, and aesthetics
26.11.2019 22
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Basic Graphing Principles
• Descriptive titles and/or captions
• Use of legends (when appropriate)
• Representative range of scale
• Properly labeled axes
• Inclusion of reference points on axes
• Graphs should reflect the statistical precision of results
• Explicit mention of any excluded data
• Data in graphs should generally be available elsewhere in the review (except
in very large reviews)
• Aesthetics (line thickness, symbol size, symbol types, parsimony)
26.11.2019 23
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Forest plots
26.11.2019 24
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Forest plots
• The “workhorse” graph in meta-analysis
• Display effect size estimates and confidence intervals for each study
included in the meta-analysis
• Effect size estimates typically shown with blocks proportionate to the
weight assigned to a given study
• Functions to draw the eye toward studies with larger sample size/larger
weights, and away from smaller studies with wider confidence intervals
26.11.2019 25
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Forest plots
• Estimated mean effect size with confidence interval shown at the
bottom, typically with a diamond
• In random effects meta-analyses, prediction intervals can be used to
display dispersion in the estimated effect
• Studies should be ordered in a meaningful way
• Effect size magnitude
• Study weight (precision)
• Chronological order
• Other meaningful study characteristic
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Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Forest plot
26.11.2019 27
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Forest plot
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Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Forest plots with subgroups
• Display effect size estimates and confidence intervals for each study,
split by some grouping variable
• Useful for depicting results from subgroup or moderator analyses
• May include the overall summary effect across groups, if appropriate
• Results from statistical tests of moderation
• (e.g., QB or b from a meta-regression) should be summarized on the
graph or in footnotes, when appropriate
26.11.2019 29
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Forest plots with subgroups
26.11.2019 30
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Forest plots with
subgroups
26.11.2019 31
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Summary forest plots
• Display summary (mean) effect sizes and confidence intervals for
different groups of studies
• Does not include effect size estimates from individual studies
• Useful for very large reviews where traditional forest plots may not be
feasible, but effects can be categorized into meaningful groups (e.g.,
across intervention, study, participant types)
• May include the overall summary effect across groups, if appropriate
• Results from statistical tests of moderation (e.g., QB or b from a meta-
regression) should be summarized on the graph or in footnotes, when
appropriate
26.11.2019 32
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Summary
forest plot
26.11.2019 33
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Cumulative meta-analysis forest plots
• Display results from iterative estimation of summary (mean) effect sizes,
cumulatively adding one study at a time
• Useful for showing the accumulation of evidence over time, or the
in/stability of intervention effects over time
• May also be used to explore small sample bias, cumulatively adding
studies according to sample size of primary studies
• Title should clearly specify it is a forest plot showing results from a
cumulative meta-analysis
26.11.2019 34
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Cumulative
forest plot
26.11.2019 35
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
General suggestions – forest plots
• Always include forest plots (or summary forest plots) if possible/appropriate
• Not recommended with fewer than 2 studies
• Plot ratio effect size measures on the log scale, but include axis labels on the
original anti-logged scale
• Include reference lines at the null value
• State the confidence level for confidence intervals
• Blocks for each study should be proportionate to study weight
• Sort studies in a meaningful order (e.g., effect size magnitude)
• State the direction of results
• Include prediction intervals for random effects analyses
• Include numerical data on plots (if possible)
26.11.2019 36
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
What’s wrong with
this forest plot?
• Uninformative study labels
• Seemingly random order of
effect sizes
• Unclear direction of effect sizes
• Does not include data
• Unspecified confidence level
• General aesthetics (white
space)
26.11.2019 37
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Funnel plots
26.11.2019 38
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Funnel plots
• Exploratory tool used to visually assess the possibility of
publication/small study bias in a meta-analysis
• Scatter plot of effect size (x-axis) against some measure of study size
(y-axis)
• x-axis: use log scale for ratio effect size measures, e.g., ln(OR), ln(RR)
• y-axis: the standard error of the effect size is generally recommended,
• y-axis: other options also available
• Not recommended in very small meta-analyses (e.g., n<10)
26.11.2019 39
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Funnel plots
• If publication bias is present, you would expect null or ‘negative’
findings from small n studies to be suppressed (i.e., missing from the
plot)
• Asymmetry in the funnel plot for small n studies may provide
evidence of possible publication bias
• Symmetry in the funnel plot provides some evidence against the
possibility of publication bias
26.11.2019 40
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 26.11.2019 41
Funnel plot
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Funnel plot
26.11.2019 42
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Funnel plot
26.11.2019 43
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Funnel plots
• Asymmetry could be due to factors other than publication bias, e.g.,
• Poor methodological quality
• Other reporting biases
• Artefactual variation
• Chance
• True heterogeneity
• Assessing funnel plot symmetry relies entirely on subjective visual
judgment
26.11.2019 44
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Contour enhanced funnel plots
• Funnel plot with additional contour lines associated with ‘milestones’
of statistical significance: p = .001, .01, .05, etc.
• If studies are missing in areas of statistical non-significance, publication bias
may be present
• If studies are missing in areas of statistical significance, asymmetry may be
due to factors other than publication bias
• If there are no studies in areas of statistical significance, publication bias may
be present
• Can help distinguish funnel plot asymmetry due to publication bias
versus other factors
26.11.2019 45
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Contour enhanced
funnel plot
26.11.2019 46
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
General suggestions – funnel plots
• Not recommended with fewer than 10 studies
• Plot effect sizes on the horizontal axis
• Plot the standard error of the effect size on the vertical axis (generally)
• Plot ratio effect size measures on the log scale, but include axis labels on the
original anti-logged scale
• All points should be the same size (weights/precision represented in the vertical
axis)
• Include 95% pseudo-confidence limits from a fixed effect analysis
• Include contours if possible
• Data in graphs should generally be available elsewhere in the review (except in
very large reviews)
• Use different plotting symbols to distinguish subgroups, when appropriate
26.11.2019 47
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
What’s wrong with
this funnel plot?
• Effect size on vertical axis
• Points are not all the same size
• Vague labeling of axes and
reference line
• No confidence bands
26.11.2019 48
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Bubble plots
• Scatter plot of a study covariate (x-axis) against effect size (y-axis)
• Useful to characterize covariates that may be a source of
heterogeneity
• Provides a visual representation of results from a bivariate meta-
regression model
26.11.2019 49
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Bubble plot
26.11.2019 50
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Bubble plot
26.11.2019 51
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
General suggestions – bubble plots
• Plot effect sizes on the vertical axis
• Plot the covariate on the horizontal axis
• Plot ratio effect size measures on the log scale, but include axis labels
on the original anti-logged scale
• Points should be proportionate to study weight
• Include fitted meta-regression line (if appropriate)
• Data in graphs should generally be available elsewhere in the review
(except in very large reviews)
26.11.2019 52
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Galbraith plot
• Scatter plot of inverse standard error (x-axis) against a standardized
effect size (i.e., effect size divided by its standard error) (y-axis)
• Includes an unweighted regression line constrained through the origin
with slope equal to the fixed effect summary effect size estimate
• Useful for displaying heterogeneity and aiding detection of outliers
• Useful for displaying effect sizes in very large reviews where forest
plots may be impractical
26.11.2019 53
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Galbraith plot
26.11.2019 54
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Galbraith plot
• Points should be the same size for study (weight/precision is
represented in the horizontal axis)
• Include confidence intervals around the fixed effect summary effect
line
• Use different plotting symbols to distinguish subgroups, when
appropriate
26.11.2019 55
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
L’abbé plot
• Plot of control group risk (x-axis) against treatment group risk (y-axis)
• Commonly used to depict risks, but can also be plotted on log risk or
log odds
• Most commonly used for binary outcome data, but can be extended
to depict means for continuous outcomes or ROC plot for
diagnostic/screening test accuracy
• Can also be used to contrast different effect size metrics (odds ratio,
risk ratio, risk difference)
26.11.2019 56
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
L’abbé plot
26.11.2019 57
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
L’abbé plot
26.11.2019 58
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
L’abbé plot
• Can be used to investigate
heterogeneity
• Ideally a L'Abbé plot should have the
symbols appropriate to the size of
the trials
• There is an inset for the symbol size,
and the two colours show trazodone
used for erectile dysfunction in two
different conditions (and with clear
clinical heterogeneity)
26.11.2019 59
Trazodone for erectile dysfunction in
psychogenic erectile dysfunction (dark
symbols) and with physiological or mixed
aetiology (light symbols)
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Other graphs
• Density strips
• Raindrop plots
• Graphical display of study heterogeneity (GOSH)
• CUSUM chart
• Veritas plot
• Summary receiver-operator curve (SROC) graphs
• Cross hairs ROC plot
• Harvest plot
• Baujat plots
26.11.2019 60
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Density strip
• Density Strip Plot of Relative
Risk of Progression to
Clinical Disease/AIDS.
Bayesian random effects
analysis (favors treatment on
the left of 1.0); density plots
on the figure on the left
represent combined data;
• on the right accounts for
individual study arms and the
impact of adding selenium or
vitamin A to MNS
26.11.2019 61
PLoS ONE 10(4):e0120113
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Raindrop
forest plot
• The width of the likelihood
raindrops corresponds to the
confidence intervals, as also
shown in the classic forest plot.
In addition, for each likelihood
drop the height (and color
shading) visualizes the
plausibility of true values given
the observed estimate.
26.11.2019 62
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
GOSH
• New method for visualizing
between-study heterogeneity using
combinatorial meta-analysis.
• The method is based on performing
separate meta-analyses on all
possible subsets of studies in a
meta-analysis.
• Summary effect sizes and other
statistics produced by the all-
subsets meta-analyses to generate
graphs that can be used to
investigate heterogeneity, identify
influential studies, and explore
subgroup effects.
26.11.2019 63
(wileyonlinelibrary.com) DOI: 10.1002/jrsm.1053
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Veritas plot
• The Veritas plot is an adaption of
the radar plot, a graphic tool for the
description of multiattribute data.
• Key elements of meta-analytical
quality such as heterogeneity,
publication bias and study design
are assessed.
26.11.2019 64
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2769126/
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
SROC plot
• Summary receiver operating
characteristic (SROC) analysis is
used in diagnostic accuracy meta-
analyses
• It is suited to this purpose with its
use of sensitivity and specificity.
• However, it is only meaningful
when similar endpoints,
diagnostic threshold, study
quality, and test characteristics
are compared.
• PLoS ONE 11(7):e0159860
26.11.2019 65
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Cross-hair
ROC plot
• The use of plots of receiver-operator
curve (ROC) space showing
individual studies and summary
estimates of diagnostic accuracy has
become common but can be
difficult to interpret.
• ‘Cross-hairs’ plots display the
individual studies in ROC space with
paired confidence intervals
representing sensitivity and
specificity, and allow for the results
of meta-analysis to be overlaid on
the plot.
26.11.2019 66
Phillips, B., Stewart, L. A., & Sutton, A. J. (2010). “Cross hairs” plots for diagnostic
meta-analysis. Research Synthesis Methods, 1(3-4), 308–315. doi:10.1002/jrsm.26
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Harvest plot
• Harvest plots are used to
graphically display evidence
from complex and diverse
studies or results.
• Overviews of reviews bring
together evidence from two
or more systematic reviews
26.11.2019 67
Harvest plots for overview of
reviews on acute otitis media
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Baujat plot
• A diagnostic plot to detect
sources of heterogeneity
• Contribution of each study to the
overall Q-test statistic for
heterogeneity on the horizontal
axis
• Influence of each study (defined
as the standardized squared
difference between the overall
estimate based on a fixed-effects
model with and without the ith
study included in the model) on
the vertical axis.
26.11.2019 68
http://www.metafor-project.org/doku.php/plots:baujat_plot
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Take home messages
• Panels and flowcharts help to understand the study methods
• Tables provide valuable information on results in glance
• Tables should be split into meaningful groups with all statistical info
• Graphs are an important part of any meta-analysis and can greatly
facilitate interpretation
• Forest plots should (almost always) be included
• Funnel plots and other various plots may also be appropriate
• Always follow standard graphing principles, and strive for accuracy,
simplicity, clarity, aesthetic appeal, and good structure
26.11.2019 69
Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Thank you
Kindly email your queries to sarizwan1986@outlook.com
26.11.2019 70

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Presenting the results of meta-analysis

  • 1. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Presenting the results of meta-analysis Dr. S. A. Rizwan M.D., Public Health Specialist & Lecturer, Saudi Board of Preventive Medicine – Riyadh, Ministry of Health, KSA 26.11.2019 1
  • 2. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Outline • Panels • Charts • Tables • Graphs 26.11.2019 2
  • 3. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Panels 26.11.2019 3
  • 4. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Panel 26.11.2019 4
  • 5. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Panel 26.11.2019 5
  • 6. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Panel 26.11.2019 6
  • 7. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Panel 26.11.2019 7
  • 8. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Charts 26.11.2019 8
  • 9. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Flowchart Study selection process 26.11.2019 9
  • 10. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Flowchart Study selection process 26.11.2019 10
  • 11. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Other charts 26.11.2019 11
  • 12. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Other charts 26.11.2019 12
  • 13. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Tables 26.11.2019 13
  • 14. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Types of analyses and tables • Main or primary analysis • The main objective of the paper • Pooled estimate of effect size • Secondary analysis • Subgroup analysis • To see if effects are different across interest groups • Need to have sufficient sample • Sensitivity analysis • To see if estimates change by changing some parameters like excluding low quality studies • Meta-regression • Publication bias analysis 26.11.2019 14
  • 15. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Description of study features 26.11.2019 15
  • 16. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Primary analyses table 26.11.2019 16
  • 17. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Subgroup analyses table 26.11.2019 17
  • 18. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Subgroup analyses table 26.11.2019 18
  • 19. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Sensitivity analyses table 26.11.2019 19
  • 20. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Meta-regression table 26.11.2019 20
  • 21. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Graphs 26.11.2019 21
  • 22. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Graphs • Graphs are an essential tool for conveying the results of a meta- analysis to readers • But if poorly constructed, graphs can be misleading and/or confuse readers • Graphs should strive for accuracy, simplicity, clarity, and aesthetics 26.11.2019 22
  • 23. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Basic Graphing Principles • Descriptive titles and/or captions • Use of legends (when appropriate) • Representative range of scale • Properly labeled axes • Inclusion of reference points on axes • Graphs should reflect the statistical precision of results • Explicit mention of any excluded data • Data in graphs should generally be available elsewhere in the review (except in very large reviews) • Aesthetics (line thickness, symbol size, symbol types, parsimony) 26.11.2019 23
  • 24. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Forest plots 26.11.2019 24
  • 25. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Forest plots • The “workhorse” graph in meta-analysis • Display effect size estimates and confidence intervals for each study included in the meta-analysis • Effect size estimates typically shown with blocks proportionate to the weight assigned to a given study • Functions to draw the eye toward studies with larger sample size/larger weights, and away from smaller studies with wider confidence intervals 26.11.2019 25
  • 26. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Forest plots • Estimated mean effect size with confidence interval shown at the bottom, typically with a diamond • In random effects meta-analyses, prediction intervals can be used to display dispersion in the estimated effect • Studies should be ordered in a meaningful way • Effect size magnitude • Study weight (precision) • Chronological order • Other meaningful study characteristic 26.11.2019 26
  • 27. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Forest plot 26.11.2019 27
  • 28. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Forest plot 26.11.2019 28
  • 29. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Forest plots with subgroups • Display effect size estimates and confidence intervals for each study, split by some grouping variable • Useful for depicting results from subgroup or moderator analyses • May include the overall summary effect across groups, if appropriate • Results from statistical tests of moderation • (e.g., QB or b from a meta-regression) should be summarized on the graph or in footnotes, when appropriate 26.11.2019 29
  • 30. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Forest plots with subgroups 26.11.2019 30
  • 31. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Forest plots with subgroups 26.11.2019 31
  • 32. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Summary forest plots • Display summary (mean) effect sizes and confidence intervals for different groups of studies • Does not include effect size estimates from individual studies • Useful for very large reviews where traditional forest plots may not be feasible, but effects can be categorized into meaningful groups (e.g., across intervention, study, participant types) • May include the overall summary effect across groups, if appropriate • Results from statistical tests of moderation (e.g., QB or b from a meta- regression) should be summarized on the graph or in footnotes, when appropriate 26.11.2019 32
  • 33. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Summary forest plot 26.11.2019 33
  • 34. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Cumulative meta-analysis forest plots • Display results from iterative estimation of summary (mean) effect sizes, cumulatively adding one study at a time • Useful for showing the accumulation of evidence over time, or the in/stability of intervention effects over time • May also be used to explore small sample bias, cumulatively adding studies according to sample size of primary studies • Title should clearly specify it is a forest plot showing results from a cumulative meta-analysis 26.11.2019 34
  • 35. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Cumulative forest plot 26.11.2019 35
  • 36. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course General suggestions – forest plots • Always include forest plots (or summary forest plots) if possible/appropriate • Not recommended with fewer than 2 studies • Plot ratio effect size measures on the log scale, but include axis labels on the original anti-logged scale • Include reference lines at the null value • State the confidence level for confidence intervals • Blocks for each study should be proportionate to study weight • Sort studies in a meaningful order (e.g., effect size magnitude) • State the direction of results • Include prediction intervals for random effects analyses • Include numerical data on plots (if possible) 26.11.2019 36
  • 37. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What’s wrong with this forest plot? • Uninformative study labels • Seemingly random order of effect sizes • Unclear direction of effect sizes • Does not include data • Unspecified confidence level • General aesthetics (white space) 26.11.2019 37
  • 38. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Funnel plots 26.11.2019 38
  • 39. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Funnel plots • Exploratory tool used to visually assess the possibility of publication/small study bias in a meta-analysis • Scatter plot of effect size (x-axis) against some measure of study size (y-axis) • x-axis: use log scale for ratio effect size measures, e.g., ln(OR), ln(RR) • y-axis: the standard error of the effect size is generally recommended, • y-axis: other options also available • Not recommended in very small meta-analyses (e.g., n<10) 26.11.2019 39
  • 40. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Funnel plots • If publication bias is present, you would expect null or ‘negative’ findings from small n studies to be suppressed (i.e., missing from the plot) • Asymmetry in the funnel plot for small n studies may provide evidence of possible publication bias • Symmetry in the funnel plot provides some evidence against the possibility of publication bias 26.11.2019 40
  • 41. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 26.11.2019 41 Funnel plot
  • 42. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Funnel plot 26.11.2019 42
  • 43. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Funnel plot 26.11.2019 43
  • 44. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Funnel plots • Asymmetry could be due to factors other than publication bias, e.g., • Poor methodological quality • Other reporting biases • Artefactual variation • Chance • True heterogeneity • Assessing funnel plot symmetry relies entirely on subjective visual judgment 26.11.2019 44
  • 45. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Contour enhanced funnel plots • Funnel plot with additional contour lines associated with ‘milestones’ of statistical significance: p = .001, .01, .05, etc. • If studies are missing in areas of statistical non-significance, publication bias may be present • If studies are missing in areas of statistical significance, asymmetry may be due to factors other than publication bias • If there are no studies in areas of statistical significance, publication bias may be present • Can help distinguish funnel plot asymmetry due to publication bias versus other factors 26.11.2019 45
  • 46. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Contour enhanced funnel plot 26.11.2019 46
  • 47. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course General suggestions – funnel plots • Not recommended with fewer than 10 studies • Plot effect sizes on the horizontal axis • Plot the standard error of the effect size on the vertical axis (generally) • Plot ratio effect size measures on the log scale, but include axis labels on the original anti-logged scale • All points should be the same size (weights/precision represented in the vertical axis) • Include 95% pseudo-confidence limits from a fixed effect analysis • Include contours if possible • Data in graphs should generally be available elsewhere in the review (except in very large reviews) • Use different plotting symbols to distinguish subgroups, when appropriate 26.11.2019 47
  • 48. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What’s wrong with this funnel plot? • Effect size on vertical axis • Points are not all the same size • Vague labeling of axes and reference line • No confidence bands 26.11.2019 48
  • 49. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Bubble plots • Scatter plot of a study covariate (x-axis) against effect size (y-axis) • Useful to characterize covariates that may be a source of heterogeneity • Provides a visual representation of results from a bivariate meta- regression model 26.11.2019 49
  • 50. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Bubble plot 26.11.2019 50
  • 51. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Bubble plot 26.11.2019 51
  • 52. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course General suggestions – bubble plots • Plot effect sizes on the vertical axis • Plot the covariate on the horizontal axis • Plot ratio effect size measures on the log scale, but include axis labels on the original anti-logged scale • Points should be proportionate to study weight • Include fitted meta-regression line (if appropriate) • Data in graphs should generally be available elsewhere in the review (except in very large reviews) 26.11.2019 52
  • 53. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Galbraith plot • Scatter plot of inverse standard error (x-axis) against a standardized effect size (i.e., effect size divided by its standard error) (y-axis) • Includes an unweighted regression line constrained through the origin with slope equal to the fixed effect summary effect size estimate • Useful for displaying heterogeneity and aiding detection of outliers • Useful for displaying effect sizes in very large reviews where forest plots may be impractical 26.11.2019 53
  • 54. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Galbraith plot 26.11.2019 54
  • 55. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Galbraith plot • Points should be the same size for study (weight/precision is represented in the horizontal axis) • Include confidence intervals around the fixed effect summary effect line • Use different plotting symbols to distinguish subgroups, when appropriate 26.11.2019 55
  • 56. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course L’abbé plot • Plot of control group risk (x-axis) against treatment group risk (y-axis) • Commonly used to depict risks, but can also be plotted on log risk or log odds • Most commonly used for binary outcome data, but can be extended to depict means for continuous outcomes or ROC plot for diagnostic/screening test accuracy • Can also be used to contrast different effect size metrics (odds ratio, risk ratio, risk difference) 26.11.2019 56
  • 57. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course L’abbé plot 26.11.2019 57
  • 58. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course L’abbé plot 26.11.2019 58
  • 59. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course L’abbé plot • Can be used to investigate heterogeneity • Ideally a L'Abbé plot should have the symbols appropriate to the size of the trials • There is an inset for the symbol size, and the two colours show trazodone used for erectile dysfunction in two different conditions (and with clear clinical heterogeneity) 26.11.2019 59 Trazodone for erectile dysfunction in psychogenic erectile dysfunction (dark symbols) and with physiological or mixed aetiology (light symbols)
  • 60. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Other graphs • Density strips • Raindrop plots • Graphical display of study heterogeneity (GOSH) • CUSUM chart • Veritas plot • Summary receiver-operator curve (SROC) graphs • Cross hairs ROC plot • Harvest plot • Baujat plots 26.11.2019 60
  • 61. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Density strip • Density Strip Plot of Relative Risk of Progression to Clinical Disease/AIDS. Bayesian random effects analysis (favors treatment on the left of 1.0); density plots on the figure on the left represent combined data; • on the right accounts for individual study arms and the impact of adding selenium or vitamin A to MNS 26.11.2019 61 PLoS ONE 10(4):e0120113
  • 62. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Raindrop forest plot • The width of the likelihood raindrops corresponds to the confidence intervals, as also shown in the classic forest plot. In addition, for each likelihood drop the height (and color shading) visualizes the plausibility of true values given the observed estimate. 26.11.2019 62
  • 63. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course GOSH • New method for visualizing between-study heterogeneity using combinatorial meta-analysis. • The method is based on performing separate meta-analyses on all possible subsets of studies in a meta-analysis. • Summary effect sizes and other statistics produced by the all- subsets meta-analyses to generate graphs that can be used to investigate heterogeneity, identify influential studies, and explore subgroup effects. 26.11.2019 63 (wileyonlinelibrary.com) DOI: 10.1002/jrsm.1053
  • 64. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Veritas plot • The Veritas plot is an adaption of the radar plot, a graphic tool for the description of multiattribute data. • Key elements of meta-analytical quality such as heterogeneity, publication bias and study design are assessed. 26.11.2019 64 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2769126/
  • 65. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course SROC plot • Summary receiver operating characteristic (SROC) analysis is used in diagnostic accuracy meta- analyses • It is suited to this purpose with its use of sensitivity and specificity. • However, it is only meaningful when similar endpoints, diagnostic threshold, study quality, and test characteristics are compared. • PLoS ONE 11(7):e0159860 26.11.2019 65
  • 66. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Cross-hair ROC plot • The use of plots of receiver-operator curve (ROC) space showing individual studies and summary estimates of diagnostic accuracy has become common but can be difficult to interpret. • ‘Cross-hairs’ plots display the individual studies in ROC space with paired confidence intervals representing sensitivity and specificity, and allow for the results of meta-analysis to be overlaid on the plot. 26.11.2019 66 Phillips, B., Stewart, L. A., & Sutton, A. J. (2010). “Cross hairs” plots for diagnostic meta-analysis. Research Synthesis Methods, 1(3-4), 308–315. doi:10.1002/jrsm.26
  • 67. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Harvest plot • Harvest plots are used to graphically display evidence from complex and diverse studies or results. • Overviews of reviews bring together evidence from two or more systematic reviews 26.11.2019 67 Harvest plots for overview of reviews on acute otitis media
  • 68. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Baujat plot • A diagnostic plot to detect sources of heterogeneity • Contribution of each study to the overall Q-test statistic for heterogeneity on the horizontal axis • Influence of each study (defined as the standardized squared difference between the overall estimate based on a fixed-effects model with and without the ith study included in the model) on the vertical axis. 26.11.2019 68 http://www.metafor-project.org/doku.php/plots:baujat_plot
  • 69. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Take home messages • Panels and flowcharts help to understand the study methods • Tables provide valuable information on results in glance • Tables should be split into meaningful groups with all statistical info • Graphs are an important part of any meta-analysis and can greatly facilitate interpretation • Forest plots should (almost always) be included • Funnel plots and other various plots may also be appropriate • Always follow standard graphing principles, and strive for accuracy, simplicity, clarity, aesthetic appeal, and good structure 26.11.2019 69
  • 70. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 09/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Thank you Kindly email your queries to sarizwan1986@outlook.com 26.11.2019 70