Meta-analysisNew using Stata
Houssein Assaad
Senior Statistician and Software Developer
StataCorp LLC
Stata Conference
July 30 , 2020
Philadelphia In-laws' basement
Outline
- What is meta-analysis? Why and when you should use it ?
- Data setup: Effect-sizes and Meta-analysis models
- The meta suite: Exploring the syntax
- Examples: Two case studies
- Summary
- Subgroup-analysis:
- Publication bias: NSAIDS data
- The meta control panel
- BCG vaccine efficacy against tuberculosis
- MA is the science of combining results from multiple studies addressing a similar scientific question
What is meta-analysis (MA) ?
- MA has been mostly used in medicine, but also in econometrics, ecology, psychology, and education to name a few
- The goal of MA is to explore consistencies and discrepancies among the studies , and if sensible, provide a unified conclusion
- Potential problem: Publication bias, which occur when the results of the published literature in a certain domain differ systematically in its results from all the relevant research results
Why would you want to use meta-analysis ?
- An increase in power and improvement in precision
- The ability to answer questions not posed by individual studies and to settle controversies arising from conflicting claims
Potential advantages of MA include:
Data setup
- K studies
treatment group
control group
- Study j estimates effect size, θj and its standard error σj
- Effect size (ES): a value that reflects the magnitude of group differences or the strength of a relationship between 2 variables
vs
ES
e.g. OR, RR, RD, Hedges's g, Cohen's d etc.
variable 1
variable 2
ES
e.g. correlation coef. r, regression coef β etc.
MA models
θ^j=θj+ϵj,ϵj∼N(0,σ^j2)
\hat{\theta}_j = \theta_j + \epsilon_j, \, \epsilon_{j}\sim N\left(0, \hat{\sigma}^2_j\right)
K independent studies, each reports:
- An estimate, θ^j, of the true (unknown) effect size θj
- An estimate, σ^j , of its standard error
- Estimating θ (and τ2 with RE model) is one of the main goals of MA
θ
\theta
| Model | Assumption | Target of inference |
|---|---|---|
| common effect (CE) | common value |
|
| fixed effects (FE) | fixed | |
| Random effects (RE) |
θ1=θ2=⋯=θK
\theta_1=\theta_2=\dots=\theta_K
θj
\theta_j
θj={θ+uj}∼N(θ,τ2)
\theta_j = \left\{\theta + u_j\right\} \sim N\left(\theta, \tau^2\right)
θ=weighted avg(θj)
\theta = \text{weighted avg}(\theta_j)
θ=E(θj)
\theta= E\left(\theta_j \right)
θ^=∑j=1kwj∑j=1kwjθ^j
\hat{\theta} = \frac{\sum_{j=1}^kw_j\hat{\theta}_j}{\sum_{j=1}^k w_j}
Forest Plot
The meta suite
Exploring the syntax
- Pre-computed (generic) effect sizes
- Effect sizes for binary data
- Effect sizes for continuous data
meta setData setup and MA declaration
create variables starting with _meta_ (e.g. _meta_es, _meta_se) to be used with all other commands
etc.
meta funnelplotmeta forestplotmeta summarizemeta esizemeta regressBinary summary data:
+----------------------------------+
| study nt1 nt0 nc1 nc0 |
|----------------------------------|
| 1 4 119 11 128 |
| 2 6 300 29 274 |
| 3 3 228 11 209 |
| 4 62 13536 248 12619 |
| 5 33 5036 47 5761 |
+----------------------------------+
Precomputed effect size data:
+----------------------+
| study ES ES_se |
|----------------------|
| 1 .03 .125 |
| 2 .12 .147 |
| 3 -.14 .167 |
| 4 1.18 .373 |
| 5 .26 .369 |
+----------------------+
Continuous summary data:
+--------------------------------------------------+
| study n1 m1 sd1 n2 m2 sd2 |
|--------------------------------------------------|
| 1 13 0.096 0.020 14 0.920 0.047 |
| 2 18 -0.000 0.066 11 1.110 0.094 |
| 3 10 0.054 0.088 11 0.956 0.040 |
| 4 15 0.000 0.019 20 0.899 0.098 |
| 5 15 0.036 0.020 10 1.102 0.014 |
+--------------------------------------------------+
Precomputed effect size data: (es and CI)
+----------------------------------------+
| study ES cil ciu |
|----------------------------------------|
| 1 .03 -.2149955 .2749955 |
| 2 .12 -.16811471 .40811471 |
| 3 -.14 -.46731399 .18731399 |
| 4 1.18 .44893343 1.9110666 |
| 5 .26 -.46322671 .98322671 |
+----------------------------------------+
meta esize nt1 nt0 nc1 nc0meta esize n1 m1 sd1 n2 m2 sd2meta set ES ES_semeta set ES cil ciuScenario II
Effect sizes computed from summary data
Binary summary data
(2×2 tables)
Continuous summary data
(sample size, mean, and standard deviation for each group)
Hedges's g, Cohen's d, Glass's Δ1 and Δ2, and (raw) mean difference D
log odds-ratio log(OR), log(ORpeto), log risk-ratio log(RR) , and risk difference RD
Scenario I
Pre-computed Effect sizes
Correlation r, log(HR), logit(p), etc.
meta esize n1 m1 sd1 n2 m2 sd2meta esize nt1 nt0 nc1 nc0meta set ES ES_seEffect sizes for binary data
. webuse bcg, clear (Efficacy of BCG vaccine against tuberculosis) . keep studylbl npost - nnegc . describe
------------------------------------------------------------------------------------------ storage display value variable name type format label variable label ------------------------------------------------------------------------------------------ studylbl str27 %27s Study label npost int %9.0g Number of TB positive cases in treated group nnegt long %9.0g Number of TB negative cases in treated group nposc int %9.0g Number of TB positive cases in control group nnegc long %9.0g Number of TB negative cases in control group ------------------------------------------------------------------------------------------
| group | TB+ | TB- |
|---|---|---|
| Vaccinated | npost = 4 | nnegt = 119 |
| control | nposc = 11 | nnegc = 128 |
each study, j, yield a 2×2 table, e.g. for study 1:
log(ORj)
\log(OR_j)
log(RRj)
\log(RR_j)
RDj
RD_j
log(ORpetoj)
\log(ORpeto_j)
+--------------------------------------------------------+ | studylbl npost nnegt nposc nnegc | |--------------------------------------------------------| 1. | Aronson, 1948 4 119 11 128 | 2. | Ferguson & Simes, 1949 6 300 29 274 | 3. | Rosenthal et al., 1960 3 228 11 209 | +--------------------------------------------------------+
. list in 1/3their SEs and CIs
computes one of
meta esizeEffect sizes for binary data
. meta esize npost nnegt nposc nnegc Meta-analysis setting information Study information No. of studies: 13 Study label: Generic <--- controlled by studylabel() Study size: _meta_studysize Summary data: npost nnegt nposc nnegc Effect size Type: lnoratio <--- controlled by esize() Label: Log Odds-Ratio <--- controlled by eslabel() Variable: _meta_es Zero-cells adj.: None; no zero cells <--- controlled by zerocells() Precision Std. Err.: _meta_se CI: [_meta_cil, _meta_ciu] CI level: 95% <--- controlled by level() Model and method <--- controlled by random[()], fixed[()], Model: Random-effects and common[()] Method: REML
Meta-analysis setting information Study information No. of studies: 13 Study label: Generic <--- controlled by studylabel() Study size: _meta_studysize Summary data: npost nnegt nposc nnegc Effect size Type: lnoratio <--- controlled by esize() Label: Log Odds-Ratio <--- controlled by eslabel() Variable: _meta_es Zero-cells adj.: None; no zero cells <--- controlled by zerocells() Precision Std. Err.: _meta_se CI: [_meta_cil, _meta_ciu] CI level: 95% <--- controlled by level() Model and method <--- controlled by random[()], fixed[()], Model: Random-effects and common[()] Method: REML
Meta-analysis setting information Study information No. of studies: 13 Study label: Generic <--- controlled by studylabel() Study size: _meta_studysize Summary data: npost nnegt nposc nnegc Effect size Type: lnoratio <--- controlled by esize() Label: Log Odds-Ratio <--- controlled by eslabel() Variable: _meta_es Zero-cells adj.: None; no zero cells <--- controlled by zerocells() Precision Std. Err.: _meta_se CI: [_meta_cil, _meta_ciu] CI level: 95% <--- controlled by level() Model and method <--- controlled by random[()], fixed[()], Model: Random-effects and common[()] Method: REML
Meta-analysis setting information Study information No. of studies: 13 Study label: Generic <--- controlled by studylabel() Study size: _meta_studysize Summary data: npost nnegt nposc nnegc Effect size Type: lnoratio <--- controlled by esize() Label: Log Odds-Ratio <--- controlled by eslabel() Variable: _meta_es Zero-cells adj.: None; no zero cells <--- controlled by zerocells() Precision Std. Err.: _meta_se CI: [_meta_cil, _meta_ciu] CI level: 95% <--- controlled by level() Model and method <--- controlled by random[()], fixed[()], Model: Random-effects and common[()] Method: REML
Meta-analysis setting information Study information No. of studies: 13 Study label: Generic <--- controlled by studylabel() Study size: _meta_studysize Summary data: npost nnegt nposc nnegc Effect size Type: lnoratio <--- controlled by esize() Label: Log Odds-Ratio <--- controlled by eslabel() Variable: _meta_es Zero-cells adj.: None; no zero cells <--- controlled by zerocells() Precision Std. Err.: _meta_se CI: [_meta_cil, _meta_ciu] CI level: 95% <--- controlled by level() Model and method <--- controlled by random[()], fixed[()], Model: Random-effects and common[()] Method: REML
- We can now use, for example, meta summarize to compute the overall effect size (mean log odds-ratio in this example)
. meta summarize Effect-size label: Log Odds-Ratio Effect size: _meta_es Std. Err.: _meta_se Meta-analysis summary Number of studies = 13 Random-effects model Heterogeneity: Method: REML tau2 = 0.3378 I2 (%) = 92.07 H2 = 12.61 -------------------------------------------------------------------- Study | Log Odds-Ratio [95% Conf. Interval] % Weight ------------------+------------------------------------------------- Study 1 | -0.939 -2.110 0.233 4.98 Study 2 | -1.666 -2.560 -0.772 6.34 Study 3 | -1.386 -2.677 -0.096 4.49 (Output omitted) Study 11 | -0.341 -0.560 -0.121 9.88 Study 12 | 0.447 -0.986 1.879 3.97 Study 13 | -0.017 -0.542 0.507 8.45 ------------------+------------------------------------------------- theta | -0.745 -1.110 -0.381 -------------------------------------------------------------------- Test of theta = 0: z = -4.01 Prob > |z| = 0.0001 Test of homogeneity: Q = chi2(12) = 163.16 Prob > Q = 0.0000
Effect-size label: Log Odds-Ratio Effect size: _meta_es Std. Err.: _meta_se Meta-analysis summary Number of studies = 13 Random-effects model Heterogeneity: Method: REML tau2 = 0.3378 I2 (%) = 92.07 H2 = 12.61 -------------------------------------------------------------------- Study | Log Odds-Ratio [95% Conf. Interval] % Weight ------------------+------------------------------------------------- Study 1 | -0.939 -2.110 0.233 4.98 Study 2 | -1.666 -2.560 -0.772 6.34 Study 3 | -1.386 -2.677 -0.096 4.49 (Output omitted) Study 11 | -0.341 -0.560 -0.121 9.88 Study 12 | 0.447 -0.986 1.879 3.97 Study 13 | -0.017 -0.542 0.507 8.45 ------------------+------------------------------------------------- theta | -0.745 -1.110 -0.381 -------------------------------------------------------------------- Test of theta = 0: z = -4.01 Prob > |z| = 0.0001 Test of homogeneity: Q = chi2(12) = 163.16 Prob > Q = 0.0000
Effect-size label: Log Odds-Ratio Effect size: _meta_es Std. Err.: _meta_se Meta-analysis summary Number of studies = 13 Random-effects model Heterogeneity: Method: REML tau2 = 0.3378 I2 (%) = 92.07 H2 = 12.61 -------------------------------------------------------------------- Study | Log Odds-Ratio [95% Conf. Interval] % Weight ------------------+------------------------------------------------- Study 1 | -0.939 -2.110 0.233 4.98 Study 2 | -1.666 -2.560 -0.772 6.34 Study 3 | -1.386 -2.677 -0.096 4.49 (Output omitted) Study 11 | -0.341 -0.560 -0.121 9.88 Study 12 | 0.447 -0.986 1.879 3.97 Study 13 | -0.017 -0.542 0.507 8.45 ------------------+------------------------------------------------- theta | -0.745 -1.110 -0.381 -------------------------------------------------------------------- Test of theta = 0: z = -4.01 Prob > |z| = 0.0001 Test of homogeneity: Q = chi2(12) = 163.16 Prob > Q = 0.0000
Effect-size label: Log Odds-Ratio Effect size: _meta_es Std. Err.: _meta_se Meta-analysis summary Number of studies = 13 Random-effects model Heterogeneity: Method: REML tau2 = 0.3378 I2 (%) = 92.07 H2 = 12.61 -------------------------------------------------------------------- Study | Log Odds-Ratio [95% Conf. Interval] % Weight ------------------+------------------------------------------------- Study 1 | -0.939 -2.110 0.233 4.98 Study 2 | -1.666 -2.560 -0.772 6.34 Study 3 | -1.386 -2.677 -0.096 4.49 (Output omitted) Study 11 | -0.341 -0.560 -0.121 9.88 Study 12 | 0.447 -0.986 1.879 3.97 Study 13 | -0.017 -0.542 0.507 8.45 ------------------+------------------------------------------------- theta | -0.745 -1.110 -0.381 -------------------------------------------------------------------- Test of theta = 0: z = -4.01 Prob > |z| = 0.0001 Test of homogeneity: Q = chi2(12) = 163.16 Prob > Q = 0.0000
Effect-size label: Log Odds-Ratio Effect size: _meta_es Std. Err.: _meta_se Meta-analysis summary Number of studies = 13 Random-effects model Heterogeneity: Method: REML tau2 = 0.3378 I2 (%) = 92.07 H2 = 12.61 -------------------------------------------------------------------- Study | Log Odds-Ratio [95% Conf. Interval] % Weight ------------------+------------------------------------------------- Study 1 | -0.939 -2.110 0.233 4.98 Study 2 | -1.666 -2.560 -0.772 6.34 Study 3 | -1.386 -2.677 -0.096 4.49 (Output omitted) Study 11 | -0.341 -0.560 -0.121 9.88 Study 12 | 0.447 -0.986 1.879 3.97 Study 13 | -0.017 -0.542 0.507 8.45 ------------------+------------------------------------------------- theta | -0.745 -1.110 -0.381 -------------------------------------------------------------------- Test of theta = 0: z = -4.01 Prob > |z| = 0.0001 Test of homogeneity: Q = chi2(12) = 163.16 Prob > Q = 0.0000
- Compute log(RR) (esize(lnrratio)) and use a RE model based on the DerSimonian-Laird method (random(dlaird))
. meta esize npost nnegt nposc nnegc, esize(lnrratio) random(dlaird). meta update, esize(lnrratio) random(dlaird)Or equivalently,
Meta-analysis setting information Study information No. of studies: 10 (omitted output) Effect size Type: lnrratio Label: Log Risk-Ratio Variable: _meta_es Zero-cells adj.: None; no zero cells (omitted output) Model and method Model: Random-effects Method: DerSimonian-Laird
You may change the default MA model using one of options random[()], common or fixed and the default effect size via option esize()
. meta update, studylabel(studylbl) eslabel("My label")You may provide more descriptive labels for the studies and the effect size using options studylabel() and eslabel()
Meta-analysis setting information from meta esize Study information No. of studies: 13 Study label: studylbl Study size: _meta_studysize Summary data: npost nnegt nposc nnegc Effect size Type: lnrratio Label: My label Variable: _meta_es Zero-cells adj.: None; no zero cells Precision Std. Err.: _meta_se CI: [_meta_cil, _meta_ciu] CI level: 95% Model and method Model: Random-effects Method: DerSimonian-Laird
- Had there been zero cells, you may specify how to handle them via the zerocells() option
. meta update, zerocells(.2)
// or
. meta update, zerocells(tacc) We will construct a forest plot for the 1st 4 studies to see the effect of adding study labels and effect size label
. meta update, studylabel(studylbl) eslabel("Log(RR)") . meta forestplot in 1/4
studylabel(studylbl)
eslabel("Log(RR)")
Forest plot without options studylabel() and eslabel()
- At any point in your analysis, you may use meta query to remind yourself of your current MA settings
. meta query -> meta esize npost nnegt nposc nnegc , esize(lnrratio) studylabel(studylbl) eslabel(My > label) random(dlaird) Meta-analysis setting information from meta esize Study information No. of studies: 13 Study label: studylbl Study size: _meta_studysize Summary data: npost nnegt nposc nnegc Effect size Type: lnrratio Label: My label Variable: _meta_es Zero-cells adj.: None; no zero cells Precision Std. Err.: _meta_se CI: [_meta_cil, _meta_ciu] CI level: 95% Model and method Model: Random-effects Method: DerSimonian-Laird
syntax
- If you have access to summary data, use meta esize to compute and declare effect sizes such as an odds ratio or a Hedges’s g.
- To check whether your data are already meta set or to see the current meta settings, use meta query
- To update some of your meta-analysis settings after the declaration, use meta update.
- Alternatively, if you have only precomputed (generic) effect sizes, use meta set.
Summary I
- meta set and meta esize create system variables with names starting with _meta_ to be used by all subsequent meta commands.
Data sets used
Two data sets (bcg.dta and nsaids.dta) will be used throughout this webinar, you may further explore them below
Exploring heterogenity
subgroup-analysis
Case study: Efficacy of BCG vaccine against tuberculosis
- Heterogeneity: Variability among the effect sizes beyond what is expected due to random sampling (chance).
- Exploring the possible reasons for heterogeneity between studies is an important aspect of a MA
. webuse bcgset, clear (Efficacy of BCG vaccine against tuberculosis; set with -meta esize-) . describe npost - studylbl
------------------------------------------------------------------------------------------ storage display value variable name type format label variable label ------------------------------------------------------------------------------------------ npost int %9.0g Number of TB positive cases in treated group nnegt long %9.0g Number of TB negative cases in treated group nposc int %9.0g Number of TB positive cases in control group nnegc long %9.0g Number of TB negative cases in control group latitude byte %9.0g Absolute latitude of the study location (in degrees) studylbl str27 %27s Study label ------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------ storage display value variable name type format label variable label ------------------------------------------------------------------------------------------ npost int %9.0g Number of TB positive cases in treated group nnegt long %9.0g Number of TB negative cases in treated group nposc int %9.0g Number of TB positive cases in control group nnegc long %9.0g Number of TB negative cases in control group latitude byte %9.0g Absolute latitude of the study location (in degrees) studylbl str27 %27s Study label ------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------ storage display value variable name type format label variable label ------------------------------------------------------------------------------------------ npost int %9.0g Number of TB positive cases in treated group nnegt long %9.0g Number of TB negative cases in treated group nposc int %9.0g Number of TB positive cases in control group nnegc long %9.0g Number of TB negative cases in control group latitude byte %9.0g Absolute latitude of the study location (in degrees) studylbl str27 %27s Study label ------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------ storage display value variable name type format label variable label ------------------------------------------------------------------------------------------ npost int %9.0g Number of TB positive cases in treated group nnegt long %9.0g Number of TB negative cases in treated group nposc int %9.0g Number of TB positive cases in control group nnegc long %9.0g Number of TB negative cases in control group latitude byte %9.0g Absolute latitude of the study location (in degrees) studylbl str27 %27s Study label ------------------------------------------------------------------------------------------
- MA consists of 13 studies (Colditz et al. [1994]) to evaluate the efficacy of the BCG vaccine against tuberculosis (TB)
- Vaccine efficacy has been controversial
+----------------------------------------------------------------+ | author npost nnegt nposc nnegc latitude | |----------------------------------------------------------------| 1. | Aronson 4 119 11 128 44 | 2. | Ferguson & Simes 6 300 29 274 55 | 3. | Rosenthal et al. 3 228 11 209 42 | +----------------------------------------------------------------+
. list author npost - nnegc latitude in 1/3. meta esize npost - nnegc, esize(lnrratio) studylabel(studylbl) . meta forestplot . meta forest, eform nullrefline
. meta esize npost - nnegc, esize(lnrratio) studylabel(studylbl) . meta forestplot . meta forest, eform nullrefline
. meta esize npost - nnegc, esize(lnrratio) studylabel(studylbl) . meta forestplot . meta forest, eform nullrefline
nonsignificant RR
nonoverlapping CIs
Quantifying heterogeneity
Sampling error
Between-study heterogeneity
I2=
I^2=
H2=
H^2=
Total observed heterogeneity
- Subgroup analysis focuses on explaining
(within-study heterogeneity)
meta summarize and meta forestplot report
92%≈
92\% \approx
12.86≈
12.86 \approx
Subgroup analysis
- Subgroup analysis involves dividing the data into subgroups, in order to make comparisons between them.
- The studies are grouped based on study or participants’ characteristics, and an overall effect-size estimate is computed for each group
- The goal of subgroup analysis is to compare these overall estimates across groups and determine whether the considered grouping helps explain some of the observed between-study heterogeneity.
Compare the BCG vaccine efficacy in cold vs hot climate
Berkey et al (1995) and Borenstein et al (2009) suggested that latitude (as a surrogate for climate) could explain some of the variation in the efficacy of the BCG vaccine
- We will dichotomize latitude into two categories: hotter climate vs colder climate
. generate byte latitude_01 = latitude_c > 0
. label define latval 0 "hot climate" 1 "cold climate"
. label values latitude_01 latval
+-------------------------------------------------------+ | studylbl latitude latitude_01 | |-------------------------------------------------------| 1. | Aronson, 1948 44 cold climate | 2. | Ferguson & Simes, 1949 55 cold climate | 3. | Rosenthal et al., 1960 42 cold climate | 4. | Hart & Sutherland, 1977 52 cold climate | 5. | Frimodt-Moller et al., 1973 13 hot climate | +-------------------------------------------------------+
. list studylbl latitude latitude_01 in 1/5
. meta forestplot, subgroup(latitude_01) nullrefline rr
summary for each group
Test of H0:θgrp1=θgrp2
- You may report your results as vaccine efficacies via the transform() option
meta forest, subgroup(latitude_01) /// transform("Vaccine efficacy": efficacy)
Other supported transformations within the transform() option are: corr, exp, invlogit, and tanh.
Summary II
- Heterogeneity is the variability among the ES beyond what is expected due to random sampling.
- I2, H2 are statistics used to quantify heterogeneity among the ES
- Whenever possible, reasons behind heterogeneity should always be explored via subgroup analysis or meta-regression.
- Large unexplained heterogeneity could mean that:
- overall ES has no meaningful interpretation in practice
- it does not make sense to conduct a meta-analysis.
Small-study effect (Publication bias)
- Small-study effects (Sterne, Gavaghan, and Egger 2000) is used in MA to describe the cases when the results of smaller studies differ systematically from the results of larger studies.
- One of the reasons behind small-study effect is publication bias (or more generally reporting bias)
- Publication bias arises when the decision to publish a study depends on the statistical significance of its results.
Random subset
- Suppose that we are missing some of the studies in our MA.
Observed studies
valid conclusions albeit wider CIs, less powerful tests (less info)
systematically different
Studies not included in the MA (missing studies)
(e.g. when smaller studies with nonsignificant findings are suppressed from publication)
our meta-analytic results will be biased and decisions based on them are invalid
Tools for small-study effects analysis
- The funnel plot
- Tests for small-study effects
- The trim-and-fill analysis
- Simple funnel plot
- Contour-enhanced funnel plot (one-sided and two-sided significance contours)
- Several precision metrics
- Egger's, Peters's, and Harbord's regression-based tests with the possibility to include moderators to account for heterogeneity
- Begg and mazumdar's test
meta funnelplot
meta bias
meta trimfill
Small-study effect (potentially due to publication bias)
Little evidence of Small-study effect
θ^j∼N(θ,σj2)
\hat{\theta}_j \sim N\left( \theta, \sigma^2_j \right )
which means the individual ES should be distributed randomly around the overall ES
Large and small studies tell the same story about θ
Large and small studies tell different stories about θ
large studies
small studies
large studies
small studies
. webuse nsaidsset, clear (Effectiveness of nonsteroidal anti-inflammatory drugs; set with -meta esize-) . meta funnelplot
Effect-size label: Log Odds-Ratio
Effect size: _meta_es
Std. Err.: _meta_se
Model: Common-effect
Method: Inverse-variance
gap (missing studies ?)
- You may enhance the contour funnel plot via the addplot() option
. scalar theta = r(theta) // obtained from previous -meta funnel- command r() results // position legend at 10 o'clock inside the graph region . local legopts ring(0) position(10) cols(1) size(small) symxsize(*0.6) . local opts horizontal range(0 1.6) lpattern(dash) lcolor("red") /// legend(order(1 2 3 4 5 6) label(6 "95% pseudo CI") `legopts') . meta funnel, contours(1 5 10) /// addplot(function theta-1.96*x, `opts' || function theta+1.96*x, `opts')
. meta bias, harbord - We will test for funnel-plot asymmetry and use the Harbord's test instead of the Egger's test as we are working with log(OR)
Effect-size label: Log Odds-Ratio Effect size: _meta_es Std. Err.: _meta_se Regression-based Harbord test for small-study effects Random-effects model Method: REML H0: beta1 = 0; no small-study effects beta1 = 3.03 SE of beta1 = 0.741 z = 4.09 Prob > |z| = 0.0000
Effect-size label: Log Odds-Ratio Effect size: _meta_es Std. Err.: _meta_se Regression-based Harbord test for small-study effects Random-effects model Method: REML H0: beta1 = 0; no small-study effects beta1 = 3.03 SE of beta1 = 0.741 z = 4.09 Prob > |z| = 0.0000
Effect-size label: Log Odds-Ratio Effect size: _meta_es Std. Err.: _meta_se Regression-based Harbord test for small-study effects Random-effects model Method: REML H0: beta1 = 0; no small-study effects beta1 = 3.03 SE of beta1 = 0.741 z = 4.09 Prob > |z| = 0.0000
Nonparametric trim-and-fill analysis of publication bias Linear estimator, imputing on the left Iteration Number of studies = 47 Model: Random-effects observed = 37 Method: REML imputed = 10 Pooling Model: Random-effects Method: REML --------------------------------------------------------------- Studies | Log Odds-Ratio [95% Conf. Interval] ---------------------+----------------------------------------- Observed | 1.322 1.031 1.613 Observed + Imputed | 1.035 0.726 1.343 ---------------------------------------------------------------
. meta trimfill, funnel(contours(1 5 10) legend(`legopts'))- We can perform a trim-and-fill analysis to assess the effect of missing studies on the overall ES and request a contour-enhanced funnel plot based on the complete (observed + filled) set studies
Summary III
- Publication bias occurs if studies with favourable results are more likely to be published than studies with unfavourable results.
- Small-study effect is manifested graphically by funnel-plot asymmetry
- Publication bias is only one of the reasons behind funnel-plot asymmetry.
- Publication bias should be assessed after you have accounted for heterogeneity in your MA (see ex8 of meta funnelpot and ex1 of meta bias)
- You can investigate small-study effects visually via meta funnelplot, test for it via meta bias, and assess its impact on the overall ES via meta trimfill
Other features
- Cumulative (and stratified-cumulative) MA forest plots
- L'Abbé plots
- Multiple subgroup analyses forest plots
- Meta-regression
- Bubble plots after meta-regression
- Knapp-Hartung (aka Sidik-Jonkman) adjustments
- Effect sizes for continuous data (Hedges's g, Cohen's d, etc.)
- Pre-computed effect sizes (correlation r, log(HR), etc.)
- Stratified funnel plots with various precision metrics
The meta control panel
Prefer to avoid typing commands ? Everything I have showed you can be done in the meta control panel with few mouse clicks
meta set
meta esizemeta summarize
meta forestplot
meta labbeplot
meta regress
estat bubbleplotmeta funnelplot
meta bias
meta trimfillA tour of the meta control panel
Summary
- Effect sizes for binary and continuous data may be computed via meta esize and generic (pre-computed) ES may be specified via meta set
- It is important to include an assessment of publication bias to insure the integrity of the MA . This may be done using the meta funnelplot, meta bias and meta trimfill commands
- When substantial heterogeneity is present among the studies, the reasons behind this heterogeneity should be explored via subgroup analysis ( meta summarize, subgroup()) or meta-regression ( meta regress)
- Use meta update and meta query to update and describe your current MA settings, respectively
- Results of a MA are best summarized numerically using meta summarize, or graphically using meta forestplot. This includes subgroup-analysis forest plots and CMA forest plots.
Thank You!
Meta-analysis New using Stata Houssein Assaad Senior Statistician and Software Developer StataCorp LLC Stata Conference July 30 , 2020 Philadelphia In-laws' basement
Meta: Stata UGM
By H Assaad
Meta: Stata UGM
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