Presentation on theme: "Meta-analysis in animal health and reproduction: methods and applications using Stata Ahmad Rabiee Ian Lean PO Box 660 Camden 2570, NSW SBScibus.com.au."— Presentation transcript:
1Meta-analysis in animal health and reproduction: methods and applications using Stata Ahmad RabieeIan LeanPO Box 660Camden 2570, NSWSBScibus.com.au
3Meta-analysis Literature search study quality assessment Selection criteriaStatistical analysisHeterogeneityPublication bias
4Methods of pooling study results Narrative procedure (conventional critical review method)Vote-counting method (significant results marked “+”, converse “–” and no significant results “neutral”)Combined tests (combining the probabilities obtain from two or more independent studies)
5Systematic Reviews & Meta-analysis Systematic review is the entire process of collecting, reviewing and presenting all available evidenceMeta-analysis is the statistical technique involved in extracting and combining data to produce a summary result
6Meta-analysisA meta-analysis is also possible without doing a systematic reviewWith no attempt to be systematic about the particular studies were chosen
7Aim of a meta-analysis To increase power To improve precision To answer questions not posed by the individual studiesTo settle controversies arising from apparently conflicting studies orTo generate new hypothesis
8Objective of a meta-analysis Assessment of strength of evidenceTo determine whether an effect exists in a particular directionStatistical pooling of resultsTo obtain a single summary resultInvestigation of heterogeneityTo examine reasons for different results
9Meta-analysis A meta-analysis is a two-stage process Stage 1 Stage 2 Extraction of data from individual studyCalculation of a result for that study (point estimate)Estimation of chance variation (confidence interval)Stage 2Deciding if it is appropriate to calculate and pool average results across studiesIf so, calculate and present the results.
10Analysis specification What are the main comparisons in your view?How will you summarise the results of the outcomes for each study?How will you decide whether to combine the results of the separate studies?Do you plan any subgroup or sensitivity analyses?
11Different types of data Dichotomous data (e.g. dead or live)Counts of events (e.g. no. of pregnancies)Short ordinal scales (e.g. pain score)Long ordinal scales (e.g. quality of life)Continuous data (e.g. cholesterol con.)Censored data or survival data (e.g. time to 1st service)
12Methods of calculating summary measures of association or effect Continuous dataCalculation of overall effect size (standardised mean difference)Rate dataMeasures of effect (difference between incidence in the population of exposed vs not exposed)Relative riskOdds ratioRisk difference
13Statistical models Fixed effect models Random effect models Mantel-Haenszel (MH)Has optimal statistical powerSoftwares are available for the analysisPeto test (modified MH method)Recommended for non-experimental studiesRandom effect modelsDerSimonian & Laird methodBayesian methodRegression models (Mixed model)
14Fixed effect modelThis model is based on a mathematical assumption that every study is evaluating a common treatment effectIn this model, the true treatment difference is considered to be the same for all trialsThe SE of each trial estimate is based on sampling variation within the trialThe summary results are specific to the trials includedThe summary results can not be generalised to the population
15Fixed effect methods Mantel-Haenszel approach Odd ratio Risk ratio Risk differenceNot recommended in review with sparse data (trials with zero events in treatment or control group)Peto methodOdds ratioUsed in studies with small treatment effect and rare eventsNot a very common methodUsed when the size of groups within trial are balancedIf the results from the trials appear to be reasonably consistent the fixed effects analysis may be more appropriate one to present.For a MA based on a small number of studies, the estimate of the heterogeneity parameters from the data is likely to be unreliable.
16Random effect modelIn this model, the assumption is that the true treatment effects in the individual studies may be different from each otherIn this model, the true treatment difference in each trial is itself assumed to be a realisation of random variable, which is usually assumed to be normally distributedThe SE of each trial estimate is increased due to the addition of this between-trial variationFor a MA based on a larger number of trials the random effect analysis may be preferred anyway.There are some concerns regarding the use of the random effect model in practice;1- First, the random effects model assumes that the results from the trials included in the MA are representative of the results would be obtained from the total population of treatment centres. In reality, centres which take part in clinical trials are not chosen at random.2- Second, when there are only a few trials for inclusion in the meta-analysis, it may inappropriate to try to fit a random effects model as any calculated estimate of the between study variance will be unreliable. When there is only one available trial, its analysis can only be based on fixed effects model.
18Fixed effect vs Random effect Fixed effects assumption“did the treatment produce benefit on average in the studies in hand”?“what is the best estimate of the treatment effect”?Random effects assumption“will the treatment produce benefit on average”?“what is the average treatment effect”?Choice between fixed and random effects may be decidedBy a formal chi-square test of homogeneityThat is whether the between study variance component is zero or not
19Dichotomous data Risk Odds A chance or probability of having a specific event (no of participants having the event in a group divided the total no. of participants)OddsThe ratio of events to not-events (risk of having an events divided by the risk of not having it)
20Dichotomous data Odds Ratio (OR) Relative risk or Risk Ratio (RR) The odds of the event occurring in one group divided by the odds of the event occurring in the other groupRelative risk or Risk Ratio (RR)The risk of the events in one group divided by the risk of the event in the other groupRisk difference (RD; -1 to +1)Risk in the experimental group minus risk in the control groupConfidence interval (CI)The level of uncertainty in the estimate of treatment effectAn estimate of the range in which the estimate would fall a fixed percentage of times if the study repeated many timesRR: The risk of still being infected on antibiotic was about 12% of the risk on controlORRR: Treatment reduced the risk to 12% of what it would have been_______________________________________________OR: Antibiotics reduced the odds of still being infected to about 2% of what they would have beenOR: Treatment reduced the odds by 88% of what they were in the control group._________________________________________________RD: Antibiotics reduced the risk of still being infected by 76% points.Switching between good and bad outcomes for the risk difference causes a change of sign, from (+ to –) or (– to +)If it reduces the risk, the RD will be bigger than 0If it increases the risk, the RD will be bigger than 0
21Risk ratio vs. Odds ratio Odds ratio (OR) will always be further from the point of no effect than a risk ratio (RR)If event rate in the treatment groupOR & RR > 1, butOR > RROR & RR < 1, butOR < RR
22Risk ratio vs. Odds ratio When the event is rareOR and RR will be similarWhen the event is commonOR and RR will differIn situations of common events, odd ratio can be misleading
23Meta-analysis features in Stata 1. metan2. labbe3. metacum4. metap5. metareg6. metafunnel7. confunnel8. metabias9. metatrim10. metandi & metandiplot11. glst12. metamiss13. mvmeta & mvmeta_make14. metannt15. metaninf16. midas17. meta_lr18. metaparmSource:
24Metan in Stata Relative Risk (Fixed and Random effect model) Fixedi= Fixed effect RR with inverse variance methodFixed= M-H RR methodmetan evtrt non_evtrt evctrl non_evctrl, rr fixed second(random)favours(reduces pregnancy rate # increases pregnancy rate)lcols(names outcome dose) by(status) sortby(outcome) forceastext(70) textsize(200) boxsca(80) xsize(10) ysize(6)pointopt( msymbol(triangle) mcolor(gold) msize(tiny)mlabel() mlabsize(vsmall) mlabcolor(forest_green) mlabposition(1))ciopt( lcolor(sienna) lwidth(medium)) rfdist rflevel(95) countsSaving the graph in different formatsgraph export "D:\Forest plot.gph", replacegraph export "D:\Forest plot.gph".png", replacegraph export "D:\Forest plot.gph".eps", replace
28HomogeneityMeta-analysis should only be considered when a group of trials is sufficiently homogeneous in terms of participations, interventions and outcomes to provide a meaningful summary
29Examination for heterogeneity Examination for “heterogeneity” involves determination of whether individual differences between study outcomes are greater than could be expected by chance alone.Analysis of “heterogeneity” is the most important function of MA, often more important than computing an “average” effect.As we are trying to use the MA to estimate a combined effect from a group of similar studies, we need to check that the effects found in the individual studies are similar enough that we are confident a combined estimate will be a meaningful description of the set of studies.In doing this, we need to remember that the individual estimates of treatment effect will vary by chance, because of randomisation. So we expect some variation. What we need to know is whether there is more variation than we would expect by chance alone. When this excessive variation occurs, we call it statistical heterogeneity or just heterogeneity. (Module 13, Page 3).
30Differences between studies By different investigatorsIn different settingsIn different countriesIn different waysFor different length of timeTo look at different outcomesEtc.
31Studies differ in 3 basic ways Clinical diversity: Variability in the participants, interventions and outcomes studiedMethodological diversity: Variability in the trial design and qualityStatistical heterogeneity: Variability in the treatment effects being evaluated in the different trials. This is a consequence of clinical and/or methodological diversity among the studies
32Clinical diversity Study location and setting Age, sex, diagnosis and disease severity of casesTiming of the treatmentsDose and density of the interventionDefinition of the outcomes
33Methods for estimation of heterogeneity Conventional chi-square (χ2) analysis (P>0.10)I2= [(Q-df)/Q x 100% (Higgins et al. 2003), whereQ is the chi-squared statistic; df is its degrees of freedomGraphical test-forest plots (OR or RR and confidence intervals)L’Abbe plots (outcome rates in treatment and control groups are plotted on the vertical and horizontal axes)Galbraith plotRegression analysisComparing the results of fixed and random effect models (a crude assessment of heterogeneity)Forest Plots: By looking at a forest plot to see how well the confidence intervals overlap. If the CI of tow studies don’t overlap at all, there is likely to be more variation between the study results than what you would expect by chance (unless there are lost of studies), and you should suspect heterogeneity.χ2 = A small P value for χ2 is often used to indicate evidence of heterogeneity. When there are few studies, the test is not very good at detecting heterogeneity if it is present (it has low power). For this reason, a P-value of < 0.10 is often used to indicate heterogeneity rather than conventional cut-point of P= Conversely, if there are a lot of studies in a MA, the χ2 test can be good at detecting heterogeneity. χ2 will tell us that heterogeneity is present, but doesn’t answer the question “how much heterogeneity is there”?If the statistics (χ2) is bigger than its degrees of freedom then there is evidence of heterogeneity.A visual inspection of the CIs will help get an idea of the amount of statistical heterogeneity, and guide you to think about whether it is reasonable to combine the results of these studies.
36Strategies for addressing heterogeneity Check again that the data are correctDo not do a meta-analysisIgnore heterogeneity (fixed effect model)Perform a random effects meta-analysisChange the effect measure (e.g. different scale or units)Split studies into subgroupsInvestigate heterogeneity using meta-regressionExclude studies
37Sensitivity analysis (sub-group) A process for re-analysing the same data setA range of principles used, depends onChoice of statistical testInclusion criteriaInclusion of both published and unpublished
38Meta-regressionTo investigate whether heterogeneity among results of multiple studies is related to specific characteristics of the studies (e.g. dose rate)To investigate whether particular covariate (potential ‘effect modifier’) explain any of the heterogeneity of treatment effect between studiesCan find out if there is evidence of different effects in different subgroups of trialsIt is appropriate to use meta-regression to explore sources of heterogeneity even if an initial overall test for heterogeneity is non-significantMeta-regression is potentially a very useful technique.If used inappropriately, its interpretation can be misleading. This is again because differences between studies, even if they are well-performed randomized trials, are entirely observational in nature and are prone to “bias” and “confounding”.If you summarize case characteristics at a trial level, you run the risk of completely failing to detect genuine relationships between these characteristics and the size of treatment effect. Further, the risk of obtaining a spurious explanation for variable treatment effects is high when you have a small number of studies and may characteristics that differ.
39Meta-regression-1metareg _ES bcalving acalving full_lact monen_other bstcode apcode, wsse(_seES) bsest(reml)Meta-regression Number of obs = 23REML estimate of between-study variance tau2 =% residual variation due to heterogeneity I-squared_res = %Proportion of between-study variance explained Adj R-squared = %Joint test for all covariates Model F(6,16) =With Knapp-Hartung modification Prob > F =_ES | Coef Std. Err t P>|t| [95% Conf. Interval]bcalving |acalving |full_lact |other s|bstcode |apcode |_cons |
40Meta-regression Meta-regression Number of obs = 23 metareg _ES full_lact monen_other apcode, wsse(_seES) bsest(reml)Meta-regression Number of obs =REML estimate of between-study variance tau =% residual variation due to heterogeneity I-squared_res = %Proportion of between-study variance explained Adj R-squared = %Joint test for all covariates Model F(3,19) =With Knapp-Hartung modification Prob > F =_ES | Coef. Std. Err t P>|t| [95% Conf. Interval]full_lact |others |apcode |_cons |
42Publication bias +ve results more likely To be published (publication bias)To be published rapidly (time lag bias)To be published in English (language bias)To be published more than once (multiple publications bias)To be cited by others (citation bias)
43Sources of Bias Bias arising from the studies included in the review Bias arising from the way the review is donePublication bias is only one of the possible reasons for asymmetrical funnel plotFunnel plot should been seen as a means of examining “small study effect”We have quite a lot of evidence that these biases exist, so it is fair to assume that most systematic reviews will be subject to reporting bias to some extent.If we accept that our review will almost certainly be subject to publication bias to some extent, we are left with the problem of estimating how big a problem it is in your review and what to do about it.
44Publication bias Funnel plot Publication bias exists (asymmetrical) Publication bias doesn’t exists (symmetrical)For continuous data- Effect size plotted vs SE or sample sizeFor dichotomous data- LogOR or RR vs logSE or sample sizeFail Safe Number (F)Z= (∑ ES/1.645)2-N: (where N= no of papers; ∑ ES is summed of effect size over all studies)-for calculation of unpublished studies that would be required to negate the results of a significantly positive ES analysis.
48Testing for funnel plot asymmetry-1 Cochrane group suggests that that tests for funnel plot asymmetry should be used in only a minority of meta-analyses (Ioannidis 2007)Begg’s rank correlation test (adjusted rank correlation-low power)This test is NOT recommended with any type of dataEggers linear regression test (regression analysis-low power)This test is mainly recommended for continuous data
49Testing for funnel plot asymmetry-2 Peters (2006) & Harbord (2006) testsThese tests are suitable for dichotomous data with odds ratiosFalse-positive results may occur in the presence of substantial between-study heterogeneityFor dichotomous outcomes with risk ratios (RR) or risk differences (RD)Firm guidance is not yet available
50Correcting for publication bias Trim and fill method (tail of the side of the funnel plot with smaller trials chopped off)Fail safe N (required studies to overturn positive results)Modelling for the probability of studies not publishedConclusion: there is no definite answer for assessing the presence of publication bias
51Influence analysismetaninf nt mean_t sd_t nc mean_c sd_c, label(namevar=study year) random cohen
52References www.stata.com/support/faqs/stat/meta.html Cochrane Collaboration Open learning material for reviewers (2002)Higgins et al. (2001). BMJ 327:Sterne et al. (2001). BMJ 323:Whitehead A (2002). Meta-analysis of Controlled Clinical Trials