Meta-analysis in animal health and reproduction: methods and applications using Stata

1. 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

3. Meta-analysis • Literature search • study quality assessment • Selection criteria • Statistical analysis • Heterogeneity • Publication bias

4. Methods 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)

5. Systematic Reviews & Meta-analysis • Systematic review is the entire process of collecting, reviewing and presenting all available evidence • Meta-analysis is the statistical technique involved in extracting and combining data to produce a summary result

6. Aim of a meta-analysis • To increase power • To improve precision • To answer questions not posed by the individual studies • To settle controversies arising from apparently conflicting studies or • To generate new hypothesis

7. Different 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)

8. Statistical models • Fixed effect models • Mantel-Haenszel (MH) • Has optimal statistical power • Softwares are available for the analysis • Peto test (modified MH method) • Recommended for non-experimental studies • Random effect models • DerSimonian & Laird method • Bayesian method • Regression models (Mixed model)

9. Fixed effect methods • Mantel-Haenszel approach • Odd ratio • Risk ratio • Risk difference • Not recommended in review with sparse data (trials with zero events in treatment or control group) • Peto method • Odds ratio • Used in studies with small treatment effect and rare events • Not a very common method • Used when the size of groups within trial are balanced

10. Random effects analytic methods • Odd ratio • Risk ratio • Risk difference

11. Dichotomous data • Odds Ratio (OR) • The odds of the event occurring in one group divided by the odds of the event occurring in the other group • Relative risk or Risk Ratio (RR) • The risk of the events in one group divided by the risk of the event in the other group • Risk difference (RD; -1 to +1) • Risk in the experimental group minus risk in the control group • Confidence interval (CI) • The level of uncertainty in the estimate of treatment effect • An estimate of the range in which the estimate would fall a fixed percentage of times if the study repeated many times

12. Risk 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 group • OR & RR > 1, but • OR > RR • If event rate in the treatment group • OR & RR < 1, but • OR < RR

13. Risk ratio vs.Odds ratio • When the event is rare • OR and RR will be similar • When the event is common • OR and RR will differ • In situations of common events, odd ratio can be misleading

14. Meta-analysis features in Stata 1. metan 2. labbe 3. metacum 4. metap 5. metareg 6. metafunnel 7. confunnel 8. metabias 9. metatrim • 10. metandi & metandiplot • 11. glst • 12. metamiss • 13. mvmeta & mvmeta_make • 14. metannt • 15. metaninf • 16. midas • 17. meta_lr • 18. metaparm Source: http://www.stata.com/support/faqs/stat/meta.html

15. Metan in Stata • Relative Risk (Fixed and Random effect model) • Fixedi= Fixed effect RR with inverse variance method • Fixed= M-H RR method metanevtrtnon_evtrtevctrlnon_evctrl, rr fixed second(random) favours(reduces pregnancy rate # increases pregnancy rate) lcols(names outcome dose) by(status) sortby(outcome) force astext(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)) rfdistrflevel(95) counts • Saving the graph in different formats graph export "D:\Forest plot.gph", replace graph export "D:\Forest plot.gph".png", replace graph export "D:\Forest plot.gph".eps", replace

16. Forest plot using Metan (Risk Ratio)

17. Forest plot using Metan (SMD)

18. Forest plot using Metan (WMD)

19. Homogeneity • Meta-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

20. Examination 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.

21. Differences between studies • By different investigators • In different settings • In different countries • In different ways • For different length of time • To look at different outcomes • Etc.

22. Studies differ in 3 basic ways • Clinical diversity: Variability in the participants, interventions and outcomes studied • Methodological diversity: Variability in the trial design and quality • Statistical 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

23. Methods for estimation of heterogeneity • Conventional chi-square (χ2) analysis (P>0.10) • I2= [(Q-df)/Q x 100% (Higgins et al. 2003), where Q is the chi-squared statistic; df is its degrees of freedom • Graphical 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 plot • Regression analysis • Comparing the results of fixed and random effect models (a crude assessment of heterogeneity)

24. L’Abbe plot labbe evtrt non evtrt evctrl nonevctrl, rr(1.21) null labbe evtrt nonevtrt evctrl nonevctrl, rr(1.21) or(1.30) null

25. Galbraith plot galbr logrr selogES (dichotomous data)

26. Strategies for addressing heterogeneity • Check again that the data are correct • Do not do a meta-analysis • Ignore heterogeneity (fixed effect model) • Perform a random effects meta-analysis • Change the effect measure (e.g. different scale or units) • Split studies into subgroups • Investigate heterogeneity using meta-regression • Exclude studies

27. Sensitivity analysis(sub-group) • A process for re-analysing the same data set • A range of principles used, depends on • Choice of statistical test • Inclusion criteria • Inclusion of both published and unpublished

28. Meta-regression • To 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 studies • Can find out if there is evidence of different effects in different subgroups of trials • It is appropriate to use meta-regression to explore sources of heterogeneity even if an initial overall test for heterogeneity is non-significant

29. Meta-regression-1 metareg _ES bcalving acalving full_lact monen_other bstcode apcode, wsse(_seES) bsest(reml) Meta-regression Number of obs = 23 REML estimate of between-study variance tau2 = .04357 % residual variation due to heterogeneity I-squared_res = 65.24% Proportion of between-study variance explained Adj R-squared = 51.05% Joint test for all covariates Model F(6,16) = 3.50 With Knapp-Hartung modification Prob > F = 0.0209 ------------------------------------------------------------------------------------------------------------- _ES | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+----------------------------------------------------------------------------------------------- bcalving | -.0028578 .0031445 -0.91 0.377 -.0095239 .0038083 acalving | -.0007429 .0013228 -0.56 0.582 -.0035472 .0020613 full_lact | .3517979 .2544234 1.38 0.186 -.1875556 .8911513 other s| .3403943 .1278838 2.66 0.017 .0692928 .6114959 bstcode | -.0333014 .1370641 -0.24 0.811 -.3238642 .2572614 apcode | .4589506 .1391693 3.30 0.005 .1639249 .7539762 _cons | -.3564435 .2521411 -1.41 0.177 -.8909586 .1780717 -----------------------------------------------------------------------------------------------------------

30. Meta-regression metareg _ES full_lact monen_other apcode, wsse(_seES) bsest(reml) Meta-regression Number of obs = 23 REML estimate of between-study variance tau2 = .04134 % residual variation due to heterogeneity I-squared_res = 66.02% Proportion of between-study variance explained Adj R-squared = 53.55% Joint test for all covariates Model F(3,19) = 6.63 With Knapp-Hartung modification Prob > F = 0.0030 --------------------------------------------------------------------------------------------------------- _ES | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+------------------------------------------------------------------------------------------- full_lact | .3138975 .117573 2.67 0.015 .0678144 .5599807 others | .3640601 .124601 2.92 0.009 .1032672 .6248529 apcode | .4385834 .1253647 3.50 0.002 .1761921 .700974 _cons | -.4478162 .1598295 -2.80 0.011 -.7823432 -.1132892 -------------------------------------------------------------------------------------------------------

31. Funnel Plots

32. Publication 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)

33. Sources of Bias • Bias arising from the studies included in the review • Bias arising from the way the review is done • Publication bias is only one of the possible reasons for asymmetrical funnel plot • Funnel plot should been seen as a means of examining “small study effect”

34. Publication bias • Funnel plot • Publication bias exists (asymmetrical) • Publication bias doesn’t exists (symmetrical) • For continuous data- Effect size plotted vs SE or sample size • For dichotomous data- LogOR or RR vs logSE or sample size • Fail 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.

36. Continuous data Funnel plot (continuous data) metabias _ES _seES, egger Contour-enhanced funnel plot confunnel _ES _seES Trim & Fill metatrim _ES _seES, funnel print

37. Dichotomus data Funnel plot metabias _logES _selogES, egger Contour-enhanced funnel plot confunnel _logES _selogES Trim & Fill metatrim _logES _selogES, funnel print

38. Testing 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 data • Eggers linear regression test (regression analysis-low power) • This test is mainly recommended for continuous data

39. Testing for funnel plot asymmetry-2 • Peters (2006) & Harbord(2006) tests • These tests are suitable for dichotomous data with odds ratios • False-positive results may occur in the presence of substantial between-study heterogeneity • For dichotomous outcomes with risk ratios (RR) or risk differences (RD) • Firm guidance is not yet available

40. Correcting 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 published • Conclusion: there is no definite answer for assessing the presence of publication bias

41. Influence analysis metaninf nt mean_t sd_t nc mean_c sd_c, label(namevar=study year) random cohen

42. References • www.stata.com/support/faqs/stat/meta.html • Cochrane Collaboration Open learning material for reviewers (2002) • Higgins et al. (2001). BMJ 327: 557-560 • Sterne et al. (2001). BMJ 323: 101-105 • Whitehead A (2002). Meta-analysis of Controlled Clinical Trials