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.
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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 Meta-analysis • • • • • • Literature search study quality assessment Selection criteria Statistical analysis Heterogeneity Publication bias 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) 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 Aim of a metaanalysis • 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 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) 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) 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 Random effects analytic methods • Odd ratio • Risk ratio • Risk difference 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 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 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 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 Metan in Stata • • • Relative Risk (Fixed and Random effect model) Fixedi= Fixed effect RR with inverse variance method Fixed= M-H RR method metan 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) 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)) rfdist rflevel(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 Forest plot using Metan (Risk Ratio) names outcome Cycling Westhuysen 1980 1st Service CP Moller & Fielden 1981 1st Service CP Fielden & Moller 1983 1st Service CP Macmillan & Taufa 1983 1st Service CP Alacam et al 1986 1st Service CP Dmitriev et al 1986 1st Service CP Klinskii et al. 1987 1st Service CP Chenault 1990 1st Service CP Schels & Mostafawi 1978 1st Service CP Lee et al 1983 1st Service CP Lee et al 1983 1st Service CP Nakao et al 1983 1st Service CP Stevenson et al 1984 1st Service CP Lee et al 1985 1st Service CP Pennington et al 1985 1st Service CP Lucy & Stevenson 1986 1st Service CP Chenault 1990 1st Service CP Lewis et al 1990 1st Service CP Goldbeck 1976 1st Service CP Anderson & Malmo 1985 1st Service CP Grunert & Schwarz 1976 1st Service CP Schels & Mostafawi 1978 2nd Service CP Westhuysen 1980 2nd Service CP Lee et atl 1983 2nd Service CP Lee et al 1983 2nd Service CP Stevenson et al 1984 2nd Service CP Anderson & Malmo 1985 2nd Service CP Pennington et al 1985 2nd Service CP Lewis et al 1990 2nd Service CP M-H Subtotal (I-squared = 31.2%, p = 0.058) D+L Subtotal .with estimated predictive interval . Repeat Breeder Lee et al 1983 Pregnancy rate Stevenson et al 1984 Pregnancy rate Pennington et al 1985 Pregnancy rate Anderson & Malmo 1985 Pregnancy rate Phatak et al 1986 Pregnancy rate Roussel et al 1988 Pregnancy rate Roussel et al 1988 Pregnancy rate Stevenson et al 1988 Pregnancy rate Stevenson et al 1990 Pregnancy rate Lewis et al 1990 Pregnancy rate Bon Durant et al 1991 Pregnancy rate M-H Subtotal (I-squared = 55.7%, p = 0.012) D+L Subtotal .with estimated predictive interval . M-H Overall (I-squared = 48.1%, p = 0.000) D+L Overall .with estimated predictive interval Events, Treatment Events, Control % Weight (M-H) 1.36 (0.98, 1.90) 1.19 (1.02, 1.39) 1.10 (1.01, 1.20) 1.03 (0.93, 1.14) 1.28 (0.95, 1.72) 1.17 (0.81, 1.71) 1.54 (0.92, 2.58) 0.82 (0.67, 1.01) 1.19 (0.93, 1.52) 1.24 (0.96, 1.60) 0.93 (0.76, 1.14) 1.15 (1.03, 1.28) 1.04 (0.82, 1.31) 1.00 (0.45, 2.23) 1.01 (0.85, 1.18) 1.94 (0.56, 6.73) 0.81 (0.66, 0.99) 0.94 (0.72, 1.22) 1.19 (1.02, 1.40) 1.09 (1.01, 1.17) 1.20 (1.04, 1.38) 1.39 (0.78, 2.45) 1.02 (0.75, 1.40) 1.24 (1.07, 1.43) 1.00 (0.87, 1.15) 1.19 (0.91, 1.57) 1.03 (0.85, 1.24) 0.98 (0.75, 1.28) 1.10 (0.74, 1.65) 1.08 (1.05, 1.12) 1.09 (1.04, 1.13) . (0.95, 1.24) 29/44 170/292 414/655 174/260 27/33 26/46 20/35 95/240 64/109 76/154 59/92 346/605 69/146 6/12 146/282 10/18 94/242 58/131 87/107 396/674 112/138 17/45 12/15 123/154 74/92 55/100 50/86 58/125 27/60 2894/4992 30/62 139/284 371/647 582/896 23/36 26/54 13/35 117/243 54/109 58/146 64/93 293/589 83/182 6/12 136/264 2/7 117/243 60/127 73/107 1529/2828 95/140 15/55 25/32 94/146 75/93 48/104 654/1156 54/114 27/66 4863/8870 0.63 3.55 9.39 6.59 0.55 0.60 0.33 2.93 1.36 1.50 1.60 7.47 1.86 0.15 3.54 0.07 2.94 1.53 1.84 14.81 2.37 0.34 0.40 2.43 1.88 1.18 2.28 1.42 0.65 76.19 1.53 (1.27, 1.83) 1.22 (0.99, 1.51) 1.18 (0.79, 1.78) 0.83 (0.61, 1.13) 1.24 (1.07, 1.44) 2.10 (1.33, 3.33) 1.41 (1.08, 1.84) 1.39 (0.95, 2.04) 1.21 (1.06, 1.39) 0.77 (0.41, 1.43) 1.10 (0.95, 1.28) 1.22 (1.15, 1.31) 1.24 (1.11, 1.38) . (0.91, 1.70) 135/185 84/144 27/49 26/59 231/492 40/45 158/283 20/37 304/765 11/32 214/495 1250/2586 77/161 75/157 20/43 160/302 177/469 11/26 38/96 40/103 235/717 13/29 184/468 1030/2571 2.07 1.81 0.54 1.32 4.56 0.35 1.43 0.53 6.11 0.34 4.76 23.81 1.12 (1.08, 1.15) 1.12 (1.07, 1.17) . (0.93, 1.35) 4144/7578 5893/11441 100.00 dose RR (95% CI) all all all all all all all all 125 125 125 125 125 125 125 125 125 125 250 250 250 all all all all all all all all all all all all all all all all all all all .149 1 reduces pregnancy rate 6.73 increases pregnancy rate Forest plot using Metan (SMD) Reference Lact Diet SMD (95% CI) N, mean (SD); Treatment N, mean (SD); Control % Weight (I-V) P Mexico study Early-Mid-late TMR Campbell et al. Early-Mid TMR+10 Snead et al. Early-Mid TMR Colorado study Early-Mid-late TMR Monardes et al. Early TMR New York study1 Early-Mid-late TMR Texas study2 Early-Mid-late TMR Texas study1 Early-Mid TMR California study-2 Early-Mid TMR California study-1 Early-Mid TMR Ferguson et al. Early-Mid-late TMR Kincaid and Socha. Early-Mid TMR Nocek et al. (Year 2) Early-Mid-late TMR Nocek et al. (Year 1) Early-Mid-late TMR I-V Subtotal (I-squared = 84.3%, p = 0.000) D+L Subtotal with estimated predictive interval 0.63 (0.22, 1.05) 0.18 (-0.32, 0.69) -0.05 (-0.56, 0.45) 0.36 (0.08, 0.63) -0.13 (-0.79, 0.54) 0.11 (-0.21, 0.43) 0.11 (-0.04, 0.27) 0.18 (-0.08, 0.43) 0.10 (-0.17, 0.37) 0.13 (-0.19, 0.44) 0.06 (-0.28, 0.39) -0.08 (-0.74, 0.57) 0.98 (0.69, 1.27) 1.25 (0.96, 1.54) 0.30 (0.22, 0.38) 0.30 (0.08, 0.52) . (-0.53, 1.13) 46, 37.3 (2.68) 30, 35.7 (6.02) 30, 33.9 (6.99) 104, 36.8 (5.25) 17, 36.7 (8.45) 93, 29.8 (10.2) 315, 36.2 (8.87) 161, 40.6 (10.9) 105, 44.6 (8.81) 105, 44.6 (8.81) 63, 28.6 (3.96) 18, 41.7 (5.94) 102, 43.5 (2.02) 107, 37.6 (2.07) 1296 46, 35.6 (2.68) 30, 34.6 (6.02) 30, 34.2 (5.31) 103, 34.8 (5.6) 18, 37.8 (8.7) 65, 28.7 (9.39) 313, 35.2 (7.96) 94, 38.8 (8.34) 109, 43.7 (8.98) 62, 43.5 (6.77) 73, 28.4 (3.91) 18, 42.2 (5.94) 106, 41.5 (2.06) 109, 35 (2.09) 1176 1.81 1.23 1.24 4.20 0.72 3.15 12.94 4.88 4.41 3.21 2.79 0.74 3.83 3.72 48.87 A Uchida at al. Early TMR McKay et al Early-Mid-late Pasture Ballantine et al. Early-Mid-late TMR California study-4 Early-Mid TMR California study-3 Early-Mid TMR Lean et al. Early-Mid-late PMR (Pasture+TMR) Toni et al. Early-Mid-late Comp New York study Early-Mid-late TMR+15 Griffiths et al. Early-Mid-late Pasture I-V Subtotal (I-squared = 27.5%, p = 0.199) D+L Subtotal with estimated predictive interval -0.25 (-0.88, 0.37) -0.03 (-0.22, 0.15) 0.36 (0.11, 0.61) 0.01 (-0.32, 0.35) 0.03 (-0.34, 0.41) -0.00 (-0.18, 0.17) 0.17 (-0.12, 0.46) 0.22 (-0.03, 0.47) 0.18 (0.01, 0.35) 0.10 (0.02, 0.18) 0.10 (0.01, 0.20) . (-0.11, 0.32) 20, 44.4 (1.97) 229, 17.1 (3.03) 128, 41.8 (3.39) 50, 43.8 (6.08) 50, 43.8 (6.08) 233, 25.7 (4.27) 90, 34.8 (5.88) 125, 37.8 (5.03) 277, 17.5 (4.99) 1202 20, 44.9 (1.97) 229, 17.2 (3.03) 123, 40.6 (3.33) 109, 43.7 (8.98) 62, 43.5 (6.77) 276, 25.7 (4.32) 90, 33.8 (5.88) 125, 36.7 (5.03) 278, 16.6 (5) 1312 0.82 9.45 5.09 2.83 2.28 10.43 3.70 5.13 11.40 51.13 Heterogeneity between groups: p = 0.000 I-V Overall (I-squared = 79.2%, p = 0.000) D+L Overall with estimated predictive interval 0.20 (0.14, 0.26) 0.22 (0.09, 0.35) . (-0.37, 0.80) 2498 2488 100.00 -1.54 0 reduces milk yield 1.54 increases milk yield Forest plot using Metan (WMD) Reference Lact Diet WMD (95% CI) N, mean (SD); Treatment N, mean (SD); Control % Weight (I-V) P Mexico study Early-Mid-late TMR Campbell et al. Early-Mid TMR+10 Snead et al. Early-Mid TMR Colorado study Early-Mid-late TMR Monardes et al. Early TMR New York study1 Early-Mid-late TMR Texas study2 Early-Mid-late TMR Texas study1 Early-Mid TMR California study-2 Early-Mid TMR California study-1 Early-Mid TMR Ferguson et al. Early-Mid-late TMR Kincaid and Socha. Early-Mid TMR Nocek et al. (Year 2) Early-Mid-late TMR Nocek et al. (Year 1) Early-Mid-late TMR I-V Subtotal (I-squared = 37.0%, p = 0.080) D+L Subtotal with estimated predictive interval 1.70 (0.60, 2.80) 1.10 (-1.95, 4.15) -0.32 (-3.46, 2.82) 1.94 (0.46, 3.42) -1.10 (-6.78, 4.58) 1.10 (-1.98, 4.18) 0.96 (-0.36, 2.28) 1.80 (-0.58, 4.18) 0.91 (-1.47, 3.29) 1.04 (-1.34, 3.42) 0.22 (-1.11, 1.55) -0.50 (-4.38, 3.38) 2.00 (1.45, 2.55) 2.60 (2.05, 3.15) 1.90 (1.58, 2.22) 1.56 (1.05, 2.07) . (0.31, 2.81) 46, 37.3 (2.68) 30, 35.7 (6.02) 30, 33.9 (6.99) 104, 36.8 (5.25) 17, 36.7 (8.45) 93, 29.8 (10.2) 315, 36.2 (8.87) 161, 40.6 (10.9) 105, 44.6 (8.81) 105, 44.6 (8.81) 63, 28.6 (3.96) 18, 41.7 (5.94) 102, 43.5 (2.02) 107, 37.6 (2.07) 1296 46, 35.6 (2.68) 30, 34.6 (6.02) 30, 34.2 (5.31) 103, 34.8 (5.6) 18, 37.8 (8.7) 65, 28.7 (9.39) 313, 35.2 (7.96) 94, 38.8 (8.34) 109, 43.7 (8.98) 62, 43.5 (6.77) 73, 28.4 (3.91) 18, 42.2 (5.94) 106, 41.5 (2.06) 109, 35 (2.09) 1176 4.21 0.54 0.51 2.31 0.16 0.53 2.90 0.89 0.89 0.89 2.86 0.34 16.42 16.42 49.86 A Uchida at al. Early TMR McKay et al Early-Mid-late Pasture Ballantine et al. Early-Mid-late TMR California study-4 Early-Mid TMR California study-3 Early-Mid TMR Lean et al. Early-Mid-late PMR (Pasture+TMR) Toni et al. Early-Mid-late Comp New York study Early-Mid-late TMR+15 Griffiths et al. Early-Mid-late Pasture I-V Subtotal (I-squared = 38.3%, p = 0.113) D+L Subtotal with estimated predictive interval -0.50 (-1.72, 0.72) -0.10 (-0.65, 0.45) 1.20 (0.37, 2.03) 0.09 (-2.29, 2.47) 0.22 (-2.16, 2.60) -0.01 (-0.76, 0.74) 1.00 (-0.72, 2.72) 1.10 (-0.15, 2.35) 0.90 (0.07, 1.73) 0.35 (0.03, 0.67) 0.42 (-0.03, 0.87) . (-0.68, 1.51) 20, 44.4 (1.97) 229, 17.1 (3.03) 128, 41.8 (3.39) 50, 43.8 (6.08) 50, 43.8 (6.08) 233, 25.7 (4.27) 90, 34.8 (5.88) 125, 37.8 (5.03) 277, 17.5 (4.99) 1202 20, 44.9 (1.97) 229, 17.2 (3.03) 123, 40.6 (3.33) 109, 43.7 (8.98) 62, 43.5 (6.77) 276, 25.7 (4.32) 90, 33.8 (5.88) 125, 36.7 (5.03) 278, 16.6 (5) 1312 3.39 16.42 7.30 0.89 0.89 9.00 1.71 3.24 7.30 50.14 Heterogeneity between groups: p = 0.000 I-V Overall (I-squared = 72.2%, p = 0.000) D+L Overall with estimated predictive interval 1.12 (0.90, 1.35) 0.93 (0.42, 1.44) . (-1.05, 2.91) 2498 2488 100.00 -6.78 0 reduces milk yield 6.78 increases milk yield 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 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. 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. 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 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) 0 .75 .5 .25 0 .25 .5 Event rate group 1 .75 1 1 L’Abbe plot 0 0 .25 .5 .75 Event rate group 2 1 labbe evtrt non evtrt evctrl nonevctrl, rr(1.21) null .25 .5 .75 Event rate group 2 Null Risk ratio 1 Odds ratio Studies labbe evtrt nonevtrt evctrl nonevctrl, rr(1.21) or(1.30) null Galbraith plot b/se(b) b/se(b) Fitted values 4.72877 Fitted values 3.8419 b/se(b) b/se(b) 2 2 0 0 -2 -2 0 14.9965 1/se(b) 0 11.5116 1/se(b) galbr logrr selogES (dichotomous data) 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 metaregression • Exclude studies 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 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 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 ----------------------------------------------------------------------------------------------------------- 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 ------------------------------------------------------------------------------------------------------- Funnel Plots 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) 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” 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. .4 .8 .6 se(SMD) .2 0 Funnel plot with pseudo 95% confidence limits -2 -1 0 1 Standardized mean difference (SMD) 2 .4 .6 1 .8 se(SMD) .2 0 Funnel plot with pseudo 95% confidence limits -2 -1 0 1 Standardized mean difference (SMD) 2 .4 .6 .8 Standard error Continuous data .2 0 Funnel plot with pseudo 95% confidence limits Funnel plot (continuous data) metabias _ES _seES, egger -2 -1 0 Effect estimate 1 0 2 Studies 0.01 0.05 0.1 Standard error .2 .4 Contour-enhanced funnel plot confunnel _ES _seES .6 .8 -2 -1 0 Effect estimate 1 2 Filled funnel plot with pseudo 95% confidence limits 2 Trim & Fill metatrim _ES _seES, funnel print theta, filled 1 0 -1 -2 0 .2 .4 s.e. of: theta, filled .6 .8 .6 .4 se(logRR) Dichotomus data .2 0 Funnel plot with pseudo 95% confidence limits Funnel plot metabias _logES _selogES, egger -1 -.5 0 .5 1 1.5 log_ES 0 Studies 0.01 0.05 0.1 Standard error .2 .4 Contour-enhanced funnel plot confunnel _logES _selogES .6 -2 -1 0 Effect estimate 1 2 Filled funnel plot with pseudo 95% confidence limits 2 Trim & Fill metatrim _logES _selogES, funnel print theta, filled 1 0 -1 0 .2 .4 s.e. of: theta, filled .6 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 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 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 Influence analysis Meta-analysis estimates, given named study is omitted Lower CI Limit Estimate Upper CI Limit Beckett (1998) Duffield (1998) Heuer (2001) Duffield (2002) Green_A (2004) Green_B (2004) Green_C(2004) Green_D (2004) Green_E(2004) Green_F(2004) Melendez (2006) 0.85 0.92 1.39 2.11 metaninf nt mean_t sd_t nc mean_c sd_c, label(namevar=study year) random cohen 2.34 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