Improving coverage probabilities of confidence intervals in random effects meta-analysis with publication bias

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1 Improvg coverage probabltes of cofdece tervals radom effects meta-aalyss th publcato bas Masayuk Hem The Isttute of Statstcal Mathematcs, Japa Joh B. Copas Uversty of Warck, UK

2 Itroducto Meta-aalyss: statstcal aalyss to stregthe some (statstcal) evdece by combg results from several studes Clcal trals, Epdemologcal studes, etc. Study heterogeety: dfferece of treatmet effect each study DerSmoa-Lard method: a popular method to deal th study heterogeety, but the cofdece terval from ths method has poor coverage probabltes, especally the presece of publcato bas I ths talk, e propose a e cofdece terval hch mproves such poor coverage probabltes, takg to accout the effect of publcato bas.

3 Fxed effects model Fxed effects θ θ Λ θ θ θ : treatmet effect of the th study Estmate of from the th study ( y ~ N θ, s ) (,, Κ ) Overall estmate ( ) θ s 00(-α)% cofdece terval z α / θ θ F F z α / y ( s the upper quatle of N 0, ) α ( ) ( ) ( ), θ + z F α /

4 adom effects adom effects model DerSmoa-Lard method Usual method to deal th study heterogeety. e. θ θ ( j k) ( ~, τ ) ( y ~ θ, + τ ) N s θ N θ j k Overall estmates ( ( ) θ s + τ y DerSmoa- Lard estmator By detfyg th ( ) % 00 α Cofdece terval τ τ, I T θ θ ~ V N θ zα / V, θ + ( 0, ) V zα / V

5 Problems of DerSmoa-Lard method Cofdece terval I θ zα / V, θ + z V α / ( ) α ) The coverage probablty teds to be belo the omal level, f e take to accout the effect of estmatg τ (Brockell ad Gordo, 00) Alteratve cofdece tervals Lkelhood rato (Hardy ad Thompso, 996) Bggerstaff ad Teede (997) Sdk ad Jokma (00)

6 Problems of DerSmoa-Lard method + / /, V z V z I α α θ θ Cofdece terval ) If there s publcato bas, the coverage probablty decreases more rapdly. Publcato bas: small studes th large stadard errors are less lkely to (typcal case) be publshed tha large studes th small stadard errors. s The radom effects estmate + τ θ s y s more sestve to publcato bas tha the fxed effects estmate, F s y θ s j s > j j j j s s s s > + + τ τ because relatve eghts of smaller studes

7 Cofdece terval based o the fxed effects estmate Uder ~ N( θ, +τ ), y V Var( θ ) s F τ ( ) + θf θ T V V τ + ( ) Calculate the exact dstrbuto to obta more accurate approxmato tha the approxmato by ormal dstrbuto approxmate 00(-α)% cofdece terval I θ F uα V, θf + u V α ( : α upper quatle of T ) u α / calculated from the above dstrbuto but t depeds o hch s replaced th here. τ τ,

8 (a) (c) M L BT SJ Smulato (o publcato bas) betee-study varace τ 0.00 τ umber of studes (b) τ 0.0 τ 0. 5 (d) Overall average effect θ 0.5 Wth-study varace s s geerated by the method of Brockell ad Gordo (00) Observed effect sze from each study y ~ N ( θ, s +τ ) (, Κ, ) Smulato sze 0000 tmes

9 Smulato (moderate publcato bas) (a) M L BT SJ τ 0.00 τ (b) Selecto fucto ( y, s) P selected exp β Φ y s γ oe-sded P-value β 4, γ 3 (c) τ 0.0 τ 0. 5 (d) moderate publcato bas (average selecto probablty 87%) (Begg ad Mazumdar, 994)

10 Smulato (strog publcato bas) (a) M L BT SJ τ 0.00 τ (b) Selecto fucto ( y, s) P selected exp β Φ y s γ oe-sded P-value β 4, γ.5 (c) τ 0.0 τ 0. 5 (d) strog publcato bas (average selecto probablty 76%) (Begg ad Mazumdar, 994)

11 Clcal trals of rst P6 acupot stmulato prevetg postoperatve ausea /(stadard error) adom effects estmate θ 0.68 Betee-study varace τ 0.33 Cofdece tervals M BT SJ (.06, 0.9) (.08, 0.9) (.43, 0.8) (., 0.4) Log odds rato (.00, 0.03)

12 Summary DerSmoa-Lard cofdece terval: loer coverage probablty tha the omal level (95%) drastcally loer f there s publcato bas Fxed effects estmate: less sestve to publcato bas tha the radom effects estmate easer to calculate the exact dstrbuto of the pvotal quatty Cofdece terval based o the fxed effects estmate: hgher coverage probablty tha the regardless of publcato bas ts dfferece becomes larger f publcato bas exsts Ths cofdece terval does ot adjust for publcato bas completely, but gves more relable formato o the overall average effect thout makg utestable assumpto o the process of study selecto.

13 efereces Brockell S.E. ad Gordo I.. (00). A comparso of statstcal methods for meta-aalyss. Statstcs Medce 0, DerSmoa. ad Lard N. (986). Meta-aalyss clcal trals. Cotrolled Clcal Trals 7, Hardy.J. ad Thompso S.G. (996). A lkelhood approach to meta-aalyss th radom effects. Statstcs Medce 5, Bggerstaff B. J. ad Teede.L. (997). Icorporatg varablty esymates of heterogeety the radom effects model meta-aalyss. Statstcs Medce 6, Sdk K. ad Jokma J.N. (00). A smple cofdece terval for meta-aalyss. Statstcs Medce, Begg C.B. ad Mazumdar M. (994). Operatg characterstcs of a rak correlato test for publcato bas. Bometrcs 50,

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