2008 JSM - Meta Study Data vs Patient Data

Comparison of Individual Patient-Level and Study-Level Meta-Analyses Using Time to Event Analysis in Drug-Eluting Stent Data Hsini Liao, Yun Lu, and Hong Wang Presented to JSM 2008 Boston Scientific Corporation JSM 2008 1

Conflict of Interest Disclosures DISCLOSURE INFORMATION: The following relationships exist related to this presentation: Hsini Liao, Yun Lu, Hong Wang Full time employees of Boston Scientific Corporation JSM 2008 2

Outlines • Motivation • Meta-Analysis • Time to Event Analysis • Stent Data • References JSM 2008 3

Motivation • Meta-analysis provides a structure of consolidating the outcomes from several studies and deriving statistical inferences of the outcomes. • Meta-analysis of time-to-event data is less common than of binary or continuous data. • Aggregate Data (AD) – Two-Step Approach • Individual Patient Data (IPD) – One-Step Approach • Comparison of the analysis of AD and IPD should be found discrepant results, but no clear general systematic differences, especially when homogeneity is assumed. • AD vs IPD in TTE DES Data JSM 2008 4

Meta-Analysis • A Systematic Review of Literature to Measure the Effect Size • Single Study/Effect • Many Studies/Narrative Review • Effect Magnitude/Adequate Precision • Combine the Effects to Give Overall Mean Effect • A Recent Survey in Practice (Simmonds et al, 2005): Majority used simple fixed-effect model; only small proportion considered among-study heterogeneity JSM 2008 5

Meta-Analysis (AD vs IPD) • Effect Size: Event Rate, • Ensuring Data Quality OR, RR, HR, Corr, etc. (e.g. Date of Outcome) • Sample Size/Standard • Detailed Data Checking Error to Assign Weight (e.g. Randomization) • Limit Analyses (e.g. • Ensuring the Fixed/Random Effect, Appropriateness of the Meta-Regression) Analyses (e.g. KM) • Less Time and Costs • More Time and costs JSM 2008 6

Fixed Effect Model (AD: FEM) • The FEM assumes that all studies in the meta-analysis are drawn from a common population. • The observed effect size varies from one study to the next only because of the random error inherent in each study. • Under the FEM there is one true effect size. The combined effect is an estimate of this value. JSM 2008 7

FEM (Cont’d) εA FEM with Study A sampling error TA (real world) εB Study B TB εC Study C e.g. TA= 0.6 – 0.1 = 0.5 TC 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 JSM 2008 8

FEM (Cont’d) • More generally, the observed effect Tj for any study is given by the population mean plus the sampling error in that study. That is, Tj = µ + εj εj~N(0,σ2) JSM 2008 j = 1,…,k 9

Random Effects Model (AD: REM) • The REM assumes that the studies are drawn from populations that differ from each other in ways that could impact on the treatment effect. • The observed effect size varies from one study to the next for two reasons. The first is random error within studies, as in the FEM. The second is true variation in effect size from one study to the next. • Under the REM there is not one true effect size, but a distribution of effect sizes. The combined effect is not an estimate of one value, but is meant to be the mean of a distribution of values. JSM 2008 10

REM (Cont’d) εA µA REM, true effect and Study A observed effect in one TA study (real world) ξA e.g. TA= 0.60 – 0.05 – 0.15 = 0.40 µ 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 JSM 2008 11

REM (Cont’d) • More generally, the observed effect Tj for any study is given by the grand mean µ, the deviation of this study’s true effect from the grand mean, and the deviation of this study’s observed effect from this study’s true effect. Tj = µ + ξj + εj ξj ~ N(0,τ2); εj~N(0,σj2) JSM 2008 j = 1,…,k 12

Heterogeneity • Using FEM/REM is based on assumption. • FEM • Ignore heterogeneity • Removing outliers causes biasness. • REM • Q Statistic is defined as total sum of squares. • I2 Statistics to describe the ratio of true/total variance • Subgroup/Sensitivity Analysis, ANOVA, Meta- Regression JSM 2008 13

Heterogeneity (Cont’d) • Total Sums of Squares: k k (∑ wiTi ) 2 Q = ∑ wiTi 2 − k Q = ∑ wi (Ti − T• ) i =1 2 k i =1 i =1 ∑w i =1 i • Test of Heterogeneity ( H 0 : θ1 = θ 2 = ... = θ k ) Q ~ χ 2 k −1 • Heterogeneity (Between-Studies Variance): ⎧ Q − df , if Q > df ⎪ τ =⎨ C 2 JSM 2008 ⎪ 0 , if Q ≤ df ⎩ 14

Time to Event Analysis (AD vs IPD) • HR derived from • Model time to event published data. • Account for censoring • Always compare 2 • Compare survival curve groups between 2+ groups • Estimate HR from KM • Assess relationship between survival time and • Not able to adjust for covariates. covariates, but able to • Univariate Method: select HR being Kaplan-Meier (KM) Curves adjusted for same covariates. • Multivariate Method: Cox- Proportional Hazards Model h(t) = λ(t)*exp(Xiβi) i = 1,…,k JSM 2008 15

Stent Data • Study Outcome: Target Vessel Revascularization • Treatment: Drug-Eluting Stent vs. Bare-Metal Stent • Data: total 825 diabetic randomized patients over 5 studies • Study A: (n=11) 5 years • Study B: (n=51) 5 years • Study C: (n=318) 5 years • Study D: (n=356) 3 years • Study E: (n=89) 5 years • The hazard ratio estimate of study outcomes from pooled IPD is compared with that from the AD to assess the treatment effect in diabetic patients. JSM 2008 16

Study Outcome: TVR In-segment 5 mm 5 mm In-stent proximal distal edge Covers entire stented length edge JSM 2008 17

Angioplasty A B C D JSM 2008 18

KM Estimate for TVR (IPD) JSM 2008 19

HR for Pooled IPD Treatment Effect without Adjustment JSM 2008 20

Meta-Analysis of TVR for Diabetic Patients (AD) Study name Statistics for each study Hazard ratio and 95% CI Hazard Lower Upper Relative ratio limit limit p-Value weight Study A 1.172 0.106 12.978 0.897 1.00 Study B 0.768 0.357 1.651 0.499 9.88 Study C 0.689 0.488 0.971 0.034 49.01 Study D 0.818 0.538 1.242 0.345 33.09 Study E 0.553 0.223 1.372 0.202 7.02 0.729 0.573 0.928 0.010 0.1 0.2 0.5 1 2 5 10 DES Better BMS Better Fixed Effect Model JSM 2008 21

Test of Heterogeneity Heterogeneity (AD) Q-value DF (Q) P-value I-squared 0.914 4 0.923 0.000 JSM 2008 22

AD vs IPD in DES Data Treatment Effect without Adjustment Hazard Log(HR) StdErr 95% CI Ratio IPD .6006 -.5098 .1370 [.4592, .7857] AD .6013 -.5087 .1387 [.4581, .7891] JSM 2008 23

AD vs IPD Study-Level Patient-Level Sample Size Always Small Relatively Large Visual Forest Plot, Sensitivity Kaplan-Meier Presentation Analysis for TTE Data Model Used Fixed/Random Effects Cox Regression Model Model with Fixed Treatment Effect Heterogeneity No by Test of No by Model Assumption Found Heterogeneity JSM 2008 24

AD vs IPD (Cont’d) Study-Level Patient-Level Subgroup Subgroup of studies is Subgroups are able to be Analysis available. Outcome for freely defined. The subgroup of baseline power for each subgroup may not be published. can be calculated. Individual vs Overall may not be Should check poolability Overall consistent with each between study and individual study. study. JSM 2008 25

Other Topics • Extracting information from survival curve • Published with insufficient details JSM 2008 26

References • Riley RD, Lambert PC, Staessen JA, Wang J, Gueyffier F, Thijs L, Boutitie, F. “Meta-Analysis of Continuous Outcomes Combining Individual Patient Data and Aggregate Data”, Stat in Med. 2008; 27:1870-1893 • Simmonds MC, Higgins JPT, Stewart LA, Tierney JF, Clarke MJ, Thompson SG. “Meta-Analysis of Individual Patient Data from Randomized Trials: A Review of Methods Used in Practice”, Clin Tri. 2005; 2:209-217 • Borenstein M, Hedges LV, Higgins JPT, Rothstein HR. “Introduction to Meta-Analysis” (Draft), 2007 • Sutton AJ, Abrams KR, Jones DR, Sheldon TA, Song F. “Methods for Meta-Analysis in Medical Research” (Reprint with Correction), 2004 • Parmar MKB, Torri V, Stewart L. “Extracting Summary Statistics to Perform Meta-Analyses to the Published Literature for Survival Endpoints”, Stat in Med. 1998; 17:2815-2834 • Smith CT, Williamson PR, Marson AG. “Investigating Heterogeneity in an Individual Patient Data Meta-Analysis of Time to Event Outcomes”, Stat in Med. 2005; 24:1307-1319 • Software: “Comprehensive Meta-Analysis” (CMA), Version 2.2.030 • Software: “SAS”, Version 9.1 JSM 2008 27

2008 JSM - Meta Study Data vs Patient Data

by Terry Liao

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