2009 JSM - Meta Time to Event Data
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2009 JSM - Meta Time to Event Data

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Hsini (Terry) Liao, Ph.D., Yun Lu, Hong Wang, “Meta-Analysis of Time-to-Event Survival Curves in Drug Eluting Stent Data”, Abstract No 304048, Joint Statistical Meetings, Session No 205, ...

Hsini (Terry) Liao, Ph.D., Yun Lu, Hong Wang, “Meta-Analysis of Time-to-Event Survival Curves in Drug Eluting Stent Data”, Abstract No 304048, Joint Statistical Meetings, Session No 205, Washington D.C., August 2009

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2009 JSM - Meta Time to Event Data 2009 JSM - Meta Time to Event Data Presentation Transcript

  • Meta-Analysis of Time-to-Event Survival Curves in Drug-Eluting Stent Data Hsini (Terry) Liao*, PhD Yun Lu, MSc Hong Wang, MSc Boston Scientific Corporation *Contact: terry.liao@bsci.com JSM 2009 1
  • Outlines • Motivation • Meta-Analysis Overview • Application to Survival Curves • Case Study and Simulation • Summary and Future Work • References JSM 2009 2
  • Motivation • Meta-analysis provides a structure of consolidating the outcomes from several studies and deriving statistical inference of the outcomes • Meta-analysis of time-to-event data is less common than meta-analysis of binary or continuous data • Fixed effect vs. random effects models • Patient-level vs. study-level data • Hazard ratio (HR) vs. Kaplan-Meier (KM) curve • Different follow-up schedules JSM 2009 3
  • Motivation (Cont’d) Sutton, A.J., Higgins, J.P. “Recent Developments in Meta-Analysis”, Stat in Med. 2008; 27:625-650 Meta- Analysis” 27:625- JSM 2009 4
  • Meta-Analysis Overview • 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 • Effect size: event rate, OR, RR, HR, etc. • Sample size/standard error to assign weight JSM 2009 5
  • (Current) Application to Survival Curves • Extract data from KM curves • Estimate ln(HRij) and var[ln(HRij)] for each study • The HR is a summary of the difference between two KM curves • Consider time-to-event and censoring, otherwise HR=RR • Variety of scenarios (e.g. CI) • MS Excel spreadsheet computation JSM 2009 6
  • HR Matrix Study 1 HR11 HR12 HR13 . . . HR1J HR21 HR22 HR23 . . . HR2J Study 2 . . . . . . . . . . . . . . . Study K HRK1 HRK2 HRK3 . . . HRKJ Time 1 Time 2 Time 3 . . . Time J JSM 2009 7
  • Application to Survival Curves (Cont’d) • Formal definition of the log hazard ratio • Reported number of observed events and number of expected events: For each study i and each time j, OTij / ETij ln( HRij ) = ln( ) OCij / ECij 1 1 var[ln(HRij )] = + ETij ECij JSM 2009 8
  • Application to Survival Curves (Cont’d) For each study i=1,…,K and each time point j, K ∑ var[ln(HR )] ln( HRij ) ij ln( HR⋅ j ) = i =1 K ∑i =1 1 var[ln(HRij )] −1 ⎡ K ⎤ var[ln(HR⋅ j )] = ⎢ ⎢ ∑ ⎢ i =1 1 ⎥ var[ln(HRij )] ⎥ ⎥ ⎣ ⎦ JSM 2009 9
  • Most Scenarios • Reported the initial #patient at risk and observed event count for each time point, or equivalent information • Take censoring into account if applicable • Able to estimate expected events JSM 2009 10
  • Method 1: Proposed (Overall Observed and Expected Events) • For each study i, compute the sum of observed events (OTi., OCi.) and the sum of expected events (ETi., ECi.) across all time points • Use the formal definition of the log hazard ratio OTi⋅ / ETi⋅ ln( HRi⋅ ) = ln( ) OCi⋅ / ECi⋅ 1 1 var[ln(HRi⋅ )] = + ETi⋅ ECi⋅ JSM 2009 11
  • Method 2: Parmar (Observed and Expected Events) • For each study i, compute log(HR) and associated variance for each time point with observed events (OTij, OCij) and expected events (ETij, ECij) • Calculate the weighted mean of log(HR) across time points for each study i OTij / ETij ln( HRij ) = ln( ) OCij / ECij 1 1 var[ln(HRij )] = + ETij ECij JSM 2009 12
  • Method 3: Williamson (Observed Events and #Patient-At-Risk) • For each study i, compute log(HR) and associated variance for each time point with the observed events (OTij, OCij) and #patient-at-risk (NTij, NCij) • Calculate the weighted mean of log(HR) across time points for each study i OTij / NTij ln( HRij ) = ln( ) OCij / NCij 1 1 1 1 var[ln(HRij )] = − + − OTij NTij OCij NCij JSM 2009 13
  • Case Study: Stent Data • Study outcome: Target Vessel Revascularization (TVR) • Post-hoc analysis set: diabetic vs. non-diabetic patients with drug-eluting stent • Propensity score adjustment (“like-to-like”): 1-to-1 match • Data: total 1,554 DES patients over 7 studies • Study 1: (n=308) 5 years • Study 2: (n=352) 4 years • Study 3: (n= 76) 5 years • Study 4: (n=436) 3 years • Study 5: (n= 84) 2 years • Study 6: (n=186) 2 years • Study 7: (n=112) 2 years • The hazard ratio estimate of study outcomes from patient level data is compared with that from the study level data to assess the treatment effect in DES patients (Diabetic vs. Non- Diabetic). JSM 2009 14
  • HR Matrix (Calculation Using Formal Definition) Year 1 Year 2 Year 3 Year 4 Year 5 Study 1 1.99 1.27 1.07 6.32 0.74 Study 2 0.91 2.48 1.39 0.11 NA Study 3 1.33 2.06x106 * 0.28 1.03 1.07 Study 4 2.23 1.44 2.18 NA NA Study 5 1.40 1.06 NA NA NA Study 6 1.24 3.90 NA NA NA Study 7 1.20 1.00 NA NA NA NA = Not Available * Due to zero event in non-diabetic arm, using tiny number (10-6) instead of zero to make formula work. 15 JSM 2009
  • Comparison of Estimates for Overall HR Fixed Effect Model Random Effects Model HR [95% CI] HR [95% CI] Method1 1.31 [1.03, 1.67] 1.34 [0.99, 1.81] (Proposed) Method 2 1.31 [1.03, 1.66] 1.46 [0.90, 2.37] (Parmar) Method 3 1.31 [1.04, 1.67] 1.33 [1.02, 1.75] (Williamson) Cox Model in 1.32 [1.03, 1.67] 1.33 [0.98, 1.82] IPD JSM 2009 IPD = Individual Patient Data 16
  • Simulation • Simulation of KM curves in terms of numbers of patient at risk, censoring and events for 5 years • Meta-analysis of 10 studies • Two-arm with initial sample size ratio 1:1 • Event rates are centered at 13%, 16%, 20%, 23%, and 24% for treatment arm based on pooling historical data • Generated 1,000 times JSM 2009 17
  • Simulation (Cont’d) • Varying the first year event rate difference ranging from 0.2% to 4% (treatment effect) • Varying heterogeneity in terms of standard deviation of event rates of 2%, 3%, 4%, 5% • Calculated the coverage probability defined as the percentage of 95% CIs that contain the true underlying value of the log HR over 1,000 simulated runs JSM 2009 18
  • STD = 2% STD = 3% 1.80 1.80 1.70 1.70 Estimated Hazard Ratio Estimated Hazard Ratio 1.60 1.60 1.50 1.50 1.40 1.40 1.30 1.30 1.20 1.20 1.10 1.10 1.00 1.00 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.20 1.22 1.24 1.26 1.28 1.30 1.32 True Hazard Ratio True Hazard Ratio Proposed Parmar Williamson Proposed Parmar Williamson STD = 4% STD = 5% 1.80 1.80 1.70 1.70 Estimated Hazard Ratio Estimated Hazard Ratio 1.60 1.60 1.50 1.50 1.40 1.40 1.30 1.30 1.20 1.20 1.10 1.10 1.00 1.00 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.20 1.22 1.24 1.26 1.28 1.30 1.32 True Hazard Ratio True Hazard Ratio JSM 2009 Proposed Parmar Williamson Proposed Parmar Williamson 19
  • STD = 2% STD = 3% 100 100 90 90 80 80 70 70 % Coverage % Coverage 60 60 50 50 40 40 30 30 20 20 10 10 0 0 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.20 1.22 1.24 1.26 1.28 1.30 1.32 True Hazard Ratio True Hazard Ratio Proposed Parmar Williamson Proposed Parmar Williamson STD = 4% STD = 5% 100 100 90 90 80 80 70 70 % Coverage % Coverage 60 60 50 50 40 40 30 30 20 20 10 10 0 0 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.20 1.22 1.24 1.26 1.28 1.30 1.32 True Hazard Ratio True Hazard Ratio JSM 2009 Proposed Parmar Williamson Proposed Parmar Williamson 20
  • Result of Simulation • Small heterogeneity - For small or large treatment effect, all three methods perform well • Increasing heterogeneity - Bias increases - Coverage decreases. Some values decrease dramatically - For large treatment effect, coverage decreases less for proposed method JSM 2009 21
  • Summary: Meta-Analysis of Kaplan-Meier Curves • Reported Kaplan-Meier curves with #patient at risk at baseline • Read off survival probabilities at each time point • Estimate the minimum and the maximum follow-up time • Assumption for distribution of censored subjects: Missing at random (uniform)? JSM 2009 22
  • HR Matrix Different Follow-Up Study 1 HR11 HR12 HR13 HR1J HR21 HR22 HR23 Study 2 . . . . . . . . . . . . Study K HRK1 . . . . . . HRKJ Time 1 Time 2 Time 3 . . . Time J JSM 2009 23
  • Future Work • Missing value imputation for the HR matrix • Constant HRs over time • Test of equality for all non-missing HRij over time (within each study) • Inclusion/exclusion criteria • Distribution of censoring • Summary KM curve of many KM curves JSM 2009 24
  • References • Parmar, M.K.B., Torri, V. and Stewart, L. “Extracting Summary Statistics to Perform Meta-Analyses to the Published Literature for Survival Endpoints”, Stat in Med. 1998; 17:2815-2834 • Tierney, J.F., Stewart, L.A., Ghersi, D., Burdett, S. and Sydes, M.R. “Practical Methods for Incorporating Summary Time-to-Event Data into Meta-Analysis”, Trials 2007; 8:16 • Arends, L.R., Hunink, M.G.M. and Stijnen, T. “Meta-Analysis of Summary Survival Data”, Stat in Med. 2008; 27:4381-4396 • Williamson, P.R., Smith, C.T., Hutton, J.L. and Marson, A.G. “Aggregate Data Meta-Analysis with Time-to-Event Outcomes”, Stat in Med. 2002; 21:3337-3351 • Sutton, A.J., Higgins, J.P. “Recent Developments in Meta- Analysis”, Stat in Med. 2008; 27:625-650 JSM 2009 25