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Using Weibull Model to Predict the Future: ATAC Trial

Using Weibull Model to Predict the Future: ATAC Trial. Anna Osmukhina, PhD Principal Statistician, AstraZeneca 15 April 2010. Survival Analysis. Rate. Example: Exponential Time to Event. Constant hazard. Overall Survival. No disease. Randomization. Death. Events in Early Breast Cancer.

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Using Weibull Model to Predict the Future: ATAC Trial

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  1. Using Weibull Model to Predict the Future: ATAC Trial Anna Osmukhina, PhD Principal Statistician, AstraZeneca 15 April 2010

  2. Survival Analysis Rate

  3. Example: Exponential Time to Event Constant hazard

  4. Overall Survival No disease Randomization Death Events in Early Breast Cancer Disease-Free-Survival: time from randomization to first recurrence or death Initial treatment: surgery, chemotherapy, radiotherapy No disease No disease New lesions Recurrence

  5. A Little Bit of History: Tamoxifen • “Tamoxifen for early breast cancer: an overview of the randomised trials “ • Early Breast Cancer Trialists' Collaborative Group • The Lancet, V 351, 1998, pp 1451-67 • Meta-analysis of 55 trials, ~37000 women • In women with hormone receptor +-ve disease, tamoxifen 5 years  • Recurrence  43% • Death (any cause)  23%

  6. ATAC Trial • Anastrozole, Tamoxifen, Alone or in Combination • >9000 early breast cancer patients; • 5 years of treatment + 5 years follow up • Analyses: • 2001: Major analysis (DFS event-driven) • 2004: Treatment completion • 2007: 5+2 • (2009)

  7. Presenting the Results: KM Plot for DFS, 2004

  8. ATAC Results by 2004(Hormone Receptor Positive Subgroup) * Cox proportional hazards model: semi-parametric **Rothman approach

  9. Questions About the Future

  10. Weibull Distribution for Survival Analysis Constant hazard “Accelerated failure time” Rate Scale (Shape)

  11. Exponential Time to Event Constant hazard

  12. Weibull Time to Event Accelerated hazard

  13. Weibull Time to Event Decelerated hazard

  14. Weibull Distribution in SAS PROC LIFEREG covariates Rates in ith individual:

  15. Questions About the Future

  16. Predictions Using Weibull Model Individual patient data so far EXPLORE BUILD Future data for each patient x1000 SIMULATE Weibull model

  17. Fit Weibull Model to the Data So Far

  18. Fitting Weibull Model • SAS PROC LIFEREG • Model events using baseline characteristics • Demography • Disease characteristics • Version 1: separately for each treatment • Version 2: treatment arms combined

  19. Weibull Models for the Data So Far

  20. Predictions Using Weibull Distribution Individual patient data so far EXPLORE BUILD Future data for each patient x1000 SIMULATE Weibull model

  21. Future Assumptions: 3 Scenarios • Optimistic: Trend continues • Middle: no difference from now on • Conditional HR=1.0 • Pessimistic: “A” worse from now on • Conditional HR=1.1 • Very optimistic (for OS only) • Conditional HR = 0.9

  22. Predictions Using Weibull Distribution Individual patient data so far EXPLORE BUILD Future data for each patient x1000 ANALYZE SIMULATE Weibull model 1000 versions of the study future/ scenario Future assumptions

  23. Predicting the Future, 31 March 2004

  24. Another Way to Look at It

  25. Predictions About the Future

  26. So, How Did That Work Out?

  27. Revisiting: Fitting Weibull Model • Model events using baseline characteristics • Demography • Disease characteristics

  28. Side Note: Loss to Follow Up

  29. Predictions Using Weibull Distribution Individual patient data so far EXPLORE BUILD Future data for each patient x1000 ANALYZE SIMULATE Weibull model 1000 versions of the study future/ scenario Future assumptions

  30. Revisiting: Fitting Weibull Model • Model events using baseline characteristics • Demography • Disease characteristics • Model discontinuation with time-dependent covariate: (time</>5 years)

  31. Future Event Prediction Good Bad Overestimated number of new events Is as good as assumptions More parameters = More assumptions (correct or not)? Adjusting for emergent risk factors? • Good HR (CI) estimates • Thanks to mature data? • Individual risk factors • Scenarios, complex questions • Describe/manage expectations • Complex models • Loss to follow up, administrative censoring

  32. References • Early Breast Cancer Trialists' Collaborative Group • Lancet 1998; 351: 1451-67 • ATAC trialists’ group • Lancet 2002; 359: 2131–39 • Lancet 2005; 365: 60–62 • Lancet Oncol 2008; 9: 45–53 • Carroll K, “On the use and utility of the Weibull model in the analysis of survival data” • Controlled Clinical Trials 24 (2003) 682–701 • Rothman M, “Design and analysis of non-inferiority mortality trials in oncology” • Statist. Med. 2003; 22:239–264

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