Dynamic survival models for predicting the future in health technology assessment and incorporating external evidence
- 1. DYNAMIC SURVIVAL MODELS FOR PREDICTING THE FUTURE IN HEALTH TECHNOLOGY ASSESSMENT
- 6. Example survival data • Varying sample size • Unequal observations • Censoring
- 8. Dynamic survival models Number of deaths at time 𝑡𝑖 = 𝑌𝑡 𝑖 𝑌𝑡 𝑖 ~ Poisson(exp 𝛽1,𝑡 𝑖 × 𝜏 𝑡 𝑖 ) 𝛽1,𝑡 𝑖 = 𝛽1,𝑡 𝑖−1 + 𝛽2,𝑡 𝑖−1 𝛽2,𝑡 𝑖 ~ Normal(𝛽2,𝑡 𝑖−1 , 𝑍) Extrapolations at time ℎ after follow-up (𝑡𝑖 = 𝑇): ො𝑦 𝑇+ℎ = exp 𝛽1,𝑇 + ℎ ∗ 𝛽2,𝑇
- 9. Extrapolation performance with a cured fraction: a simulation study.
- 10. Curative treatments Survival data simulated from a Weibull cure model. Cure fraction = 25% Mean survival: • Cured ≈ 20 years • Uncured ≈ 2 years Each dataset had 100 people with follow-up = 4 years. 200 datasets were simulated.
- 11. Dynamic survival models with a cured fraction
- 12. Extrapolation models 1. Weibull cure model (correctly specified) 2. Lognormal cure model (misspecified) 3. Royston Parmar cure model (over-specified) 4. Dynamic survival cure model (over-specified)
- 13. Simulation study
- 14. Simulation study
- 15. Simulation study
- 16. Simulation study
- 17. Simulation study
- 18. Simulation study
- 19. Simulation study
- 20. Shorter follow-up (Two years)
- 21. Models without a cure fraction (Follow-up = 4 years, n = 100)
- 22. Dynamic survival models in HTA: a case-study
- 23. Company ICER: £86,000 Evidence review group (ERG): company extrapolations “wholly implausible”. ICER: £133,000 Impacts on £ discount required
- 24. Dynamic survival models + general population mortality = Dynamic relative survival models General population mortality = 𝜆 𝑡 𝑖 𝑃 𝑌𝑡 𝑖 ~ Poisson( exp 𝛽1,𝑡 𝑖 + 𝜆 𝑡 𝑖 𝑃 × 𝜏 𝑡 𝑖 ) exp 𝛽1,𝑡 𝑖 = disease-specific (excess) hazard.
- 25. Dynamic survival models + general population mortality = Dynamic relative survival models Use different time series models for different assumptions about extrapolated excess hazard: • Decrease to zero = local trend model • Constant = local level model • Short-term decrease, long-term constant = damped trend model.
- 26. Within-sample estimates and extrapolations
- 27. Impact on cost-effectiveness Model ICER Company (log-logistic) £86,000 Excess risk ↘ 0 £122,000 ERG (hybrid) £133,000 Constant excess risk £140,000 Excess risk ↘ constant £143,000
- 28. Sensitivity of the ERG ICER to cut-point
- 30. Winning method: 1. Dynamic model 2. Model averaging 3. Incorporate external data (via long short- term memory recurrent neural network)
- 31. Conclusions “Survival data is inherently time series data” (https://www.jstor.org/stable/2348523)
- 32. Thank you for listening! Any questions? Acknowledgements: I would like to thank my supervisors. I am funded by the National Institute for Health Research (DRF-2016-09-119). This research was supported by the NIHR CLAHRC Yorkshire and Humber (NIHR CLAHRC YH). www.clahrc-yh.nihr.ac.uk. The views expressed are those of the author, and not necessarily those of the NIHR or the Department of Health and Social Care.