1. Patricia Guyot1,2, Nicky J Welton1, AE Ades1
Extrapolation of trial-based survival curves: constraints based on external information
Patricia Guyot1,2, Nicky J Welton1, AE Ades1
Thanks to: M Beasley3
1School of Social and Community Medicine, University of Bristol
2Mapi Consultancy
3Bristol Haematology and Oncology Centre
BAYES2014, University College London, London
11th- 13th June 2014

2. Why Extrapolate Survival Curves?
Health Technology Assessment requires a comparison of the expected quality-adjusted life-years between different technologies
A key element is difference in life expectancy
End-Of-Life criterion also require estimates of:
life expectancy
gains in life expectancy

3. Life Expectancy Difference
Difference in mean survival times
Can be calculated as the difference in areas between the curves over lifetime
But trials typically follow-up for just a few years
Mean survival times very sensitive to assumptions on what happens after the trial follow-up (in the “tails” of the curves)

4. Cetuximab+Radiotherapy vs Radiotherapy for Head and Neck Cancer
NICE TA145 June 2008
Bonner et al (2006) trial
5-year follow-up

5. Overall Survival (Bonner et al 2006)?

6. Overall Survival (Bonner et al 2006)?

7. Overall Survival (Bonner et al 2006)?!

8. How to Extrapolate? Need to assume something about:
the survival time distribution
Eg: Exponential, Weibull, Log-Normal ...
Cox models don’t help with this
the hazard ratio
proportional hazards (constant hazard ratio)
increasing or decreasing hazard ratio
“bath-tub” hazard ratio
Helps to have individual patient data, or sufficient statistics to explore alternative curves

9. Recontructing data from published Kaplan-Meier curves
Guyot et al. (2012) method to approximate the data used to produce kaplan-meier curves
Inputs:
Uses software to obtain co-ordinates from image from a .pdf file (we used digitizeit)
Numbers at risk published below the curve (defines fixed number of intervals)
Total number of deaths/events (if reported)

10. Cetuximab: Locoregional Disease Control
Reconstructed KM data
Original publication 10

11. Cetuximab Reconstruction Results
Original publication
Reconstructed KM data
Radiotherapy arm
2-year survival (%) 55
55 (49, 63)
3-year survival (%) 45
45 (39, 52)
median survival (months)
29.3
29.6 (22.6,43.0)
Radiotherapy plus cetuximab arm
survival rate (2 years) 62
62 (55, 69)
survival rate (3 years)
55 (48, 62)
median duration
49.0
48.9 (34.2, NA)
Hazard ratio with 95%CI
0.74 (0.57, 0.97)
0.77 (0.59, 0.996) 11

12. Back to Extrapolation ...
Using reconstructed data we can estimate a variety of different survival models ...

13. Exponential Extrapolation (poor fit)

14. Weibull Extrapolation (poor fit)

15. Log-Normal Extrapolation (good fit)

16. Assessing Fit to Trial Data Doesn’t Help
Mean Survival Difference:
Log-normal FSEA: 80.4months (2.0,237.0); DIC=2314
Log-normal AFT: 32.3months (-3.1,78.6); DIC=2315

17. Possible Solution: Use External Data To Inform Extrapolation
Observational evidence e.g.
General population
Registry (e.g. Surveillance Epidemiology and End Results)
Other RCT evidence e.g.
Meta-analyses (e.g. Pignon et al. 2009)
longer RCTs
Expert opinion

18. Estimation
Model RCT and external data simultaneously with linked parameters
Bayesian approach
Eg constraint that general population overall survival better than that in Bonner control arm
Linking function:
Prior:

19. Matched General Population (Expect OS better than Bonner Control Arm)
Rules out all parametric models
We used flexible spline models (Royston & Parmar (2002))

20. Expert view on Bonner trial
In H&N, relapse is high for first 2 years, and then declines
Effect of cetuximab is to increase the proportion of cells sensitive to radiotherapy and so lower the risk of relapse
Duration of treatment effect should be the same as the time interval over which the relapses occur
Those who die of H&N cancer tend to die in first 5 years
Conditional survival in both arms should “stabilize” and converge after 5 years (i.e. HR tends to 1)

21. Data: SEER 1-yr Conditional Survival

22. Data: Pignon meta-analysis 1-yr Conditional Survival

23. All Constraints
Control arm overall survival less than matched UK general population
1-year conditional survival in control arm is no different to that in SEER database
Hazard ratio tends to 1 as time from treatment increases

24. Implementation: Gen Pop Survival
Likelihood for the external data:
r: number alive at time T; n: number at risk at time 0
Linking function
Overall survival , e.g.
Prior:
Constrain general population survival to be better than that for advanced head and neck cancer patients

25. Implementation: SEER 1-year Conditional Survival
Belief that 1-year conditional survival on radiotherapy equal to that from SEER
Linking functions
Binomial likelihood (each time-point conditionally independent)
1-year Conditional survival on control arm

26. Implementation: HR tends to 1
Belief that HR tends to 1
Likelihood for the external data
Normal for external HR
Linking functions
Normal likelihood for hazard ratios:
Hazard ratio of treatment vs. control

27. Results: Overall Survival
Kaplan-Meier
Matched General Population
Constrained Extrapolation

28. 1-year Conditional Survival
Kaplan-Meier
Matched SEER
Constrained Extrapolation

29. Hazard Ratio

30. Overall Survival Difference in life expectancy:
5 months [95%CrL: 0; 9]

31. Discussion Spline models tricky to estimate
Possible alternative flexible models include fractional polynomials, mixture models
Relies on identification of relevant external evidence sources
Clinical input essential to help identify relevant sources

32. References Bonner et al. 2006. NEJM 354: 567-78
Pignon JP et al Radiotherapy and Oncology 92:4-14
Surveillance, Epidemiology, and End Results (SEER) Database (
Guyot P, Welton NJ, Ades AE. Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan-Meier survival curves. BMC Medical Research Methodology :9
Royston P, Parmar MK Stats in Med 21: