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

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

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)

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

Overall Survival (Bonner et al 2006) ?

Overall Survival (Bonner et al 2006) ?

Overall Survival (Bonner et al 2006) ?!

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

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)

Cetuximab: Locoregional Disease Control Reconstructed KM data Original publication 10

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

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

Exponential Extrapolation (poor fit)

Weibull Extrapolation (poor fit)

Log-Normal Extrapolation (good fit)

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

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

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:

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

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)

Data: SEER 1-yr Conditional Survival

Data: Pignon meta-analysis 1-yr Conditional Survival

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

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

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

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

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

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

Hazard Ratio

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

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

References Bonner et al. 2006. NEJM 354: 567-78 Pignon JP et al. 2009. Radiotherapy and Oncology 92:4-14 Surveillance, Epidemiology, and End Results (SEER) Database (www.seer.cancer.gov) 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 2012. 12:9 Royston P, Parmar MK. 2002. Stats in Med 21:2175-2197