Extrapolation of trial-based survival curves: constraints based

on external information

BAYES2014, University College London, London11th- 13th June 2014

Patricia Guyot1,2, Nicky J Welton1, AE Ades1

Thanks to: M Beasley3

1School of Social and Community Medicine, University of Bristol2Mapi Consultancy3Bristol Haematology and Oncology Centre

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

Original publicationReconstructed KM data

0 10 20 30 40 50 60

0.0

0.2

0.4

0.6

0.8

1.0

Time (months)

Pro

po

rtio

n A

live

Cetuximab+Radiotherapy

Radiotherapy

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 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)

Back to Extrapolation ...

• Using reconstructed data we can estimate a variety of different survival models ...

Exponential Extrapolation (poor fit)

0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

Years

ove

rall

su

rviv

al (

%)

Mean survival difference: 17mths (2.1, 33.45)

Weibull Extrapolation (poor fit)

0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

Years

ove

rall

su

rviv

al (

%)

Mean survival difference: 23.3mths (0.7, 54.5)

Log-Normal Extrapolation (good fit)

0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

Years

ove

rall

su

rviv

al (

%)

Mean survival difference: 80.4mths (2.0, 237.0)

0 5 10 15 20 25 30 35 400

10

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50

60

70

80

90

100

Years

ove

rall

su

rviv

al (

%)

Assessing Fit to Trial Data Doesn’t Help

Mean Survival Difference:Log-normal FSEA: 80.4months (2.0,237.0); DIC=2314Log-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:

0,( ) ( )GP RCTS T S T )1,0(~Uniform

0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

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80

90

100

Years

ove

rall

su

rviv

al (

%)

Kaplan-MeierLog-Normal ExtrapolationMatched General Population

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

0 5 10 15 20 2540

50

60

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80

90

100

matched SEER population with Bonner trial character-istics

radiotherapy from Bonner trial

radiotherapy plus cetuximab from Bonner trial

Years after the start of the RCT

1-ye

ar c

on

dit

ion

al s

urv

ival

(%

)

Data: Pignon meta-analysis 1-yr Conditional Survival

0 1 2 3 4 5 6 7 8 9 1050

55

60

65

70

75

80

85

90

95

100

radiotherapy from Pignon meta-analysissurgery +/- radiotherapy from Pignon meta-analysisradiotherapy from Bonner trialradiotherapy plus cetuximab from Bonner trial

Years after the start of the RCT

1-y

ea

r c

on

dit

ion

al

su

rviv

al

(%)

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

0,( ) ( )GP RCTS T S T

)1,0(~Uniform

years 40T

~ ( ( ), )GPr Bin S T n

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

0,( | 1) ( | 1)SEER S S RCT S SCS t t CS t t

years 26,...,7,6st

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

1, 0,( ) ( ) / ( )EXT EXT RCT EXT RCT EXTt h t h t

years 35,34,26,25,..,7 ,6EXTt

2( ) ~ ( ( ), ( ))EXT EXT EXT EXT EXT EXTHR t N t t

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.00

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100

Ove

rall

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100%

)

Years

Results: Overall SurvivalKaplan-MeierMatched General PopulationConstrained Extrapolation

1-year Conditional Survival

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.00

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1-ye

ar c

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al s

urv

ival

(%

)

Years

Kaplan-MeierMatched SEERConstrained Extrapolation

Hazard Ratio

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.00.4

0.5

0.6

0.7

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1.0

1.1

1.2

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1.4

constrained spline ExpertKM HR

Haz

ard

Rat

io

Years

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.00

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100

Kaplan-Meier radiotherapy armconstrained spline radio-therapy arm General population

Ove

rall

Su

rviv

al (

100%

)

Years

Overall SurvivalDifference 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