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Cure models within the framework of flexible parametric survival models. T.M-L. Andersson 1 , S. Eloranta 1 , P.W. Dickman 1 , P.C. Lambert 1,2 1 Medical Epidemiology and Biostatistics , Karolinska Institutet, Stockholm, Sweden

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cure models within the framework of flexible parametric survival models

Cure models within the framework of flexible parametric survival models

T.M-L. Andersson1,

S. Eloranta1,

P.W. Dickman1,

P.C. Lambert1,2

1 Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden

2 Department of Health Sciences, University of Leicester, UK

relative survival
Relative survival

Cancer patient survival is often measured as 5-year relative survival,

Expected survival, , obtained from national population life tables stratified by age, sex, calendar year and possibly other covariates.

Estimate mortality associated with a disease without requiring information on cause of death.

Stata Users Group Meeting UK 2010

Therese Andersson

definition of statistical cure
Definition of statistical cure

When the mortality rate observed in the patients eventually returns to the same level as that in the general population

Stata Users Group Meeting UK 2010

Therese Andersson

cure models
Cure models
  • Mixture cure model
  • Non-mixture cure model
  • As well as the cure proportion, the survival of the “uncured” can be estimated
  • The commands strsmix and strsnmix in Stata1

1. P.C. Lambert. 2007. Modeling of the curefraction in survival studies. Stata Journal 7:351-375.

Stata Users Group Meeting UK 2010

Therese Andersson

cure models5
Cure models
  • We need to choose a parametric form for or . For many scenarios the Weibull distribution provides a good fit.
  • Hard to fit survival functions flexible enough to capture high excess hazard within a few months from diagnosis.
  • Hard to fit high cure proportion.
  • Flexible parametric approach for cure models would enable inclusion of these patient groups.

Stata Users Group Meeting UK 2010

Therese Andersson

flexible parametric survival model
Flexible parametricsurvivalmodel
  • First introduced by Royston and Parmar2, stpm in Stata3
  • Consider a Weibull survivalcurve
  • Transforming to the log cumulative hazard scale gives
  • Rather than assuming linearity with flexible parametric models use restricted cubic splines

2. P. Royston and M. K. B. Parmar. 2002. Flexible proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine 21:2175-2197.

3. P. Royston. 2001. Flexible alternatives to the Cox model, and more. The Stata Journal 1:1-28.

Stata Users Group Meeting UK 2010

Therese Andersson

flexible parametric survival model7
Flexible parametricsurvivalmodel
  • Why model on log cumulative hazard scale?
      • a generally stable function, easy to capture the shape
      • easy to transform to the survival and hazard functions
      • under the proportional hazards assumption covariate effects areinterpreted as hazardratios
  • Restricted cubic splines with k number of knots are used to model the log baselinecumulativehazard

where is a function of

Stata Users Group Meeting UK 2010

Therese Andersson

flexible parametric survival model8
Flexible parametricsurvivalmodel
  • When introducing covariates
  • Possible to include time-dependant effects (non-proportional hazards)
  • Extended to relative survival4, stpm2 in Stata5

4. C. P. Nelson, P. C. Lambert, I. B. Squire and D. R. Jones. 2007. Flexible parametric models for relative survival, with application in coronary heart disease. Statistics in Medicine 26:5486–5498.

5. P. C. Lambert and P. Royston. 2009. Further development of flexible parametric models for survival analysis. Stata Journal 9: 265-290.

Project presentation Leicester 29 April 2010 www.ki.se/research/thereseandersson

flexible parametric cure model
Flexible parametriccure model
  • When cure is reached the excess hazard rate is zero, and the cumulative excess hazard is constant.
  • By incorporating an extra constraint on the log cumulative excess hazard after the last knot, so that we force it not only to be linear but also to have zero slope, we are able to estimate the cure proportion.
  • This is done by calculating the splines backwards and introduce a constraint on the linear spline parameter in the regression model.

Stata Users Group Meeting UK 2010

Therese Andersson

flexible parametric cure model10
Flexible parametriccure model

Stata Users Group Meeting UK 2010

Therese Andersson

comparing non mixture and flexible parametric cure model
Comparing non-mixture and flexible parametriccure model
  • The FPCM looks like this:

which is a special case of a non-mixture model where

Stata Users Group Meeting UK 2010

Therese Andersson

comparing non mixture and flexible cure model
Comparing non-mixture and flexible cure model

If we introduce covariates:

This means that the constant parameters are used to model the cure proportion and the time-dependent parameters are used to model the distribution function.

Stata Users Group Meeting UK 2010

Therese Andersson

flexible parametric cure model13
Flexible parametriccuremodel

Project presentation Leicester 29 April 2010 www.ki.se/research/thereseandersson

comparing non mixture and flexible cure model14
Comparing non-mixture and flexible cure model

Stata Users Group Meeting UK 2010

Therese Andersson

comparing non mixture and flexible cure model15
Comparingnon-mixture and flexible curemodel

Stata Users Group Meeting UK 2010

Therese Andersson

comparing non mixture and flexible cure model16
Comparingnon-mixture and flexible curemodel

Stata Users Group Meeting UK 2010

Therese Andersson

thank you for listening ssc install stpm2
Thank you for listening!.sscinstall stpm2

Stata Users Group Meeting UK 2010

Therese Andersson