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					     Cure models within the framework of flexible parametric
                        survival models
     Therese M-L Andersson1, Paul W Dickman1, Sandra Eloranta1, Paul C Lambert1,2


  Introduction
  Cure models can be used to estimate the proportion of cancer
  patients that are eventually cured of their disease and at the same
  time get an estimate of the survival of those “uncured”.

  One limitation of parametric cure models is that a parametric
  distribution has to be used. It can sometimes be hard to fit survival
  functions flexible enough to capture a high excess hazard within a
  few months from diagnosis, or a very high survival.

  By using a flexible parametric approach we are able to capture the
  shape of the survival curve in cases where the standard methods
  don’t give a good fit.


                                                                                 Methods
                                                                                 In the flexible parametric survival model the baseline log
                                                                                 cumulative excess hazard is modeled using restricted cubic
                                                                                 splines.

                                                                                 When cure is reached the excess hazard rate is zero, and the
                                                                                 cumulative excess hazard is constant.

                                                                                 We incorporate an extra constraint on the log cumulative excess
                                                                                 hazard after the last knot, so that it is forced not only to be linear
                                                                                 but also to have zero slope, which enables estimation of the
                                                                                 cure proportion.

                                                                                 It can be shown that the flexible parametric cure model is a
                                                                                 special case of a non-mixture cure model, which means that the
                                                                                 survival of the uncured can be estimated in the same way as for
                                                                                 a non-mixture cure model.

                                                                                 We have updated the Stata package for flexible parametric
                                                                                 survival models to enable flexible parametric cure modeling.



Conclusion
In a published study [1] using data from the Finnish Cancer Registry
patients 80 years and older at diagnosis were excluded because of
poor fit of the cure models. We have now compared the fit from
standard cure models to our flexible cure model, and the results look
promising.

The fit of the flexible cure model is fairly robust to the number and
location of the knots, but some care needs to be taken regarding the
location of the last knot.
Reference 1. Lambert PC, Dickman PW, Osterlund P, Andersson T, Sankila R,
Glimelius B. Temporal trends in the proportion cured for cancer of the colon and
rectum: a population-based study using data from the Finnish Cancer Registry. Int
J Cancer. 2007;121(9):2052-9.                                                                             Sensitivity to the number and location of the knots




    Karolinska Institutet                           Affiliations
    Therese Andersson                               1. Department of Medical Epidemiology and
    Biostatistician, PhD student                       Biostatistics, Karolinska Institutet, Stockholm,
    E-mail: therese.m-l.andersson@.ki.se               Sweden
    Telephone: +46 (0)8-524 861 38                  2. Department of Health Sciences, University of
                                                       Leicester, UK

				
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posted:4/29/2011
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