Estimating and modelling the cure fraction in population based

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					           Estimating and modelling the cure fraction in
             population-based cancer survival analysis

        Paul W Dickman1 , Paul C Lambert2 , Sandra Eloranta1 , Therese
                           Andersson1 , and others

      1 Department   of Medical Epidemiology & Biostatistics, Karolinska Institutet, Stockholm,
                                             Sweden
         2 Centre   for Biostatistics and Genetic Epidemiology, University of Leicester, UK


                                             11 Dec 2008




               Dickman et al.   Cure models for cancer patient survival                           1/21



Specific aims of the research




  1    Develop statistical methods for estimating and modelling the cure
       fraction in population-based cancer survival analysis.
  2    Apply the methods to data from Sweden, Finland, England, and the
       USA with the joint aim of evaluating the new methodology as well as
       studying temporal trends in cancer patient survival.




               Dickman et al.   Cure models for cancer patient survival                           2/21




Background: Relative Survival

                                    Observed Survival
        Relative Survival =                                               R(t) = S(t)/S ∗ (t)
                                    Expected Survival

       Expected survival obtained from national population life tables
       stratified by age, sex, year of diagnosis, other covariates.
       Estimate of mortality associated with a disease without requiring
       information on cause of death(1; 2; 3).
       On hazard scale


                                       λ(t) = h(t) − h∗ (t)

                Excess          Observed         Expected
                            =                –
             Mortality Rate   Mortality Rate   Mortality Rate


               Dickman et al.   Cure models for cancer patient survival                           3/21
Definition of Cure (1)




    For many cancers the excess mortality (hazard) rate returns to the
    same level as that in the general population.
    When this occurs the relative survival curve is seen to reach a plateau.
    This is Population or Statistical Cure.
    Information of cure at the individual level not available.
    For the ‘uncured’ we can obtain a summary measure of survival.




                           Dickman et al.   Cure models for cancer patient survival                   4/21



Definition of Cure (2)

                          1.0



                          0.8
      Relative Survival




                          0.6



                          0.4



                          0.2



                          0.0
                                0            2               4             6          8          10
                                                           Years from Diagnosis


                           Dickman et al.   Cure models for cancer patient survival                   5/21




Relative Survival for Cancer of the Colon in Finland

                          1.0
                                                                                          1953−1964
                                                                                          1965−1974
                                                                                          1975−1984
                          0.8                                                             1985−1994
                                                                                          1995−2003
      Relative Survival




                          0.6



                          0.4



                          0.2



                          0.0
                                0            2               4             6          8          10
                                                           Years from Diagnosis


                           Dickman et al.   Cure models for cancer patient survival                   6/21
Relative Survival for Cancer of the Colon in Finland

                                            1.0




      Interval Specific Relative Survival
                                            0.8



                                            0.6



                                            0.4

                                                              1953−1964
                                            0.2               1965−1974
                                                              1975−1984
                                                              1985−1994
                                                              1995−2003
                                            0.0
                                                  0              2               4             6          8   10
                                                                               Years from Diagnosis


                                             Dickman et al.     Cure models for cancer patient survival            7/21



Relative Survival Models and Cure Models


Relative Survival Models
                                                                        S(t) = S ∗ (t)R(t)
                                                                       h(t) = h∗ (t) + λ(t)

    When modelling cure we define an asymptote at the cure fraction, π,
    for the relative survival function, R(t)(4; 5).

Mixture Cure Model
                                                              S(t) = S ∗ (t)(π + (1 − π)Su (t))




                                             Dickman et al.     Cure models for cancer patient survival            8/21




Survival for the ‘Uncured’




    As well as the cure fraction, summaries of the ‘uncured’ (those
    ‘bound to die’) are potentially useful.
    For example, mean or median survival or some other percentile of the
    survival distribution.
    We need to choose parametric form for S(t).
    For many scenarios the Weibull distribution provides a good fit.




                                             Dickman et al.     Cure models for cancer patient survival            9/21
Interpreting changes over time




                                                                                                     (a) General Improvement
 Survival of Uncured
                                                                                                     (b) Selective
                                                                                                         Improvement
                                                                                                     (c) Improved palliative
                                                                                                         care
                                                                                                     (d) Inclusion of subjects
                                                                                                         with no excess risk
                                                   Cure Fraction
                       Adapted from Verdeccia (1998)




                                      Dickman et al.       Cure models for cancer patient survival                         10/21



Interpreting changes over time




                                                                                                     (a) General Improvement
 Survival of Uncured




                                                                (a)
                                                                                                     (b) Selective
                                                                                                         Improvement
                                                                                                     (c) Improved palliative
                                                                                                         care
                                                                                                     (d) Inclusion of subjects
                                                                                                         with no excess risk
                                                   Cure Fraction
                       Adapted from Verdeccia (1998)




                                      Dickman et al.       Cure models for cancer patient survival                         10/21




Interpreting changes over time




                                                                                                     (a) General Improvement
 Survival of Uncured




                                                                (a)
                                                                                                     (b) Selective
                                                                                                         Improvement
                                                                                                     (c) Improved palliative
                                                                                                         care
                                                                                                     (d) Inclusion of subjects
                                                                (b)                                      with no excess risk
                                                   Cure Fraction
                       Adapted from Verdeccia (1998)




                                      Dickman et al.       Cure models for cancer patient survival                         10/21
Interpreting changes over time




                                                                                                     (a) General Improvement
 Survival of Uncured
                                   (c)                          (a)
                                                                                                     (b) Selective
                                                                                                         Improvement
                                                                                                     (c) Improved palliative
                                                                                                         care
                                                                                                     (d) Inclusion of subjects
                                                                (b)                                      with no excess risk
                                                   Cure Fraction
                       Adapted from Verdeccia (1998)




                                      Dickman et al.       Cure models for cancer patient survival                                  10/21



Interpreting changes over time




                                                                                                     (a) General Improvement
 Survival of Uncured




                                   (c)                          (a)
                                                                                                     (b) Selective
                                                                                                         Improvement
                                                                                                     (c) Improved palliative
                                                                   (d)                                   care
                                                                                                     (d) Inclusion of subjects
                                                                (b)                                      with no excess risk
                                                   Cure Fraction
                       Adapted from Verdeccia (1998)




                                      Dickman et al.       Cure models for cancer patient survival                                  10/21




The cure proportion is not affected by lead time



                          Onset            Detectability                          Symptoms                      Death
                                                             DETECTABLE
                                                             PRECLINICAL
                                                               PHASE                                                          Time

                                                                             LEAD                    SURVIVAL
                                                                             TIME                      TIME
                                                                                                     SURVIVAL
                                                                                                       TIME
                                                             Early                           Clinical                   Postponed
                                                           diagnosis                        diagnosis                     death




                                      Dickman et al.       Cure models for cancer patient survival                                  11/21
Time Trends for Cancer of the Colon

                                                                               Cure Fraction
                                  1.00
                                                      <50 years
                                                      50−59 years
                                                      60−69 years
                                  0.80
                                                      70−80 years




                                  0.60



     Cure Fraction
                                  0.40




                                  0.20




                                  0.00

                                         1950            1960               1970               1980   1990   2000
                                                                               Year of Diagnosis




                                     Dickman et al.        Cure models for cancer patient survival                  12/21



Time Trends for Cancer of the Colon

                                                                      Median Survival of ’Uncured’
                                  2.50
                                                      <50 years
                                                      50−59 years
                                                      60−69 years
                                  2.00
                                                      70−80 years
     Median Survival of Uncured




                                  1.50




                                  1.00




                                  0.50




                                  0.00

                                         1950            1960               1970               1980   1990   2000
                                                                               Year of Diagnosis




                                     Dickman et al.        Cure models for cancer patient survival                  12/21




Quantifying Differences

                                           Relative Odds of Cure (Age Group 70−79 / Age Group <50)
                                   2.0

                                   1.5


                                   1.0
     Odds Ratio




                                   0.5




                                   0.3



                                         1950            1960              1970         1980          1990   2000
                                                                          Years from Diagnosis


                                     Dickman et al.        Cure models for cancer patient survival                  13/21
Quantifying Differences

                                      Difference in Cure Fraction (Age Group <50 − Age Group 70−79)
                                    0.2



                                    0.1




     Difference in Cure Fraction
                                    0.0



                                  −0.1



                                  −0.2



                                  −0.3
                                          1950            1960              1970         1980          1990   2000
                                                                           Years from Diagnosis


                                      Dickman et al.        Cure models for cancer patient survival                  14/21



Time Trends for Cancer of the Rectum

                                                                                Cure Fraction
                                   1.00
                                                       <50 years
                                                       50−59 years
                                                       60−69 years
                                   0.80
                                                       70−80 years




                                   0.60
     Cure Fraction




                                   0.40




                                   0.20




                                   0.00

                                          1950            1960               1970               1980   1990   2000
                                                                                Year of Diagnosis




                                      Dickman et al.        Cure models for cancer patient survival                  15/21




Time Trends for Cancer of the Rectum

                                                                       Median Survival of ’Uncured’
                                   2.50
                                                       <50 years
                                                       50−59 years

                                                       60−69 years
                                   2.00
                                                       70−80 years
     Median Survival of Uncured




                                   1.50




                                   1.00




                                   0.50




                                   0.00

                                          1950            1960               1970               1980   1990   2000
                                                                                Year of Diagnosis




                                      Dickman et al.        Cure models for cancer patient survival                  15/21
Factors contributing to improvements



    Surgical and anaestesiological techniques have become more
    aggressive and sophisticated over time.
    The age of the patient at which surgeons are prepared to operate has
    increased over time, which may explain the reduced differences in the
    proportion cured between age groups.
    Better awareness among the public and doctors about the importance
    of early diagnosis for cure.
    Some of the trends over time are likely to be due to the ”learning
    period” when gradually introducing new techniques within and
    between hospitals.




          Dickman et al.   Cure models for cancer patient survival       16/21



Greater improvements for rectal than colon cancer

    Rectal cancer surgery is much more demanding than colon cancer
    surgery, and the general improvements in anaesthesiology and
    postoperative care seen in the late 1960s/early 1970s were relatively
    much more important for rectal than colon cancer.
    The steep increase during the 1990s seen in all age groups likely
    reflects the marked decrease in the risk of a local failure after rectal
    cancer surgery seen after the introduction of total mesorectal excision
    (TME) and increased use of preoperative radiotherapy or
    postoperative radiochemotherapy.
    A local failure is a much less clinical problem in cancer of the colon
    than in cancer of the rectum.
    Metastatic disease has been the predominant cause of death among
    colon cancer patients.
    The natural course of local failure is longer than that of metastatic
    disease (which often involves the liver).
          Dickman et al.   Cure models for cancer patient survival       17/21




Time Trends for AML in Sweden




          Dickman et al.   Cure models for cancer patient survival       18/21
Challenges and current/future research




    How to assess goodness-of-fit? Standard methods not appropriate.
    How do the models behave when cure is not reached (e.g., female
    breast cancer).
    Preliminary evidence suggests the models perform best when
    mortality is neither high nor low.




                            Dickman et al.   Cure models for cancer patient survival                          19/21



Cure models may fit poorly when early mortality is high:
Cancer of the Colon: Weibull and Mixture of Weibulls

                                                             Age Group 80+
                            1.0
                                                                                       Ederer II
                                                                                       Weibull
                                                                                       Mixture of Weibulls
                            0.8
        Relative Survival




                            0.6



                            0.4



                            0.2



                            0.0
                                  0            2               4             6             8             10
                                                             Years from Diagnosis


                            Dickman et al.   Cure models for cancer patient survival                          20/21




Cure models may fit poorly when early mortality is high:
Cancer of the Colon: Weibull and Mixture of Weibulls

                                                             Age Group 80+
                            1.0
                                                                                       Ederer II
                                                                                       Weibull
                                                                                       Mixture of Weibulls
                            0.8
        Relative Survival




                            0.6



                            0.4



                            0.2



                            0.0
                                  0            2               4             6             8             10
                                                             Years from Diagnosis


                            Dickman et al.   Cure models for cancer patient survival                          20/21
Cure models may fit poorly when early mortality is high:
Cancer of the Colon: Weibull and Mixture of Weibulls

                                                              Age Group 80+
                             1.0
                                                                                        Ederer II
                                                                                        Weibull
                                                                                        Mixture of Weibulls
                             0.8




         Relative Survival
                             0.6



                             0.4



                             0.2



                             0.0
                                   0            2               4             6             8             10
                                                              Years from Diagnosis


                             Dickman et al.   Cure models for cancer patient survival                          20/21




[1] Dickman PW, Adami HO. Interpreting trends in cancer patient
    survival. J Intern Med Aug 2006;260:103–117.
[2] Ederer F, Axtell LM, Cutler SJ. The relative survival rate: A statistical
    methodology. National Cancer Institute Monograph 1961;6:101–121.
[3] Ederer F, Heise H. The effect of eliminating deaths from cancer on
    general population survival rates. Methodological note No. 11, End
    Results Evaluation Section, National Cancer Institute, Bethesda MD,
    1959.
[4] 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 Nov 2007;121:2052–2059.
[5] Lambert PC, Thompson JR, Weston CL, Dickman PW. Estimating
    and modeling the cure fraction in population-based cancer survival
    analysis. Biostatistics Jul 2007;8:576–594.


                             Dickman et al.   Cure models for cancer patient survival                          21/21

				
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