Cure Models - European Commission | Choose your … · 2016-06-03 · ( Cure Models Silvia...

Cure Models

Silvia FrancisciSilvia FrancisciSilvia FrancisciSilvia Francisci

Cure Models

Silvia FrancisciSilvia FrancisciSilvia FrancisciSilvia FrancisciSilvia FrancisciSilvia FrancisciSilvia FrancisciSilvia Francisci

Istituto Superiore di SanitàIstituto Superiore di SanitàIstituto Superiore di SanitàIstituto Superiore di Sanità

Ispra - January 23, 2014

Silvia FrancisciSilvia FrancisciSilvia FrancisciSilvia Francisci

Istituto Superiore di SanitàIstituto Superiore di SanitàIstituto Superiore di SanitàIstituto Superiore di Sanità

Ispra - January 23, 2014

OUTLINE

�The concept of cure in the relative survival framework

�Modelling the cure of cancer

�Mixture models

�Non mixture models

�Direct/Indirect use of cure models�Direct/Indirect use of cure models

�Eurocare-4 application

�Advantages and drawbacks of cure models

� Software availability

�Open questions

Cure Cure Cure Cure ModelsModelsModelsModels Silvia Francisci Silvia Francisci Silvia Francisci Silvia Francisci –––– ISSISSISSISS outlineoutlineoutlineoutline

THE CONCEPT OF CURE IN THE

RELATIVE SURVIVAL FRAMEWORK

• Attainment and maintenance of an interval specific relative survival of 1 (corresponding to a flattening of the cumulative relative survival curve) indicates that there is no excess mortality due to cancer and the patients are assumed to be ‘statistically cured’patients are assumed to be ‘statistically cured’

• It is a definition from a population perspective, it does not provide any information on individuals, therefore it does not necessarily imply that all patients are medically cured (no longer display of disease symptoms)

Cure Cure Cure Cure ModelsModelsModelsModels Silvia Francisci Silvia Francisci Silvia Francisci Silvia Francisci –––– ISSISSISSISS PagPagPagPag 1/161/161/161/16

STOMACH CANCER

0

0,1

0,2

0,3

0,4

0,5

0,6

CU

MU

LAT

IVE

RE

LAT

IVE

SU

RV

IVA

L (%

)

Relative Survival (Cum)

0

0,2

0,4

0,6

0,8

1

1,2

INT

ER

VA

L R

ELA

TIV

E S

UR

VIV

AL

(%)

Relative Survival (Interval)

For many cancers, the pattern of excess mortality shows high

excess mortality soon after diagnosis and statistical cure reached

after approximately 6–8 years (as is the case for stomach, colon …

cancers)

Data Source: SEER 9 data, cohort 1981- 88, 20 years of follow-up


0

CU

MU

LAT

IVE

RE

LAT

IVE

SU

RV

IVA

L (%

)

YEARS OF FOLLOW-UP

0

YEARS OF FOLLOW-UP

BREAST CANCER

0,4

0,5

0,6

0,7

0,8

0,9

1

1,1

INT

ER

VA

L R

ELA

TIV

E S

UR

VIV

AL

(%)

Relative Survival (Interval)

0,4

0,5

0,6

0,7

0,8

0,9

1

1,1

CU

MU

LAT

IVE

RE

LAT

IVE

SU

RV

IVA

L (%

)

Relative Survival (Cum)

A notable exception is female breast cancer where excess

mortality remains at a relatively constant level for many years

following diagnosis.


0,3

0,4

INT

ER

VA

L R

ELA

TIV

E S

UR

VIV

AL

(%)

YEARS OF FOLLOW-UP

0,3

0,4

CU

MU

LAT

IVE

RE

LAT

IVE

SU

RV

IVA

L (%

)

YEARS OF FOLLOW-UP

Data Source: SEER 9 data, cohort 1981- 88, 20 years of follow-up

MODELLING THE CURE OF CANCER

• When the assumption of cure for a proportion of patients is reasonable, it may be appropriate to fit models that explicitly allow the estimation of a cure fraction

• There are two main types of cure fraction • There are two main types of cure fraction models based on the same two assumptions:

1. a proportion of cancer patients is cured

2. survival time of uncured patients can be described by a chosen parametric distribution


– Mixture cure fraction models1

S(t)= C + (1-C) Su(t)

HP: two groups exist: those who are ‘cured’ of their disease, and

thus have a similar mortality rate to that expected in the general

population, and those who are ‘uncured’, or ‘bound to die’, of

their cancer

– Non mixture cure fraction (or promotion time cure, orbounded cumulative hazard) models2

S(t)= C Fz(t)

Originally developed in the modelling of tumour3 recurrences ,

the motivation behind non-mixture cure fraction models is that

“after treatment,” it is assumed that an individual is left with Ni

“metastatic-competent” cancer cells, i.e. a tumor cell that has the

potential of metastasizing.1 Verdecchia 1998, De Angelis 1999, Yu 20042 Lambert 2007, Andersson 2011 3 Tsodikov et al., 2003


MODEL SPECIFICATIONS

A key point for the model specification is the choice of the

survival distribution for uncured patients:

– Mixture cure models use standard parametric survival curve functions (Weibull, exponential are the most frequently used, but also lognormal , log-logistic, Gompertz)Gompertz)

– flexible parametric survival model is as special case of non-mixture cure models where restricted cubic splines are used to estimate the cumulative excess hazard

Structure of input data: aggregated versus individual data


THE USE OF CURE MODELS

1. Direct use � for description and interpretation of survival trends and geographical patterns, addressed to:– Clinicians (to improve understanding and communication

with patients community)

– Policy makers (to better allocate health care resources)– Policy makers (to better allocate health care resources)

2. Indirect use � to provide information needed for other analyses:– Survival models used in MIAMOD/PIAMOD method

– Survival models used in COMPLETENESS INDEX method

– For estimating the CURE PREVALENCE


Cure model parameters plan:

framework for results intepretation

Time to

Diagnostic anticipation

Proportion of cured

Time to

death a

d

c

b

Increasing survival

Improvement of

cure

Selective improvement


THE EUROCARE EXPERIENCE:

CURE PROPORTION IN EUROPEAN

COUNTRIES

• Aim: description and interpretation of cancer survival in 18 European countries, for major cancer sites, over the period 1988-1999

• Input data: stratified by age class and period of diagnosis • Input data: stratified by age class and period of diagnosis (source: EUROCARE-4 study data base), six-months follow-up intervals

• Analysis: lung, stomach, colon-rectum, breast, prostate, all cancer combined

• Mixture cure survival models, with Weibull distribution for uncured patients,


Geographical patterns: lung and

colon-rectum cancer

2

3

4

T

Lung

CZ

PL

A

DK

UK

FIN

F

D

ICE

I

NL

N

SCO

SLOE

S

CH

WAL2

3

4

T

Colon-Rectum

Time

to

A = AUSTRIA CZ = CZECH REP. D = GERMANY DK = DENMARK E = SPAIN F = FRANCE

FIN = FINLAND I = ITALY ICE = ICELAND N = NORWAY NL = NETHERLAND PL = POLAND

S = SWEDEN SCO = SCOTLAND SLO = SLOVENIA CH = SWITZERLAND UK = ENGLAND WAL = WALES

A

CZ

DK

UK

F

D

ICEI NL

NPL

SCO

SLOES

CH

WAL

FIN

0

1

0 0.05 0.1 0.15 0.2

P

PL

0

1

0 0.1 0.2 0.3 0.4 0.5 0.6

P


Proportion of cured

to

death

15-44

55-64

45-544

5

All CancersFemales

Age (all cancers in women) and period

trends (colon and rectum, men and

women combined)

1997-99

2.3

2.5

Colon-Rectum

Time 55-64

65-74

75-99

0

1

2

3

0.20 0.30 0.40 0.50 0.60 0.70 0.80

P

T

1988-90

1991-93

1994-96

1997-99

1.5

1.7

1.9

2.1

0.40 0.42 0.44 0.46 0.48 0.50

P

T


Proportion of cured

Time

to

death

COMPARISON OF DIFFERENT MODELS

X.Q.Yu (Cancer Epidemiology, 2013) compares different modelling approaches using three different examples (breast female, ovary, colon) in order to give some practical advise to model users.


CRITICISMS OF USING CURE MODELSA crucial issue with the cure models is the

identifiability of the cure fraction and parameters of

latency distribution and the length of follow-up time- First scenario (breast cancer any age group)� cure assumption is not

reasonable … just producing an estimate does not mean the approach is sensible

- Second and third scenarios � cure is reasonable - Second and third scenarios � cure is reasonable

�(colon, ovary, two younger age groups <60, 60-74) uncured survival distribution is appropriate, all models fit and produce similar estimates

�(colon, ovary, 75+) distributional assumption is not appropriate, results widely vary according to the uncured survival distribution and the structure of input data, … the use of grouped data with annual fup intervals, averages out the high excess mortality in the first few months since diagnosis.


SOME ADVICE FOR USERS- test the reasonability of cure assumption� visual

examination of relative survival life tables estimates by key prognostic factors to determine whether or not survival curves tend to level off after a certain period of follow-up

- test the uncured survival distribution� compare results from models with different survival results from models with different survival distributions (Weibull vs flexible) and/or using different data input (aggregated versus individual, yearly versus monthly follow-up intervals)

- Input data prerequisites� large samples, long follow-up, individual versus grouped data


Software availability• Stata commands (http://www.stata-journal.com/):

Lambert Stata J 2007: strsmix, strsnmix allow to estimate the cure

fraction in population-based cancer studies; Lambert- Andersson Stata

J 2012: have updated the stpm2 command for flexible parametric

models to enable cure modeling.

• SAS routine, mixture-grouped data (available on request

http://www.eurocare.it/MiamodPiamod/tabid/60/Default.asphttp://www.eurocare.it/MiamodPiamod/tabid/60/Default.asp

x#software)

• CANSURV is a statistical software to analyze population-based

survival data. For grouped survival data, it can fit both the standard

survival models and the mixture cure survival models

(http://surveillance.cancer.gov/cansurv/)


OPEN QUESTIONS• Is the assumption of cure reasonable for all

cancers/age groups? How much levelling is sufficient to allow the application of cure models?

• How do we choose the appropriate models features (survival distribution features (survival distribution weibull/flexible, grouped/individual data)?

• Is there any caution we should take according to the specific purpose of our estimate (either description/interpretation or information for other analyses)?


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