1

Equipe BioStatistique-Santé (BSS)

Pascal ROY PU-PH

2

Incidence Prévalence Survie

Variabilité populationnelle, Biologique

et Erreur de mesure

Méthodes d’inférence dans l’analyse de

la décision médicale

Mesures de distances

Ingénierie des connaissances

AXES DE RECHERCHE

Nadine Bossard

Michel Cucherat

René Ecochard

Muriel Rabilloud

Pascal Roy

3

1. Modélisation pronostique

1. Patients à haut risque

2. Adaptation du traitement

3. Evaluation des thérapeutiques

-1- Incidence / Prévalence /Survie

Approche clinique

4

Follicular Lymphoma International Prognostic Index(age, Aastage, Hb level, LDH, Nb nodal sites)

0 12 24 36 48 60 72 84 96 108 120

0.0

0.2

0.4

0.6

0.8

1.0

Time (months)

Sur

viva

l Pro

babi

lity

Low

Intermediate

High

No. of EventsLowIntermediateHigh

No. at RiskLowIntermediateHigh

- 12 25 29 46 60 83 95 106 113 125- 19 49 79 118 150 192 225 247 255 261- 54 109 152 202 229 245 260 268 274 278

641 629 616 612 595 581 450 337 241 157 93670 651 621 591 552 519 385 263 178 108 68484 430 375 332 282 255 193 139 98 56 33

Follicular lymphoma international prognostic index. Blood 2004; (104): 1258-1265.

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PSS

EORTC/GELA

GSHG

NCIC/ECOG

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Lymphome de Hodgkin’s

Stages N° Patients (%) EFS % (SE) D CVL HR (95% CI)

PSS EarlyIntermediateAdvanced

465 (48.7)329 (34.4)161 (16.9)

92.7 (1.2)80.2 (2.2)59.0 (3.9)

0.40 -1237 12.9** (1.9-4.5)7.2** (4.7-10.9)

EORTC/GELA EarlyIntermediateAdvanced

299 (31.3)356 (37.3)300 (31.4)

92.6 (1.5)86.8 (1.8)68.0 (2.7)

0.35 -1249 11.8* (1.1-3.1)5.1** (1.5-8.2)

GSHG EarlyIntermediateAdvanced

270 (28.3)318 (33.3)367 (38.4)

91.1 (1.7)89.0 (1.7)71.1 (2.4)

0.29 -1255 11.3 (0.7-2.1)3.7** (2.4-5.9)

NCIC/ECOG EarlyIntermediateAdvanced

205 (21.5)271 (28.4)479 (50.1)

93.7 (1.7)89.3 (1.9)74.3 (2.0)

0.29 -1257 11.7 (0.9-3.4)4.6** (2.5-8.2)

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1. Evaluer les propriétés prédictives des modèles

2. Estimer la part du pronostic attribuable

1. aux caractéristiques cliniques et biologiques classiques

2. aux caractéristiques transcriptomique ou protéomique des

tumeurs

Perspectives

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1. Estimation de l’incidence et de la survie du cancer en France.Cancer incidence and mortality in France over the period 1978-2000. Rev Epidemiol

Sante Publique 2003; (51): 3-30.

Evolution de l'incidence et de la mortalité par cancer en France de 1978 à 2000. INVS,

1-217. 2003. Ref Type: Serial (Book,Monograph)

2. Estimation of relative survival in cancer patients The FRANCIM

population based study

-1- Incidence / Prévalence /Survie

Approche épidémiologique

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Statistical methodsExcess rate model (1)

For each subject, mortality rate at time t has two components

)z,(),(),,( 1txztzxt expcobs

Z= vector of explanatory covariates

Potentially: sex, département, year of diagnosis, age at diagnosis…. Z1 = vector of the 3 covariates

defining expected mortality rates:

sex , département ,year of death

x = age at diagnosisCalculated for age at exit (=x+t)

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Excess Rate model (2)f(t) zztc )exp(),(

with f(t) beingconstant within intervals defined a priori

A smoothed parametric function

Exc

ess

rate

Exc

ess

rate

t0 1 2 3 4 5

0.0

0.0

50

.10

0.1

50

.20

0.2

50

.30

t0 1 2 3 4 5

0.0

0.0

50

.10

0.1

50

.20

0.2

50

.30

10 intervals

10 parameters

Cubic spline with 1 knot

5 parameters

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Estimating the model parameters Maximum Likelihood Estimation (MLE)

n

iiiiexpiic

n

iiiic zxtztlnztl

11

1

),(),(),(),(

If f(t) is a step function:The survival likelihood is equal to a Poisson likelihood, up to a constant.

Making feasible the estimation of ML in the framework of generalized linear models,

With any computer software where a weighted least squares is available

This was implemented in Splus (Iwls)

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If f(t) is a smoothed parametric function

n

iiiiexpiic

n

iiiic zxtztlnztl

11

1

),(),(),(),(

MLE is directly applicable: approximate c with a numerical

integration method (Simpson)

IWLS is not directly applicable:

an « appropriate » time ti for the calculation of the likelihood has to be choosen:

Time at exit if is 1 / Mid-point of the interval if is 0

13time since diagnosis

Exc

ess

Ra

te

0 2 4 6 8 10

0.0

0.1

0.2

0.3

0.4

0.5

0.0

0.1

0.2

0.3

0.4

0.5

Large interval

constant within intervalsIWLSML

time since diagnosis

Exc

ess

Ra

te

0 2 4 6 8 10

0.0

0.1

0.2

0.3

0.4

0.5

0.0

0.1

0.2

0.3

0.4

0.5

Short interval

constant within intervalsIWLSML

Quality of IWLS approximation (Kidney cancer)

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Estimating of relative survival at fixed times (1..3..5 years..)

)(),( tfztc With f(t) being a smoothed parametric

function

on the whole follow-up time (up to 10 years)

Selection of the « best » function (AIC) among:Polynomial up to cubic,

cubic spline with 1 or 2 knots.

Need for an « optimal » modeling of the excess rate

being able to deal with sparse data (stability of estimates)

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Estimating the proper effects of covariates

)() yod sex )(exp(),( dy tfdeptagegzt sc

Need for a multivariate use of the model

With an optimal modelling of the effect of covariates

Especially : age at diagnosis

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Example (1)Kidney cancer

Multivariate analysis

Effect of covariates sex and year of diagnosis : Covariate Log HR HR and 95%CI

P value

Sex* -0,11 0,90 [0,81 ; 1,00]

0,05

Year of diagnosis -0,02 0,98 [0,96 ; 1,00]

0,04

*reference : men

Effect of département and year of diagnosis Covariate Model likelihood gain p

Département Effect / no effect 10,0 0,01

Age Linear effect /no effect 75,6 <0,001

Non linear effect / linear effect 8,7 <0,001

17département

Ha

zard

Ra

tio

2 4 6 8

0.5

0.6

0.7

0.8

0.9

1.0

2.0

1 2 3 4 5 6 7 8 9

0.5

0.6

0.7

0.8

0.9

1.0

2.0

Effect of département: Hazard Ratio with 95% CI (/ mean rate)

age at diagnosis

Ha

zard

ra

tio

20 40 60 80 100

0.5

1.0

5.0

10

.0

Effect of age at diagnosis: Hazard Ratio (/ rate at mean age)

20

mean age: 65 years

0.5

1.0

5.0

10

.0

- relative survival: kidney cancer -

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Time varying age effect (Kidney cancer)

Large effect of age at early follow up

Small effect of age at late follow up