Modelled prevalence. Marc COLONNA. January 22-23, 2014 Ispra

Transcription

1 STATE OF ART OF METHODS FOR THE ANALYSIS OF POPULATION-BASED CANCER DATA : Session 4 :PREVALENCE Modelled prevalence Marc COLONNA Isere Cancer Registry FRANCIM network (France) January 22-23, 2014 Ispra

2 DEFINITIONS OF PREVALENCE The prevalence of a particular cancer is defined as the number of persons who have been diagnosed with that cancer, and who are still alive at the endofagivenyear. Complete(total) prevalence represents the number of previously diagnosed persons alive at the end of a year regardless of how long ago the diagnosis was. Overall measure of cancer burden and survivorship Partial (limited duration) prevalence limits the number of patients to those diagnosedduringafixedtimeinthepast(e.g:1,3,5or10years). Measure of cancer burden at different steps of cancer therapy

3 THREE REASONS WHY THE USE OF MODELING IS NEEDED TO MEASURE PREVALENCE 1- Too short period of observation 2- Need of recent and future estimates of prevalence Prevalence at First year of cancer registration and follow up of cancers cases Last year of cancer registration and follow up of cancer cases Curent date beyond current date Unobserved data for prevalence Observed data for prevalence Projection period 3- Partial territory coverage by cancer registries (lack of national cancer registration)

4 MODELLED PREVALENCE 1- Model using mortality data and observed survival (MIAMOD) 2- Model using Incidence data and observed survival (PIAMOD) 3- Model using Incidence and mortality data

5 MODELLED COMPLETE AND PARTIAL PREVALENCE Mortality data and survival model (MIAMOD) Incidence data and survival model (PIAMOD) These models use transition rates equations relating Prevalence and Mortality to Incidence and Survival(Verdecchia, 1989) M(x) = x t= 0 (1 P(t)) I(t) S(t,x) d(t,x) (1) P(x) = x 1 t= 0 (1 P(t)) I(t) S(t,x) (2) P(t) : Prevalence at age t 1-P(t) : Probability to be free from cancer at age t I(t) : Probability of being diagnosed with cancer between t and t+1 S(t,x) : Relative survival probability up to age x for patient diagnosed at age t d(t,x) : Probability of dying from cancer at age x for patients diagnosed between age t and t+1 who survive until age x

6 MODELLED COMPLETE AND PARTIAL PREVALENCE Mortality data and survival model (MIAMOD) M(x) = P(x) = x t= 0 x 1 t=0= (1 P(t)) (1 P(t)) I(t) I(t) S(t,x) S(t,x) d(t,x) Miamod approach : Mortality and Survival Incidence and Prevalence Incidence: (1) (2) es x Estimated prevalence Polynomial or spline parametric model function of age, period and cohort Parameters are estimated by regressing mortality data Relative survival: Crude rate S Observed Estimated & incidence Estimated incidence S Observed & Estimated mortality Year tabulated (no modeling) extrapolation (backward) fixed at the most «recent» date Survival modelled with cure-models : more flexible Software: MIAMOD S(t, x) = P + (1-P) S D (t,x) S D -> relative survival for fatal cases Parametric Weibull model

7 MODELLED COMPLETE AND PARTIAL PREVALENCE Incidence data and survival model (PIAMOD) M(x) = P(x) = x t= 0 x 1 t= 0 (1 P(t)) I(t) S(t,x) d(t,x) (1) (1 P(t)) I(t) S(t,x) (2) Piamod approach : Incidence and survival Mortality and Prevalence s x Crude rates Estimated prevalence S S Observed & Estimated incidence Estimated mortality Year Incidencemodelled as a polynomial (or spline) function of age, year (period) and year of birth (cohort) cohort by regressing observed incidence data Relative survival: tabulated (no modeling) extrapolation (backward) fixed at the most «recent» date Survival modelled with cure-models : more flexible Software: PIAMOD S(t, x) = P + (1-P) S D (t,x) S D -> relative survival for fatal cases Parametric Weibull model

8 MODELLED COMPLETE AND PARTIAL PREVALENCE: PROJECTIONS Partial and complete prevalence using Miamod & Piamod How to extrapolate prevalence beyond last year of observations? 1) Incidence In MIAMOD, Incidence is projected beyond the last period of observation on the basis of the estimated age-period-cohort parameter, non-linear period effect being removed from Age- Period-Cohort model In PIAMOD, incidence is projected 1) Same scenario as above 2) Incidence remains constant at the same level as the most recent year(s) 2) Relative survival Relative survival is projected under 2 two scenarios (MIAMOD & PIAMOD approach) : 1) optimistic hypothesis : Survival will continue to change at the same rate as that observed during the whole period 2) conservative hypothesis : Survival remains constant as its current level until the end of the study period

9 MODELLED COMPLETE AND PARTIAL PREVALENCE ESTIMATIONS IN AREAS NOT COVERED BY OBSERVATIONS Areas covered by cancer registries National prevalence MIAMOD approach Observed national Mortality National Relative Survival: weighted age and time specific CR survival estimates weights = proportion of expected incidents cases in CRs areas PIAMOD approach National incidence = Crs areas specific incidence rates National Relative Survival = Crs areas Relative Survival Estimates

10 MODELLED COMPLETE PREVALENCE IN AREAS COVERED BY CRs : Incidence/Mortality/Prevalence approach This approach uses the relationship that exists between Incidence, Mortality and Prevalence under the hypothesis that the probability of death from causesotherthanthediseaseisthesameforsickandhealthypeople p(x,u) 1 p(x,u) = R(x,u) i Rd(x,u) 1 R(x,u) i p(x,u): Prevalenceforsubjectsagedxborninyearu(prevalenceatt=x+u) R i (x,u): Net risk of disease before age x (incidence cumulated between ages 0 and x for a generation born in year u) R d (x,u): Net risk of dying from the cancer (mortality cumulated between ages 0 and x for a generation born in year u

11 MODELLED COMPLETE PREVALENCE IN AREAS COVERED BY CRs : Incidence/Mortality/Prevalence approach p(x,u) 1 p(x,u) = R(x,u) i Rd(x,u) 1 R(x,u) i R R i d (x,u) = 1 exp( (x,u) = 1 exp( x 0 x 0 λ(y,u) dy) µ(y,u) dy) λ(t, x) : incidence rate at age for patients born in u µ(t, x): mortality rate at age for patients born in u y y These cumulated risks can be estimated from observed incidence and mortality using agecohort Poisson regression models that take into account the effects of age x and the birth cohort u (smoothing spline), with backward extrapolation and, if projections are done, forward extrapolation Software:classicalsoftwarecanbeused(e.g:S+,R)

12 MODELLED COMPLETE PREVALENCE IN AREAS NOT COVERED BY CRs : Incidence/Mortality/Prevalence approach Areas covered by cancer registries National prevalence The cumulated risks are obtained from estimated incidence and observed mortality using age-cohort Poisson regression models with backward extrapolation and, if projections are done, forward extrapolation National estimated incidence using Incidence / Mortality ratio λˆ National (x,u) = λˆ CRs (x,u) μˆ μˆ National CRs (x,u) (x,u) (λ:incidence ; μ:mortality) The underlying hypothesis is that the incidence/mortality ratio in the area covered by the cancer registries is representative of the National ratio Less restrictive as the hypothesis that incidence in area covered by CRs is the same as national incidence National estimations of incidence using I/M ratio have been validated using the ratio of incidence over hospital discharge(i/hd) or the ratio of incidence over health insurance data

13 Incidence/Mortality/Prevalence approach : Results This approach has been used toestimate prevalence of cancer in France at the end of the year 2008 with observed incidence and mortality data covering the period Complete prevalence (number of cases and proportion per ), France, 2008 among adults (age > 15) Sex and site Men Lip, oral cavity, pharynx Colon-rectum Prostate All cancers (Non melanoma skin excluded) Women Colon-rectum Breast All cancers (Non melanoma skin excluded)

14 Incidence/Mortality/Prevalence approach : Comments Comments: This approach is probably less adapted for cancer sites with possibility of multiple primaries: -Riskofcancer:possibilityofmultipleeventsforapatient -Riskofdyingfromthecancer:onlyonecancer(ifcanceristhecause) - Situation that may occur for complete prevalence - Situation that concerns particularly some cancers(lip-mouth-pharynx, oesophagus) This approach is not adapted for cancer sites where mortality is higher than incidence (e.g : liver;ovaryand lungoramongelderly). Prevalence estimation in areas not covered by CRs : I/M approach is not adapted to infranational incidence( prevalence) estimations

15 DISCUSSION : Modelled Whydoweneedprevalence? Cancer affects a high number of individuals and has social and economic consequences. It requires regular evaluation and anticipation of future needs, especially in terms of healthcare and surveillance. Whatcanbedoneusingmodelingapproach? Prevalence in areas covered by cancer registries - Partial prevalence observation/estimation: miamod, piamod - Complete prevalence: miamod, piamod, I/M: => hypothesis on backward extrapolation(survival, incidence, mortality) - Projection of partial and complete prevalence: miamod, piamod, I/M => hypothesis on backward and forward extrapolation(survival, incidence, mortality) Prevalence in areas not covered by cancer registries(national level) - Partial prevalence estimation: miamod,(estimated number of incident cases x crude survival) - Complete prevalence: miamod, I/M => Hypothesis 1) representativeness of CRs data 2) on backward extrapolation - Projection of partial prevalence(miamod) and complete prevalence(miamod, I/M) => Hypothesis 1) representativeness of CRs data 2) on backward and forward extrapolation Comment about projections Prevalence projections are very sensitive to incidence variations and, in a less extent, to survival variations: is long and middle term prevalence estimates easy to interpret?