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Cause-of-Death Mortality: What Can Be Learned From Population - - PowerPoint PPT Presentation

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Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? A Study of a Heterogeneous Portfolio Dynamic Hlose Labit Hardy PhD Student, University of Lausanne, Switzerland joint work with S. Arnold, A. Boumezoued and N. El

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Cause-of-Death Mortality: What Can Be Learned From Population Dynamics?

A Study of a Heterogeneous Portfolio Dynamic Héloïse Labit Hardy

PhD Student, University of Lausanne, Switzerland

joint work with S. Arnold, A. Boumezoued and N. El Karoui

Longevity 11 Conference, Lyon, France September 7, 2015

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 1/18

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SLIDE 2

Introduction

20 40 60 80 −10 −8 −6 −4 −2

French death rates for cancers in 2008

Age ln mu

Men Women

20 40 60 80 −10 −8 −6 −4 −2

French death rates for external causes in 2008

Age ln mu

Men Women

Source : The World Health Organization (WHO) Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 2/18

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SLIDE 3

Introduction

Death rates by socio-economic category in 2007 for males in England

−12 −10 −8 −6 −4 −2 Age log(mu)

25−29 30−34 35−39 40−44 45−49 50−54 55−59 60−64 65−69 70−74 75−79 80−84 85+

sec1 sec2 sec3 sec4 sec5

Figure : Cancers

−12 −10 −8 −6 −4 −2 Age log(mu)

25−29 30−34 35−39 40−44 45−49 50−54 55−59 60−64 65−69 70−74 75−79 80−84 85+

sec1 sec2 sec3 sec4 sec5

Figure : External causes

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 3/18

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SLIDE 4
  • 1. Population Dynamics Model
  • 2. Portfolio Dynamics Model
  • 1. Population Dynamics Model

1.1 Deterministic equation without population flows 1.2 Application : French data

  • 2. Portfolio Dynamics Model

2.1 Deterministic equation without arrivals 2.2 Application : English data

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 4/18

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SLIDE 5
  • 1. Population Dynamics Model
  • 2. Portfolio Dynamics Model

1.1 Deterministic equation without population flows 1.2 Application : French data

  • 1. Population Dynamics Model

1.1 Deterministic equation without population flows 1.2 Application : French data

  • 2. Portfolio Dynamics Model

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 5/18

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SLIDE 6
  • 1. Population Dynamics Model
  • 2. Portfolio Dynamics Model

1.1 Deterministic equation without population flows 1.2 Application : French data

Objective : Study impacts of changes in cause-of-death mortality on the whole population age structure ➤ Model population dynamics ⊲ By taking into account deaths and births : with birth and death rates depending on gender and age, invariant over time ⊲ Reference : Bensusan, Boumezoued, El Karoui and Loisel (working paper)

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 6/18

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SLIDE 7
  • 1. Population Dynamics Model
  • 2. Portfolio Dynamics Model

1.1 Deterministic equation without population flows 1.2 Application : French data

➤ The population structure described by the vector : g(a, t) = g(f , a, t) g(m, a, t)

  • ⊲ g(a, t) : average number of individual with age a at time t

➤ The population dynamics without population flows is defined by : ⊲ Deaths : ( ∂a + ∂t)g(a, t) = − µf (a) µm(a)

  • g(a, t)

⊲ Births : g(0, t) =

  • R+ g(f , a, t)bf (a) da

p 1 − p

  • µ depends on age a ; p : probability for a newborn to be a female

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 7/18

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SLIDE 8
  • 1. Population Dynamics Model
  • 2. Portfolio Dynamics Model

1.1 Deterministic equation without population flows 1.2 Application : French data

Population modelling

Age pyramid in 2008 Age pyramid in 2008

1000 500 500 1000 7 15 24 33 42 51 60 69 78 87 96 107 119 Number of males Number of females Age

Age pyramid in 2108 Age pyramid in 2108

1000 500 500 1000 7 15 24 33 42 51 60 69 78 87 96 107 119 Number of males Number of females Age

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 8/18

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Cause removal : Age Dependency Ratio from 2008 to 2108

20 40 60 80 100 25 30 35 40 45 50 Time (years) Dependency ratio (%) Cancers removal (e0h=82.2, e0f=87.7) External causes removal (e0h=79.1, e0f=85.1) All causes (e0h=77.7, e0f=84.4)

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 9/18

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Cause reduction : Age Dependency Ratio from 2008 to 2108

20 40 60 80 100 25 30 35 40 45 50 Time (years) Dependency ratio (%) Cancers removal (e0h=82.2, e0f=87.7) Reduction of cancers (e0h=79.1, e0f=85.1) External causes removal (e0h=79.1, e0f=85.1) All causes (e0h=77.7, e0f=84.4)

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 10/18

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SLIDE 11

Results

➤ With a population dynamics model, we study impacts of cause-of-death reductions on the population age structure : ⇒ Studying the whole population dynamics gives additional informations : ⊲ With the same life expectancy at birth, causes reductions can have different impacts on the age dependency ratio ⇒ Test the sensitivity to population flows and fertility : ⊲ Population flows modify the age dependency ratio : cause reductions have similar impacts

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 11/18

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SLIDE 12
  • 1. Population Dynamics Model
  • 2. Portfolio Dynamics Model

2.1 Deterministic equation without arrivals 2.2 Application : English data

  • 1. Population Dynamics Model
  • 2. Portfolio Dynamics Model

2.1 Deterministic equation without arrivals 2.2 Application : English data

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 12/18

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SLIDE 13
  • 1. Population Dynamics Model
  • 2. Portfolio Dynamics Model

2.1 Deterministic equation without arrivals 2.2 Application : English data

Objective : Study impacts of changes in cause-of-death mortality on insurance portfolio composed of cohorts with different socio-economic categories ➤ Model portfolio dynamics ⊲ By taking into account deaths and arrivals : with cause-of-death rates depending on age, time, gender and socio-economic categories

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 13/18

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SLIDE 14
  • 1. Population Dynamics Model
  • 2. Portfolio Dynamics Model

2.1 Deterministic equation without arrivals 2.2 Application : English data

➤ The portfolio is compounded by cohorts with k different socio-economic categories. The cohort structure is described by the vector : G(a, t) = G(a) =   g1(a) ... gk(a)   , ⊲ G(a, t) : average number of individual with age a at time t ➤ The cohort dynamics without arrivals is defined by deaths : dg(a) da = g

′(a) = −d(a)g(a)

➤ Cohort death rate : d(a) = −g

′(a)

g(a) = −

  • 1≤k≤5 g

′

k(a)

  • 1≤k≤5 gk(a); gk(a) = gk(a0)Sk(a0, a)

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 14/18

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SLIDE 15

Aggregate death rate for different compositions :

English females with age 50 in 1981

−8 −7 −6 −5 −4 −3 −2 −1 Age log(mu)

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 (20,20,20,20,20) (100,0,0,0,0) (0,0,0,0,100)

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 15/18

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SLIDE 16

Cause removal : relative difference of aggregate death rate

English females with age 50 in 1981

−60 −50 −40 −30 −20 −10 Age Relative difference (%)

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 sec: (100,0,0,0,0); cause (1,0,1,1,1,1,1) sec: (0,0,0,0,100); cause (1,0,1,1,1,1,1)

Figure : Cancers removal

−60 −50 −40 −30 −20 −10 Age Relative difference (%)

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 sec: (100,0,0,0,0); cause (1,1,0,1,1,1,1) sec: (0,0,0,0,100); cause (1,1,0,1,1,1,1)

Figure : Circulatory diseases removal

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 16/18

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First results

➤ With a population dynamics model, we study impacts of cause-of-death reductions on a portfolio mortality composed by different socio-economic category : ⇒ Following the portfolio structure, causes reductions can have different impacts on the aggregate mortality ➤ Following ⊲ Portfolio dynamics with arrivals ⊲ Portfolio dynamics with arrivals and seniority ⊲ Study aggregate mortality of a population composed with different socio-economic categories

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 17/18

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Bibliographie

[1] Alai, D.H., Arnold(-Gaille), S., Sherris, M. (2015) Modelling Cause-of-Death Mortality and the Impact of Cause-Elimination. Annals of Actuarial Science [2] Arnold, S., Boumezoued, A., Labit Hardy, H., El Karoui., N. (2015) Cause-of-Death Mortality : What Can Be Learned From Population Dynamics ? Working paper, https ://hal.archives-ouvertes.fr/hal-01157900 [3] Bensusan, H. (2010) Risques de taux et de longévité : Modélisation dynamique et applications aux produits dérivés et á l’assurance vie. PhD thesis, Ecole Polytechnique [4] Chiang, C. L. (1968) Introduction to Stochastic Process in Biostatistics. John Wiley and Sons, New York [5] Bensusan, H., A. Boumezoued, N. El Karoui, S. Loisel. Impact of heterogeneity in human population dynamics. working paper [6] Tran, V.C. (2006) Modéles particulaires stochastiques pour des problémes d’évolution adaptative et pour l’approximation de solutions statistiques. PhD thesis, Université Paris X - Nanterre

Héloïse Labit Hardy Cause-of-Death Mortality: What Can Be Learned From Population Dynamics? 18/18