cristian redondo loures, andrew j. g. cairns · cristian redondo loures, andrew j. g. cairns cause...

,

Cause of death specific cohort effects in USmortality

Cristian Redondo Loures, Andrew J. G. Cairns

Heriot-Watt University, Edinburgh

Longevity 15, Washington, September 2019

Cristian Redondo Loures, Andrew J. G. Cairns Cause of death specific cohort effects in US mortality

,

Outline

• Introduction

• Data availability

• A look at crude death rates

• Stochastic modelling

• Conclusions


,

Introduction

Gain insight into the impact of socioeconomicstatus on mortality to inform projections.

Analyse which causes of death affect differentgroups within a population.

Try to understand the drivers of the observedbehaviour through the analysis of cohort effects.

US mortality by single ages and calendar years,independently for each gender, CoD, and educationlevel.


,

Introduction

Education as a covariate in death rates

Education ⇒ Socioeconomic status.

“Fixed” through adulthood.

Data readily available (quality to be assesedthough!).

Case and Deaton (2015) found interesting trends incause of death mortality in the US by educationlevel.


,

Data availability

Data combines the Centers for Disease Control andPrevention public database (number of deaths) andHuman Mortality Database/Current PopulationSurvey mid-year population estimates.

Calendar years 1989-2015

Years of birth 1914-1970

2 genders

2 education levels

13 groups of causes of death (more possibletoo!)


,

Data availability

List of causes of death:

1- Lung and bronchus cancer

2- Lifestyle cancers

3- Prostate or breast cancer

4- Other cancers

5- Chronic lower respiratorydisease

6- Diabetes

7- Heart disease

8- Cerebrovascular disease

9- Other circulatory disease

10- Dementia and othermental illness

11- Accidental

12- Suicide, poisoning, andcirrhosis

13- All other


,

A look at crude death rates

ALL CAUSE MORTALITY


,

A look at crude death rates

40 50 60 70 80 905e−

045e

−03

5e−

02Year 2010, males

Age

Dea

th r

ate

(log

scal

e)

LowHigh

40 50 60 70 80 905e−

045e

−03

5e−

02

Year 2010, females

Age

Dea

th r

ate

(log

scal

e)

LowHigh

Initial/final gap males: 2.86 → 1.20Initial/final gap females: 2.62 → 1.12


,

Death rates by education, age 60 by year

1990 2000 2010

0.00

50.

010

0.02

0Age 60, males

All cause mortality

Year

Dea

th r

ate

(log

scal

e)

ROI for low: 0.28%

ROI for high: 1.67%

LowHigh

1990 2000 2010

0.00

50.

010

0.02

0

Age 60, femalesAll cause mortality

Year

Dea

th r

ate

(log

scal

e)

ROI for low: 0.08%

ROI for high: 1.09%

LowHigh

Initial/final gap males: 1.75 → 2.54Initial/final gap females: 1.63 → 2.13


,

CAUSE OF DEATH MORTALITY


,


1990 2000 20101e−

041e

−03

1e−

02Age 60, males

Prostate cancer

Year

Dea

th r

ate

(log

scal

e) LowHigh

1990 2000 20101e−

041e

−03

1e−

02

Age 60, malesLung cancer etc

Year

Dea

th r

ate

(log

scal

e) LowHigh

Initial→final ratio for prostate cancer: 1.24 → 1.76Initial→final ratio for lung cancer: 2.21 → 3.49


,


1990 2000 20101e−

041e

−03

1e−

02Age 60, femalesBreast cancer

Year

Dea

th r

ate

(log

scal

e) LowHigh

1990 2000 20101e−

041e

−03

1e−

02

Age 60, femalesLung cancer etc

Year

Dea

th r

ate

(log

scal

e) LowHigh

Initial→final ratio for breast cancer: 1.05 → 1.14Initial→final ratio for lung cancer: 1.63 → 2.84


,

Modelling

STOCHASTIC MODELLING


,

Modelling

We will fit a stochastic model for the mortality ratesindependently to each gender, education group, andgroup of causes of death, for ages 50-75 and years1989-2015.

Our goal is to identify distinct trends in the cohorteffects for different causes of death that point atboth the drivers behind mortality for each cause andthe changing behaviours of the population analysed.


,

Modelling

Model for the mortality rates m(x , t):

D(x , t) ∼ Poisson(m(x , t)E (x , t)),

where

log(m(x , t)) = αx + κ(1)t + (x̄ − x)κ

(2)t + γt−x

Plat model restricted to high ages.

γt−x ≡ γc cohort effect. From a formal standpoint:mortality is a function of year of birth.


,

Modelling

How do cohort effects arise in practice?

Non-homogeneities that are strongly linked to whena person was born, and not to the period they livein. Examples:

- Smoking

- Type of work (blue collar, white collar)

- Diet (home cooked/processed food)

Typically, health behaviours fall into this category.


,

Modelling

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Ratio

1990 1995 2000 2005 2010 2015

45

50

55

60

65

70

Males, Lung Cancer Death RatesRatio of Low Education to High Education

Year

Age


,

Modelling

Identifiability constraints for the Plat model:

∑t

κ(1)t = 0,

∑t

κ(2)t = 0,

∑c

γc = 0,∑c

cγc = 0,∑c

c2γc = 0.

All time series parameters will average to zero, andthe cohort effectc will have no linear or quadratictrends!


,

Modelling

Two approaches:

Estimate the α’s, κ’s, and γ’s from maximumlikelihood, bootstrap to obtain CIs.

Assume time series structure for γc , κ(1)t , and

κ(2)t , and use Bayesian techniques.

For the second approach we assume:

γc is an AR(2) process,

κt =

(κ(1)t

κ(2)t

)is a RW with drift µ.


,

Bayesian approach

Priors for the AR(2) parameters:

σ2c∼ Inv -Gamma(a, b)

logit(ρ) ∼ N (0, σ2ρ)

logit(τ) ∼ N (0, σ2τ )

Priors for the random walk:

Σ ∼ Inv -Wishart(ν,S)

µ1 ∼ N (0, σ2µ1)

µ2 ∼ N (0, σ2µ2)


,

Bayesian approach

The final contributions to the log posterior are:

log(P(αx , κ

(1)t , κ

(2)t , γc , σc , ρ, τ,Σ, µ1, µ2|D,E )

)∝

`P + `arγ + `rwκ+

log(π(σc)) + log(π(τ)) + log(π(ρ))+

log(π(Σ)) + log(π(µ1)) + log(π(µ2))

Not known analytical solutions. MCMC methodsrequired.


,

Cohort effects

1920 1940 1960

−0.

100.

000.

050.

10

High educated malesLung cancer

Year of birth

γ c

BayesianBootstrap ML

1920 1940 1960−

0.10

0.00

0.05

0.10

High educated malesChronic lower respiratory disease

Year of birth

γ c



,

Cohort effects

1920 1940 1960

−0.

100.

000.

050.

10

Low educated femalesLung cancer

Year of birth

γ c


1920 1940 1960−

0.10

0.00

0.05

0.10

Low educated femalesChronic lower respiratory disease

Year of birth

γ c



,

Cohort effects

1920 1940 1960

−0.

100.

000.

050.

10

Low educated malesLung cancer

Year of birth

γ c


1920 1940 1960−

0.10

0.00

0.05

0.10

Low educated malesDiabetes

Year of birth

γ c



,

Cohort effects

1920 1930 1940 1950 1960

−0.

100.

000.

050.

10

Cohort effects with 60%, 75%, and 90% CIsLow educated males, heart disease

Year of birth

γ c


,

Cohort effects

1920 1930 1940 1950 1960

−0.

100.

000.

050.

10

Cohort effects for different causes of deathLow educated males, heart disease

Year of birth

γ c

Heart diseaseDiabetes

Lung cancerLinear comb


,

Cohort effects

1920 1930 1940 1950 1960

−0.

100.

000.

050.

10

Cohort effects for different causes of deathHigh educated males, heart disease

Year of birth

γ c




,

Cohort effects

1920 1930 1940 1950 1960

−0.

100.

000.

050.

10

Cohort effects for different causes of deathLow educated females, heart disease

Year of birth

γ c




,

Cohort effects

1920 1930 1940 1950 1960

−0.

100.

000.

050.

10

Cohort effects for different causes of deathHigh educated females, heart disease

Year of birth

γ c




,

Conclusions

→ Modelling cause of death data provides insightinto the reasons behind the evolution of all causemortality.

→ The shape of the cohort effects for differentcauses of death is linked to different underlyingrisk factors.

→ Different groups show different cohort effectpatterns, reflecting different health behaviours.

→ Complex interactions between lifestyle factorsare behind inequalities in death rates in the US.


,

Future work

There are several parts of this work that can beextended in the future:

Systematise the cohort effect analysis.

Mortality projections.

Applications to annuities and life insurance.

Extension of the analysis to other populations.


,

Thank You!

Questions?


,

Poisson log-likelihood (both approaches):

`P ∝∑x ,t

[−Ext exp(αx +κ

(1)t + (x̄− x)κ

(2)t +γc)+

Dxt(αx + κ(1)t + (x̄ − x)κ

(2)t + γc)

]Parameters easily estimated using R (StMoMolibrary). Bootstrapping techniques help obtainconfidence intervals.


,

Random walk log-likelihood for γc :

`rwγ ∝ −1

2σ2c

nc∑c=3

(γc − (ρ + τ)γc−1 + ρτγc−2)2

− nc − 2

2log(σ2c

)− 1

2log(σac)− 1

2σacγ22 ,

where we have used the autocovariance

σac =1 + ρτ

1− ρτσ2c

(1 + ρτ)2 − (ρ + τ)2.


,

Random walk log-likelihood for κt :

`rwκ ∝ −1

2

nt∑t=2

[(κd)TΣ−1κd

]− nt − 1

2log (|Σ|) ,

with

κd =

(κ(1)t − (κ

(1)t−1 + µ1)

κ(2)t − (κ

(2)t−1 + µ2)

)


,

Priors:

σc ∼ Inv -Gamma(10, 5 · 10−4),

Σ ∼ Inv -Wishart

(10,

(10−4 0

0 10−4

)),

µ1 ∼ N (0, 12),

µ2 ∼ N (0, 12),

logit(ρ) ∼ N (0, 0.52),

logit(τ ) ∼ N (0, 0.52).


,

50 55 60 65 70 75

−6.

0−

5.5

−5.

0−

4.5

Parameters with 60%, 75%, and 90% CIsLow educated males, heart disease

Year of birth

α x


50 55 60 65 70 75

−7.

0−

6.5

−6.

0−

5.5

Parameters with 60%, 75%, and 90% CIsLow educated males, lung cancer

Year of birthα x



,

1990 2000 2010

−0.

20.

00.

10.

20.

3


Year of birth

κ t(1)


1990 2000 2010

−0.

005

0.00

00.

005


Year of birthκ t(2

)



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1920 1940 1960

−3

−2

−1

01

23

Birth

Sta

ndar

dise

d re

sidu

als

Residuals for lung cancer, low educated males


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1990 2000 2010

−3

−2

−1

01

23

Year

Sta

ndar

dise

d re

sidu

als

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50 55 60 65 70 75

−3

−2

−1

01

23

Age

Sta

ndar

dise

d re

sidu

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1920 1940 1960

−3

−2

−1

01

23

Birth

Sta

ndar

dise

d re

sidu

als

Residuals for diabetes, low educated males


,

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1990 2000 2010

−3

−2

−1

01

23

Year

Sta

ndar

dise

d re

sidu

als

●

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23

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ndar

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1920 1940 1960

−3

−2

−1

01

23

Birth

Sta

ndar

dise

d re

sidu

als

Residuals for heart disease, low educated males


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1990 2000 2010

−3

−2

−1

01

23

Year

Sta

ndar

dise

d re

sidu

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01

23

Age

Sta

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d re

sidu

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1920 1940 1960

−3

−2

−1

01

23

Birth

Sta

ndar

dise

d re

sidu

als

Residuals for all cause, low educated males


,

1920 1940 1960

−0.

100.

000.

050.

10

Low educated malesLifestyle cancers

Year of birth

γ c


1920 1940 1960

−0.

100.

000.

050.

10

Low educated malesProstate and breast cancer

Year of birthγ c



,

1920 1940 1960

−0.

100.

000.

050.

10

Low educated malesOther cancer

Year of birth

γ c


1920 1940 1960

−0.

100.

000.

050.

10

Low educated malesCerebrovascular disease

Year of birthγ c



,

1920 1940 1960

−0.

100.

000.

050.

10

Low educated malesOther circulatory disease

Year of birth

γ c


1920 1940 1960

−0.

100.

000.

050.

10

Low educated malesDementia and other mental illness

Year of birthγ c



,

1920 1940 1960

−0.

100.

000.

050.

10

Low educated malesAccidental death

Year of birth

γ c


1920 1940 1960

−0.

100.

000.

050.

10

Low educated malesSuicide, poisoning, and cirrhosis

Year of birthγ c



,

1920 1940 1960

−0.

100.

000.

050.

10

Low educated malesOther causes of death

Year of birth

γ c


1920 1940 1960

−0.

100.

000.

050.

10

Low educated malesAll cause mortality

Year of birthγ c



cristian redondo loures, andrew j. g. cairns · cristian redondo loures, andrew j. g. cairns cause...

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