actuarial projections for mesothelioma: an epidemiological … clements.pdf · 2010-05-18 ·...
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Actuarial projections for mesothelioma:
an epidemiological perspective
Mark Clements, Geoffrey Berry
and Jill Shi
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Who are we?• I am an epidemiologist/biostatistician from
the Australian National University (ANU)• Geoffrey is an epidemiologist/biostatistician
from the University of Sydney• Jill is a trainee actuary from Mercer HR
Consulting (actuarial honours from ANU)
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Outline• Background• Theoretical model• Model comparisons• Discussion
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Background• Compensation for asbestos-related diseases
continues to be an important issue for government and industry (Huszczo et al 2004)
• Focus on mesothelioma:– Cancer of the pleura and the peritoneum
caused by asbestos exposure – Very important marker of exposure
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Background: Challenges• Poor measures of asbestos exposure• Complexity in the epidemiological
relationship between asbestos exposure and disease onset
• Uncertainty in the propensity to claim• Uncertainty in future costs
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Background: Aim• Prediction of population-level mesothelioma
incidence– Applicable to portfolios that follow
population-wide asbestos exposure– We are not:
• Predicting claims• Predicting costs
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Background: Mesothelioma epidemiology
1. Incidence proportional to linear dose of asbestos exposure
2. Incidence depends on time from exposure 3. Incidence rises by a power of time from exposure 4. Evidence for asbestos clearance from the lungs5. Several years between initial malignancy and
diagnosis6. Survival is poor and death is rapid.
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Theoretical model: Notation for time, where (a,t) = (age, calendar year)
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u
(0,t-a) (a,t)(a-u,t-u)
Asbestos exposureBirth Current time
u: time since asbestos exposure
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Theoretical model: Individuals• For an individual i exposed to asbestos at time t-u,
the rate function is:
where
for constant β, lag τ, power k and lung clearance rate λ (Armitage-Doll model with clearance).
)(),(),,( ugutuadoseutarate ii −−=
)()()( τλτβ −−−= uk euug
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Theoretical model: Populations• The population rate is modelled by
integrating (summing) across dose and times u since exposure:
∫ −−=a
duugutuadosetarate0
)(),(),(
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Theoretical model: Simplification• Hodgson et al (2005):
– Dose is proportional to an age effect W() and a period effect D()
• That is (Equation 1):
∫ −−=a
duugutDuaWtarate0
)()()(),(
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Theoretical model: Cases
• The total numbers of cases for a year is:
• The number of cases is Poisson-distributed
∫∞
×=0
),(),()( dataPoptaratetcases
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Model comparisons: Data sources
• Mesothelioma incidence for males– Australia for 1983-2001– New South Wales for 1972-2004
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Model comparisons: Outline
Model Model descriptionAndrews and Atkins (1993)
cases(t) from Berry (1991)
Peto et al (1995) Age-cohort model (sub- model of Equation 1)
KPMG Exposure model with delay distribution (sub-model of Equation 1)
Clements et al (2007) Equation 114 slides to go
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Mesothelioma incidence, calibrated Andrews and Atkins (1993), Australian males
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1980 2000 2020 2040 2060
010
030
050
070
0
Year
Num
ber
Observed (prior to publication)Observed (after publication)Andrews and Atkins "high"Andrews and Atkins "low"
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Mesothelioma incidence, age-cohort model, Australian males
1980 2000 2020 2040 2060
020
040
060
080
010
00
Year
Num
ber
ObservedPredicted+95% CI
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KPMG (2006)• Model as used to predict mesothelioma
claims for former James Hardie entities• Cases modelled by exposure data D() and a
delay distribution f() (Normal(μ=35, σ2=102)):
• D() based on consumption data:∫∞
−=0
)()()( duufutDtcases
∫ −=16
0
)(16
)( duutnConsumptiotD β
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Mesothelioma incidence, calibrated KPMG, Australian males
1980 2000 2020 2040 2060
010
030
050
070
0
Year
Num
ber
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Re-implementation of KPMG model• Re-fit the model, estimating the intercept and
the mean/SD for the delay distribution• Maximum likelihood estimates:
– Mean delay = 39.0 (se=5.0)– SD for delay = 10.4 (se=4.5)
• Interval estimation using the bootstrap– Assumes SD fixed as estimated
(otherwise: uninformative)9 slides to go
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Mesothelioma incidence, KPMG re- implementation, Australian males
1980 2000 2020 2040 2060
010
030
050
070
0
Year
Num
ber
ObservedPredicted+95% CI
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Clements et al (2007)• Hodgson et al (2005) modelled Equation 1
for the United Kingdom• We re-implemented their model for NSW
– Natural splines for the dose functions– Fitted for five parameters using maximum
likelihood estimation– Interval estimation using the bootstrap
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Mesothelioma incidence, Clements et al (2007), New South Wales males
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1980 2000 2020 2040 2060
050
100
150
200
250
Year
Num
ber
ObservedPredicted+ 95% CI
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Mesothelioma incidence, Clements et al (2007) model, Australian males
1980 2000 2020 2040 2060
020
040
060
080
0
Year
Num
ber
ObservedPredicted+95% CI
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Model comparison: Summary
Australian malesNew South Wales
males
Model PeakTotal count 2006-2060 Peak
Total count 2006-2060
Andrews and Atkins “high” 2001 2905 2001 1040
Age-cohort model 2028 39850 2029 14855
KPMG (2006) 2010 10970 2010 3530
KPMG re-implementation 2014 15045 2013 4880
Clements et al (2007) 2017 21700 2014 6430
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Model comparison: Summary
Australian malesNew South Wales
males
Model PeakTotal count 2006-2060 Peak
Total count 2006-2060
Andrews and Atkins “high” 2001 2905 2001 1040
Age-cohort model 2028 39850 2029 14855
KPMG (2006) 2010 10970 2010 3530
KPMG re-implementation 2014 15045 2013 4880
Clements et al (2007) 2017 21700 2014 6430
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95% confidence
interval: 16460, 30165
95% confidence
interval: 4920, 9060
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Discussion: Summary• Support for KPMG (2006), the KPMG re-
implementation and Clements et al (2007)– Theoretically, these models are closely
related• Reasonable evidence that the peak for
mesothelioma is after 2010– Total number of cases for 2006-2060 may
be in excess of 35% higher than numbers predicted by KPMG
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Specific recommendations• Consider using the KPMG models or the
model from Clements et al (2007)• Investigate methods used by Stallard et al
(2005) in the Manville Asbestos Case (also related to Equation 1) for large portfolios
• Investigate using direct estimates of asbestos exposure by occupation
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General recommendations• Fit models to observed data rather than
simply calibrate• Fully represent statistical uncertainty in
model predictions• The epidemiological literature is potentially a
very useful resource to actuaries
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References• Andrews T, Atkins G. Asbestos-Related Diseases – The Insurance Cost – Part
2. Institute of Actuaries of Australia Biennial Convention. 1993.• Berry G. Prediction of mesothelioma, lung cancer, and asbestosis in former
Wittenoom asbestos workers. British Journal of Industrial Medicine 1991;48:793-802.
• Clements MS, Berry G, Shi J, Ware S, Yates D, Johnson A. Projected mesothelioma incidence in men in New South Wales. Occupational and Environmental Medicine 2007 (in press).
• Hodgson JT, McElvenny DM, Darnton AJ, Price MJ, Peto J. The expected burden of mesothelioma mortality in Great Britain from 2002 to 2050. British Journal of Cancer 2005;92:587-93.
• Huszczo A, Martin P, Parameswaran S, Price C, Smith A, Walker D, Watson B, Whitehead G. IAAust Asbestos Working Group Discussion Paper. Institute of Actuaries of Australia Accident Compensation Seminar. 2004.
• Peto J, Hodgson JT, Matthews FE, Jones JR. Continuing increase in mesothelioma mortality in Britain. Lancet 1995;345:535-9.
• Stallard E, Manton KG, Cohen JE. Forecasting Product Liability Claims: Epidemiology and modeling in the Manville asbestos case. Springer Science+Business Media, Inc., New York. 2005.
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Additional slides
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Asbestos products available for consumption and a lagged exposure distribution, Australia
1900 1920 1940 1960 1980 2000
020
4060
80
Year
Met
ric to
nnes
(milli
on)
Products available for consumptionLagged exposure distribution
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Estimated dose function by age, Clements et al (2007), NSW males
0 10 20 30 40 50 60 70
0.0
1.0
2.0
3.0
Age (years)
W(a
ge)
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Estimated dose function by calendar period, Clements et al (2007), NSW males
1920 1940 1960 1980 2000
0.0
0.4
0.8
1.2
Year
D(y
ear)
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Number of cases, by age at cancer, Clements et al (2007), NSW males
1980 2000 2020 2040 2060
050
100
150
200
Year
Cum
ulat
ive
num
ber
85+80-8475-7970-7465-6960-6455-5950-5445-4940-44
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Number of cases, by period of exposure, Clements et al (2007), NSW males
1980 2000 2020 2040 2060
050
100
150
Year
Cum
ulat
ive
num
ber
1985-19891980-19841975-19791970-19741965-19691960-19641955-19591950-1954