Improved life tables: by geography, socio-economic status…
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Improved life tables: by geography, socio-economic status…
Bernard Rachet and Michel Coleman
Methods and applications for population-based survival 20-21 September 2010
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Age (years)
true ratesobserved ratessmoothed rates
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Methods of smoothing life tables• Model life tables
– Brass (Ewbank) – Kostaki
• Smoothing formulae / interpolation– Elandt-Johnson– Akima
• Flexible multivariable models– Splines
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Poisson regression
ndeprivatioagerateLn gf
Baseline mortality function
Effect of deprivation on the baseline mortality function
Model effects of covariates on observed mortality rates (nmx obs)
ationage.deprivh
Non-proportional effects
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Objective and methods• Goal: generating complete, smoothed, variable-specific and
national life tables from sparse data
• Method: Start from a “true” complete life table (England & Wales)
Draw 100 samples (20%, 10%, 1%)
Generate different datasetscomplete or abridgedup to 80 or 100 years of age
Estimate complete smoothed life tables using three methods
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• Univariable• Elandt-Johnson
• Multivariable• Flexible regression of the logit of lx on a standard life table
• Flexible Poisson Model
Both using spline functions
Models
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Results 1/4
“Truth”Flexible PoissonRegressionElandt-Johnson
From observed abridged up to 80 years, group 5, men, 1% sample
• Using the flexible Poisson model we observe Less variability in the results
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From observed abridged up to 80 years, national, men, 1% sample
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“Truth”Flexible PoissonRegressionElandt-Johnson
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Results 2/4 Less variability with the quality of data
From a 20% sampleNational Life Tables Best available data (C100 or AB95)
Least Sum of Squares Flexible Poisson Elandt-Johnson Regression
All age LSSmin 0 0 0
mean 0.0000769 0.0036792 0.0017946
max 0.0009848 0.0696748 0.0129517
From a 1% sampleNational Life Tables Worst available data (AB80)
Least Sum of Squares Flexible Poisson Elandt-Johnson Regression
All age LSSmin 0 0 0
mean 0.0018073 0.0176438 0.1302963
max 0.0478559 3.274633 2.206511
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Results 3/4 Better estimation of life expectancy
From abridged up to 80 years, group 3, men, 1% sample
RegressionFlexible PoissonRegressionElandt-Johnson
Poisson Elandt-Johnson
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Results 4/4
Better estimation of relative survival
From a 1% sample
National Life Tables Best available data (C100 or AB95)
Difference in Relative Survival Flexible Poisson Elandt-Johnson Regression
BREAST 10 year relative survival
min 0.002049 0.0073967 0.012661
mean 0.1881 0.9404236 0.287412
max 0.727291 3.49868 0.735535
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Life tables and cancer survival
Background mortality hazard (age, sex) Reduce bias in survival comparisons How finely to specify life tables by
covariables: Period or year of death Country or region Socio-economic status Race and/or ethnicity
May require large number of life tables
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0 10 20 30 40 50 60 70 80 90 100Age at death (years)
Rate per 100,000
Most deprived
Least deprived
Background mortality by deprivationmales, England and Wales, 1990-92
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Woods LM et al., J Epidemiol Comm Hlth 2005; 59: 115-20
Life expectancy: deprivation, sex, region
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1996-99
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Affluent 2 3 4 DeprivedDeprivation category
Rectal cancer survival, men, England and Wales
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Rich 2 3 4 PoorSocio-economic category
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relative
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Affluent group: low background mortalityDeprivation life table, lower survival estimate
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National life table
Deprivation life table
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Deprived group: high background mortality Deprivation life table, higher survival estimate
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Deprivation life table
National life table
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‘Deprivation gap’ in relative survival:smaller with deprivation life tables
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National life table
Region- and deprivation-specific life table
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Life tables – “adjust” for exposure?
Underlies cancer and competing hazard of death Carcinogenic exposure High population attributable risk fraction
Tobacco, alcohol Substantial hazard of non-cancer death May complicate treatment and thus survival
Co-morbidity
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Life tables – how to “adjust”? Information on exposure at death certification
Available, complete, accurately recorded ? Reliability of data from proxy of deceased ? Crudity of exposure variable (binary) ? Time-lag between exposure and death (relevance)? Length of mortality data time series ?
Equivalent information on all cancer patients? If not, assume that all patients were exposed ? What threshold of hazard to decide when to adjust ?
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Implications for principle of relative survival?
Co-morbidity affects non-cancer hazard Standardised approach to life table
adjustment ? Relative survival adjusted for risk factors:
Interpretable ? Comparable between cancers ? Comparable between populations ? Comparable over time ? Intelligible ?