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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alit

y ra

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Age (years)

true ratesobserved ratessmoothed rates

Methods of smoothing life tables

• Model life tables– Brass (Ewbank) – Kostaki

• Smoothing formulae / interpolation– Elandt-Johnson– Akima

• Flexible multivariable models– Splines

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

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 abridged

up to 80 or 100 years of age

Estimate complete smoothed life tables using three methods

• 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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lx -

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rviv

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Results 1/4

“Truth”

Flexible Poisson

Regression

Elandt-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

From observed abridged up to 80 years, national, men, 1% sample

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“Truth”

Flexible Poisson

Regression

Elandt-Johnson

Results 2/4

Less variability with the quality of data

From a 20% sample

National Life Tables   Best available data (C100 or AB95)

Least Sum of Squares   Flexible Poisson Elandt-Johnson Regression

All age LSS

min 0 0 0

mean 0.0000769 0.0036792 0.0017946

max 0.0009848 0.0696748 0.0129517

From a 1% sample

National Life Tables   Worst available data (AB80)

Least Sum of Squares   Flexible Poisson Elandt-Johnson Regression

All age LSS

min 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

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

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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100

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10,000

100,000

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Age at death (years)

Rate per 100,000

Most deprived

Least deprived

Background mortality by deprivationmales, England and Wales, 1990-92

Woods LM et al., J Epidemiol Comm Hlth 2005; 59: 115-20

Life expectancy: deprivation, sex, region

1996-99

1991-95

1986-90

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Rel

ativ

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rviv

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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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viva

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)expected

relative

observed

Affluent group: low background mortalityDeprivation life table, lower survival estimate

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Rel

ativ

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rviv

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National life table

Deprivation life table

Deprived group: high background mortality Deprivation life table, higher survival estimate

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Rel

ativ

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rviv

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0 1 2 3 4 5Years since diagnosis

Deprivation life table

National life table

‘Deprivation gap’ in relative survival:smaller with deprivation life tables

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Re

lativ

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urvi

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%)

0 1 2 3 4 5Years since diagnosis

Affluent

Deprived

National life tableDeprivation-specific life table

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Abs

olu

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epr

ivat

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gap

(%

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0 1 2 3 4 5 6 7 8 9 10Follow-up time (years)

National life table

Region- and deprivation-specific life table

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

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 ?

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 ?