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Improved life tables: by geography, socio-economic status…. Bernard Rachet and Michel Coleman. smoothed rates. 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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Improved life tables: by geography, socio-economic status… Bernard Rachet and Michel Coleman Methods and applications for population-based survival 20-21 September 2010
Methods of smoothing life tables • Model life tables • Brass (Ewbank) • Kostaki • Smoothing formulae / interpolation • Elandt-Johnson • Akima • Flexible multivariable models • Splines
Baseline mortality function Non-proportional effects Effect of deprivation on the baseline mortality function Poisson regression Model effects of covariates on observed mortality rates (nmx obs)
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 datasets complete or abridged up to 80 or 100 years of age • Estimate complete smoothed life tables using three methods
Models • Univariable • Elandt-Johnson • Multivariable • Flexible regression of the logit of lx on a standard life table • Flexible Poisson Model Both using spline functions
“Truth” Flexible Poisson Regression Elandt-Johnson Results 1/4 • Using the flexible Poisson model we observe • Less variability in the results From observed abridged up to 80 years, group 5, men, 1% sample
“Truth” Flexible Poisson Regression Elandt-Johnson From observed abridged up to 80 years, national, men, 1% sample
Results 2/4 • Less variability with the quality of data
Flexible Poisson Regression Elandt-Johnson Results 3/4 Elandt-Johnson Regression Poisson • Better estimation of life expectancy From abridged up to 80 years, group 3, men, 1% sample
Results 4/4 • Better estimation of relative survival
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
Background mortality by deprivationmales, England and Wales, 1990-92 Rate per 100,000 100,000 10,000 1,000 Most deprived 100 Least deprived 10 0 10 20 30 40 50 60 70 80 90 100 Age at death (years)
Life expectancy: deprivation, sex, region Woods LM et al., J Epidemiol Comm Hlth 2005; 59: 115-20
Rectal cancer survival, men, England and Wales 60 55 50 Relative survival (%) 45 1996-99 40 1991-95 35 1986-90 30 2 3 4 Deprived Affluent Deprivation category
100 expected 90 80 Survival (%) relative 70 60 observed 50 Rich 2 3 4 Poor Socio-economic category
Affluent group: lowbackground mortalityDeprivation life table,lower survival estimate National life table Deprivation life table
Deprived group: high background mortality Deprivation life table, higher survival estimate Deprivation life table National life table
‘Deprivation gap’ in relative survival:smaller with deprivation life tables National life table Deprivation-specific life table Affluent Deprived
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 ?