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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
0
.001
.01
.1
.2
.3
.4M
ort
alit
y ra
te
0 10 20 30 40 50 60 70 80 90 100
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
0.2
0.4
0.6
0.8
1.0
lx -
nu
mbe
r o
f su
rviv
ors
0 20 40 60 80 100age
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
0.2
0.4
0.6
0.8
1.0lx
- n
um
ber
of s
urvi
vors
0 20 40 60 80 100age
“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
-10
-8
-6
-4
-2
0
2
4
0 20 40 60 80 100diff
ere
nce
be
twe
en
est
ima
ted a
nd 't
rue
' life
exp
ect
an
cy
age
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
10
100
1,000
10,000
100,000
0 10 20 30 40 50 60 70 80 90 100
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
30
35
40
45
50
55
60
Rel
ativ
e su
rviv
al (
%)
Affluent 2 3 4 DeprivedDeprivation category
Rectal cancer survival, men, England and Wales
50
60
70
80
90
100
Rich 2 3 4 PoorSocio-economic category
Sur
viva
l (%
)expected
relative
observed
Affluent group: low background mortalityDeprivation life table, lower survival estimate
40
50
60
70
80
90
100
Rel
ativ
e su
rviv
al (
%)
0 1 2 3 4 5Years since diagnosis
National life table
Deprivation life table
Deprived group: high background mortality Deprivation life table, higher survival estimate
40
50
60
70
80
90
100
Rel
ativ
e su
rviv
al (
%)
0 1 2 3 4 5Years since diagnosis
Deprivation life table
National life table
‘Deprivation gap’ in relative survival:smaller with deprivation life tables
40
50
60
70
80
90
100
Re
lativ
e s
urvi
val (
%)
0 1 2 3 4 5Years since diagnosis
Affluent
Deprived
National life tableDeprivation-specific life table
05
1015
Abs
olu
te d
epr
ivat
ion
gap
(%
)
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 ?