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Does it matter what estimation method I use to provide
small area populations at risk in standardised mortality
ratios?
CCSR Seminar: 16th December 2003
Paul Norman
Context• Rates of health may need to be calculated for small geographical areas
• Census years we have age-sex population counts for a range of geographical areas, but outside census years …
• Annual age-sex disaggregated mid-year estimates only available down to local authority level
• Various small area population estimation methods commonly used
• Studies have shown variation in population sizes & age structures
• Lunn et al. (1998)
• Middleton (1996)
• Simpson et al. (1996 and 1997)
• Rees (1994)
• Differently estimated small area ‘populations at risk’ may lead to different SMRs if different size &/or age-sex structure
Indirect Standardised Mortality Ratio (SMR)
SMR = Observed mortality events
Expected mortality events
SMR = 100 x
Deaths in a location of interest
Deaths in a standard area population
Population in the standard area
Population in the
location of interestX
Observed
Expected
Data sources for indirect SMRs at ward level
SMR = 100 x Deaths in a location of interest
Mortality data for the ward (VS4)
Mortality data at national level
Population estimate at national level
Population estimate for the ward
Deaths in a standard area population
Population in the standard area
Population in the location of interestX
By matching age-sex
information
This work …• Estimate a time-series of ward populations using various methods
• Use outputs in SMRs
• Address denominator uncertainties
Research definitions• Small area: electoral wards (caveat)
• Mortality measure: indirect SMRs (caveat)
• Time period: annual mid-year estimates 1990-1998
• Geography: 1998 wards in GOR East
• Output detail: age-groups (11) and sex (2)
• Data acquisition: nationally consistent, public domain sources
• Base population: Estimating with Confidence Populations (EwCPOP) based on 1991 Census (caveat)
Steps to achieve this …Input data preparation
• Geographical harmonisation• Temporal harmonisation• Single year of age
Estimation methods• Indicator of sub-district, ward level change (electorate)• Cohort-component
Optional enhancements• Allowances for special sub-populations• Hybrid methods• Constraints
Standardised mortality ratios• Use ward age-sex estimates as populations at risk
2001 Census implications?
Geographical harmonisation
Postcode locations as building-bricks: assumptions• Residential postcode distribution is a proxy for population distribution (enhanced by household or address counts)• At a point in time a set of postcodes constitutes a ward
Haldens 1991 Haldens & Panshanger 1998
Temporal harmonisation
J F M A M J J A S O N D
Population estimates needed for the mid-year
ONS mid-year estimates
Electorate
Census
Vital statistics
Disaggregation to single year of age• For annual ageing-on• For aggregation into appropriate age-groups
Estimation methods data scheme
Data at time t
Data at time t + 1
Males Females
Age 0-90+ Age 0-90+
Wards (within LA
district)
? ?
LA district totals
Ward totals
Electorates as sub-district indicator
147500
150000
152500
155000
157500
160000
1990 1991 1992 1993 1994 1995 1996 1997 1998
Dis
tric
t p
op
ula
tio
ns
3000
6000
9000
Ele
cto
rs
District Electorate 1 Electorate 2
Electorates as sub-district indicator• Annual time-series available, but• Collected 10th October• Only adult ages• Variable enumeration space & time
Indicators of change
ONS MYEs• Annual mid-year time-series available• Age-sex detail, but• Only district level
Apportionment, additive & ratio methods
Data at time t
Data at time t + 1
Electorate derived ward totals
ONS district MYEs
Electorate derived ward totals
ONS district MYEs Change betweent & t + 1
Apply previous age structure &/or constrain
to MYE
Cohort-component method (includes Vital Statistics)
Data at time t
Data at time t + 1
+ - + -
Ageing-onBirths Deaths In-migration Out-migration
ONS district MYEs
Electorate derived ward totals
Cohort-component enhancement: Suppressed aging-on of special populations• Students
• Armed forces
• Communal establishments
Method option: Constraints
Ward age-sex estimates are controlled to sum to district-level age-sex information, ONS annual MYE
• Larger area estimates tend to be more reliable
• Ensures consistency with ONS published data & thus …
• More acceptable, but …
• Some LAs disagree with the ONS MYE
Wards in LA
district
FemalesMales1
n
Age-group (column) totals
Ages
0 90+ 0 90+
Age-group district-level constraints
Ward (row) totals
Ward constraints
Constraints and Iterative Proportional Fitting (IPF)
t + 1 initial age-sex estimates
Estimation methods
MYE Apportion-ment
Additive Ratio IPF Cohort-component
Without Vital Statistics &ageing on
District District District District District/ward
-
- Unconstrained Unconstrained Unconstrained - -
With Vital Statistics &ageing on
- - - District District/ward
District, ward, IPF
- - - Unconstrained - Unconstrained
With Vital Statistics,ageing &special populations
- - - District District/ward
District, ward, IPF
- - - Unconstrained - Unconstrained
Estimation methods & options
Strategy Method / option Population at risk
Do nothing approach
Use the ward populations from EwCPOP for 1991 in all subsequent years
EwCPOP
Minimal approachEwCPOP 1991 constrained to ONS MYEs for each year
ONS-MYE
Simpler methodRatio method with initial age-sex counts constrained to be consistent with ONS MYEs for each year
Ratio-constrained
More complex methods
Cohort-component including births, deaths and ageing and hybrid with IPF
CC-IPF
Cohort-component with gross migration flows and allowances for special populations and hybrid with IPF
CC-mig-sp-IPF
Many method / option combinations …Strategy for the choice of population at risk
Differences in estimate outputs …
Differences in outputs (1991 cf 1998)
Newnham: simpler methods constrained Coggeshall: simpler methods constrained
Coggeshall: cohort-component, plus migration and special populations
Newnham: cohort-component, plus migration and special populations
Differences in outputs (1991 cf 1998)
abs(1991 - 1998)
1991
Most variation in estimate outputs for:
• Youngest ages
• Young adults
• Most elderly
* 100
Using 1998 outputs in SMR calculations (Newnham)
Using 1998 outputs in SMR calculations (Newnham)
Smaller base population leads to lower expected
Student ages suppressed, elderly enhanced
Similar structure to base, total & elderly enhanced
Structure erroneously aged-on
Students enhanced, elderly suppressed
Smaller base population leads to lower expected
Student ages suppressed, elderly enhanced
Similar structure to base, total & elderly enhanced
Structure erroneously aged-on
Students enhanced, elderly suppressed
Lower expected leads to higher SMR
Higher expected leads to lower SMR
Youthful population leads to lower expected & higher SMR
Using 1998 outputs in SMR calculations (Newnham)
Comparison of 1998 SMRs: cf no population change
Are the differences enough to make a difference?!?Overlapping SMR confidence intervals?
• Yes, but observations small numbers leading to wide CIs
Do wards fall in the same SMR quintile?
Ranking by SMR:• Quintile 1: 29% wards consistently most healthy • Quintile 5: 6% wards least healthy
Differently estimated populations at risk and SMRs …• If a larger population is estimated by a method compared with another, but with the same age-sex structure, a lower SMR results because more events are expected (and vice versa)
• If a method estimates an older population structure than another, a higher expected is calculated, resulting in lower SMRs (and vice versa)
• Population size is more critical in simpler methods (as little or no new age information)
• Poorly specified cohort-component models tend to result in lower SMRs, because incorrectly aged-on populations lead to higher expected mortality
• Fully specified cohort-component models tend to result in greater range of SMRs, due to populations kept youthful in certain locations by migration data and suppressed ageing of sub-groups (proxy for migration)
• Areas with the best health consistently have lowest SMRs calculated
• Areas with the very worst health similarly identified but not the same consistency
• Fair level of tolerance in SMRs for all-ages
• Not necessarily the case with age-specific mortality rates (Rees et al., 2003a)
Following 2001 Census outputs (& rebased MYEs) …• Uncertainty in the EwCPOP base population used
• Uncertainty in the annual district level ONS MYEs used as constraints
In the light of the 2001 Census outputs …• Uncertainty in the annual national level ONS MYEs used for ASMRs
National ASMRs differ
Populations at risk differ
Thus: Expected changes
Events don’t change
SMRs alter
Uncertainty in SMR calculations …
SMR = 100 x Deaths in a location of interest
Mortality data for the ward (VS4)
Mortality data at national level
Population estimate at national level
Population estimate for the ward
Deaths in a standard area population
Population in the standard area
Population in the location of interestX
Uncertainty in estimated populations at risk• By total size & by age
Newnham
• Maximum
• Average
• Minimum
• CC-mig-sp-IPF
Coggeshall
• Maximum
• Average
• Minimum
• CC-mig-sp-IPF
No consideration here for rebasing MYEs!
Uncertainty in SMR calculations …
How confident can we be in our SMR results?
Confidence limits (c. 95%) are calculated using:
The assumption is that the ‘expected’ is reliable
But it is not!
Event counts may well be more reliable!!
Expected
ObservedSMR 10096.1 (or Byar’s
approximation)
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