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 interest X Observed Expected

Data sources for indirect SMRs at ward level SMR = 100 xDeaths 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 interest X 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 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 JFMAMJJASOND 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 MalesFemales Age Wards (within LA district) ?? LA district totals Ward totals

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 between t & t + 1 Apply previous age structure &/or constrain to MYE

Cohort-component method (includes Vital Statistics) Data at time t Data at time t Ageing-onBirthsDeathsIn-migrationOut-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 FemalesMales 1 n Age-group (column) totals Ages Age-group district-level constraints Ward (row) totals Ward constraints Constraints and Iterative Proportional Fitting (IPF) t + 1 initial age-sex estimates

Estimation methods MYEApportion- ment AdditiveRatioIPFCohort- component Without Vital Statistics & ageing on District District /ward - -Unconstrained -- With Vital Statistics & ageing on ---DistrictDistrict /ward District, ward, IPF ---Unconstrained- With Vital Statistics, ageing & special populations ---DistrictDistrict /ward District, ward, IPF ---Unconstrained- Estimation methods & options

StrategyMethod / optionPopulation at risk Do nothing approach Use the ward populations from EwCPOP for 1991 in all subsequent years EwCPOP Minimal approach EwCPOP 1991 constrained to ONS MYEs for each year ONS-MYE Simpler method Ratio 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 constrainedCoggeshall: 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 Most variation in estimate outputs for: Youngest ages Young adults Most elderly * 100

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 dont change SMRs alter

Uncertainty in SMR calculations … SMR = 100 xDeaths 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 interest X

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!! (or Byars approximation)