Stability of Age Standardised Rates for
Deaths at Small Geographies and Use of
the 95+ Age Group
Background
The European Standard Population (ESP) is an artificial population structure which is used in the
weighting of mortality or incidence data to produce age standardised ratesi. Eurostat, the statistical
institute of the European Union, has decided to bring this population structure up to date.
ONS has consulted on how to implement the change in the UK, on behalf of the Government
Statistical Service (GSS) as a whole. This paper considers data for England and Wales only, but its
conclusions are likely to hold for the UK as a whole.
The ESP is used to calculate age standardised rates (ASRs), which allow comparison of rates,
including those across populations that may have different age and sex structures. This paper
focuses on the ASR for deaths.
The terms ASR and ASR for deaths are used in this paper to mean age standardised rates for deaths.
Different authors use different conventions and these rates may be known variously elsewhere as
age standardised mortality rates – ASMRs or age standardised death rates - ASDRs. Furthermore,
some authors may use ASRs to mean age specific (death) rates. Rates may be calculated for a range
of events, including deaths, cancer diagnosis, cancer deaths: this paper uses the term ‘events’ when
making general comments that apply to different sorts of events, and ‘deaths’ where specifically
deaths are concerned.
Size of different area types
This document focuses on small areas; Low and Middle level Super Output Areas. Other work has
been undertaken looking at larger areas. Table 1 below shows the number, minimum, maximum,
and mean population size (2011) for the different types of areas (in England and Wales) as context to
this work.
Table 1: Mid-2011 populations by type of area
Area type
Lower level Super Output Area (LSOA)
Middle level Super Output Area (MSOA) (1)
Local authority
Parliamentary constituency
Clinical Commisioning Group
National Park
No. of Areas
34,753
7,201
348
573
211
13
England and Wales total
Minimum
987
2,224
2,224
56,543
61,607
1,994
1
Population
Mean Maximum
1,616
7,800
161,411
98,030
251,693
31,022
8,159
16,439
1,074,283
159,456
863,433
112,492
56,170,927
Source: ONS, mid-2011 population estimates
(1) Lowest value is for Isles of Scilly, which is a 'pseudo-MSOA'.
Note: all areas are for England and Wales except for CCGs (England only)
Data are internally consistent. One or more whole LSOAs make up a MSOA so data can be exactly
aggregated from LSOA to MSOA. Similarly, one or more whole MSOAs make up a local authority.
Local authorities cover, and can be added to give, the whole of England and Wales. Parliamentary
constituencies are on a different set of boundaries, but data for these areas can be added to give
data for England and Wales. Similarly Clinical Commissioning Groups can be added to give totals for
England (not Wales). National Parks, however, only cover part of the country.
Further information on area types (referred to as geographies) is available on the ONS websiteii.
Introduction
This paper looks at the stability of ASRs for deaths at small geographies, specifically lower level super
output areas (LSOAs) and middle level super output areas (MSOAs). In particular it looks at the
advisability of using upper age groups in the calculation of rates of 85–89, and 90+, compared with
85–89, 90–94, and 95+.
The ESP has an upper age of band 95+, but suggests “... caution should be applied because of the
potential quality issues of the data at older ages.”
Variability of Age Standardised Rates
Number of deaths
There is natural variability in the number of events in a particular area. For a given area, with the
same underlying rate, the number of events will change from one period (year) to another due to
chance alone.
The variability in ASRs for deaths can be assessed by calculating the standard error for a particular
areaiii. To assess the likely stability of the rate the relative standard error (RSE) can then be
calculated. For example, consider an area with a stable underlying death rate:
For one year the ASR for deaths is calculated as 17 per 1,000.
The standard error is calculated as 3.4.
The RSE is therefore 20%.
The 95% confidence interval is ±1.96 x 3.4 ≈ ±6.8 or 10.2 to 23.8 deaths per 1,000.
Rates based on 20 events (when summed across all age bands) typically have an RSE of about 22%,
below this level of events the size of the RSE starts to increase quickly. For this reason, rates based
on fewer events may be considered to be unreliable, that is natural variation will have too large an
impact to give stable and reliable rates.iv This is consistent with ONS policy on standardised rates
that says that rates based on fewer than 20 events across all age-bands, if quoted, should be labelled
as potentially unreliable. This guideline is used to inform this paper.
Population size
Population estimates are subject to a degree of uncertainty. Unlike deaths, the population in an area
is typically likely to be fairly stable from year to year. However, there is a degree of uncertainty in
the estimates of population size. This uncertainty is higher for the more elderly age groups where
estimation of the population size is more difficult; small population sizes in these age groups
(relative to the number of events) means that any source of error in the estimates is likely to have a
proportionately larger impact.
Data used
This paper is based on the following data:
 ONS published LSOA mid-year population estimatesv
 Research figures for the eldest population age groups, that is splitting the 90+ into 90 to 94
and 95+, produced by ONS in order to meet requirements for the ESPvi
 Calendar year deaths data from the ONS Mortality Analysis team
Three years of data are used (2010, 2011, and 2012). Three years of data are used in order to give
enough deaths to enable calculation of rates. In some years seasonal increases in the number of
deaths may start before the end of the calendar year, in others this increase may occur later and
into the next calendar year. Using three years of data also helps reduce the impact of these timing
issues.
LSOAs
There are 34,753 lower level super output areas, LSOAs, (2011 boundaries) in England and Wales.
Zero population estimates
Even aggregating over three years there are still a considerable number of LSOAs that have one or
more age groups with no population, particularly when the older, 95+ age band, is used (Table 2).
Table 2: Number of LSOAs with zero population in a quinary age
group
2010 to 2012, by sex and oldest age used
Males
Females
90 +
95+
701
274
16,741
6,839
Source: Office for National Statistics
ASR for deaths can still be calculated for these LSOAs. Where an age group has zero population, a
crude age specific death rate for the age-group cannot be calculated (this would involve a division by
zero). Instead the local authority (LA) average rate for the relevant age group has been used in the
calculations. This issue does not occur where there are zero deaths, as a rate of zero can be used in
the calculation of the ASR for deaths.
Estimates for age groups with zero population can occur for a number of reasons; importantly, the
population numbers are estimates and subject to a margin of error. Other reasons where there may
be a death with no population include (but are not limited to): a death occurring before the mid-year
point leaving no remaining population (population is a mid-near snapshot estimate and deaths data
are for the full year); no population recorded on NHS data (used in the calculation of these
estimates) in either one or other of the 90 to 95 or 95+ age groups; and deaths (e.g. in a nursing
home) where someone has moved from one area to another, but where they have not been resident
long enough to update their address with the NHS.
Summary statistics on LSOA age standardised rates for deaths
Tables 3 and 4 below show some key summary statistics for ASRs for deaths for these areas,
calculated using upper age groups of (separately) 90+ and 95+, and the difference between the two.
Because of the number of LSOAs with zero population estimates for some age-groups the
calculations have been replicated based only on those LSOAs that have population estimates in all
age groups (Table 4). To enable fair comparison LSOAs are excluded from all the calculations, even if
the zero occurs only in the upper age groups, and the 90+ calculations could be made without use of
LA level data.
Table 3: Age standardised rates for deaths (per 1,000 population) of LSOAs in England and Wales, summary data
by sex, based on upper age groups of 90+ and 95+, using revised European Standard Population
1
Average SMR
Males
Females
90+
11.3
7.7
95+ Change
13.2
1.9
9.2
1.5
1
Average standard error
90+
3.1
2.1
95+
3.5
2.4
Change
0.4
0.3
Average1 Relative Standard Error
90+
0.34
0.29
95+
0.33
0.27
Change
-0.01
-0.02
Number of
LSOAs
34,753
34,753
2
Source: Office for National Statistics
Notes
1 Averages quoted are simple unweighted means, and therefore will differ from rates calculated at the national level.
2 Including up to 5 LSOAs for males and 30 LSOAs for females where ASR is calculated as zero, which are excluded from RSE
calculation.
Table 4: Age standardised rates for deaths (per 1,000 population) of LSOAs in England and Wales, summary data
by sex, based on upper age groups of 90+ and 95+, using revised European Standard Population
Excluding LSOAs where the population for one or more age groups is estimated as zero
1
Average SMR
Males
Females
90+
11.1
7.6
95+ Change
13.1
2.0
9.1
1.5
1
Average standard error
90+
2.7
1.9
95+
3.3
2.2
Change
0.5
0.3
Average1 Relative Standard Error
90+
0.24
0.25
95+
0.25
0.25
Change
0.00
0.00
Number of
LSOAs
18,012
27,914
2
Source: Office for National Statistics
Notes
1 Averages quoted are simple unweighted means, and therefore will differ from rates calculated at the national level.
2 Including up to 5 LSOAs for males and 30 LSOAs for females where ASR is calculated as zero, which are excluded from RSE
calculation.
Key points on age standardised rates for deaths and standard errors
Increasing the upper age range to 95+ tends to increase the size of the ASR. This occurs because the
England and Wales population has a lower proportion (by sex) of those aged 95+ than the new ESP;
thus the higher death rate in the 95+ age group is given a greater weight in the calculation. An
implication of this is that it matters whether the 95+ age group is used or not. Further, when
comparing rates they should be compared on the same basis, i.e. all using the same upper age band.
The average standard error increases when calculated using the 95+ age group. However, this is
somewhat misleading as the ASR for deaths also increases. Instead the relative standard error is a
better indicator. If all LSOAs are included, this actually decreases. However, if only those LSOAs
where no use of LA level data are included, the RSE remains virtually unchanged. Thus using the
upper age-band does not affect the average relative variability of the ASR. The use of LA level
averages has an impact on conclusions drawn about LSOAs, and care needs to be taken when
drawing conclusions on rates with and without the use of LA level data. Related to this, the size of
the RSE for all LSOAs taken together is larger than for only those that have no zero population
estimates in age groups: this is because LSOAs with larger populations overall are less likely to have a
zero estimate, and will also have less variation in the number of deaths from year to year.
Overall only 46% of LSOAs have 20 or more male deaths over three years, and 43% have more than
20 female deaths. This is reflected in the RSEs of 33 or 34% for males, and 27 or 29% for females
(depending on whether the upper age group is used). Even if only those LSOAs where there are no
zero age group estimates are used, the RSE is still around 25%. Given this reliability, it should be
concluded that there is too much natural variation in the number of deaths at LSOA for reliable
conclusions about the underlying ASR for deaths to be drawn – ASRs for deaths for this level of
geography should be treated with great caution, and are not suitable for general usage. The use of
more years would help with this reliability – but will limit the usefulness or the data in other ways.
Stability of LSOAs to the upper age band
The previous section shows that using the upper age band tends to increases the ASR for deaths. It
also shows that there is no indication that the relative variability of the ASR changes. However, this
does not show that individual LSOAs show a stable pattern of change when the upper age band is
used. The following charts (Figures 1 and 2) show, for males and females respectively, the range of
change to the ASR when the upper age band is used, compared to those LSOAs where LA level data
are not used.
Figure 1: Increase in ASR for deaths when the upper age band is increased from 90+ to 95+, males,
LSOAs where no age groups have a population estimate of zero
Figure 2: Increase in ASR for deaths when the upper age band is increased from 90+ to 95+,
females, LSOAs where no age groups have a population estimate of zero
These charts show that there is a wide range in the distribution of the increase in the ASR rates for
deaths when moving to the 95+ age group. This is consistent with degree of natural variation in the
number of deaths for these small geographies. This variation supports the conclusion that ASRs for
deaths for LSOAs should not be used for general purposes.
A point of interest is the number of zero changes (most notable in the male histogram). This reflects
that there are a number of LSOAs with no deaths at aged 85+ in the three year period, meaning that
the ASR is the same irrespective of which upper age band is used.
Significance and multiple testing
We have observed above that increasing the upper age group from 90+ to 95+ tends to increase the
ASR for deaths. It is therefore reasonable to ask the questions ‘is the increase for this area
significant?’ and ‘is the increase for this area significantly different from the national average?’
Given there are 34,753 LSOAs, a number of them are likely to have a ‘significant’ difference due to
chance alone. Sophisticated analysis can be undertaken to deal with the issue of multiple testing.
However, as a crude starting point, sophisticated consideration would only be required if the
number of ‘significant’ differences across all LSOAs starts to approach 5% of areas (if using a 95%
confidence interval), that is 1,738 areas.
Over all the LSOAs, 672 areas for males and 893 areas for females have an apparently significant
increase in ASR for deaths when moving from 90+ to 95+. These numbers are significantly less than
5% of areas. Thus any apparently significant change in any particular LSOA should be considered
with caution, as chance alone may well be the reason for the reason for the apparent significance of
the change.
Similarly, in 209 LSOAs for males and 557 LSOAs for females, there is again an apparently significant
difference from the national increase, when moving from 90+ to 95+. Again these numbers are well
below the 5% level. Consequently any apparently significant change when compared to the national
increase should be considered with caution, as chance alone may well be the reason for the
apparent significance of the change.
Population denominators
As set out above there is uncertainty in the population denominators used to calculate these rates,
and this uncertainty is higher for smaller areas and for the upper age groups. It is not currently
possible to quantify this uncertainty well. However, this uncertainty adds further weight to the
conclusion that ASRs for deaths at LSOA level are not suitable for general usage.
LSOA Summary






ASR death rates for LSOAs are subject to too much natural variation to make them useful for
general purposes.
Uncertainty in measurement of population estimates adds to the weight of evidence against
use of LSOA ASR for deaths for general purposes.
There is no indication that use of the higher upper age group (95+) makes the ASRs more
unreliable in relative terms.
Using the 95+ age group tends to increase the calculated ASR rate for deaths.
The increase in ASR for deaths, in moving to the 95+ age group, is not stable across LSOAs –
it has a wide variation (that includes decreases in some LSOAs).
Comparisons of ASRs should be made only if the same (upper) age bands are used.
MSOAs
There are 7,201 Middle level Super Output Areas (MSOAs) (2011 Boundaries) in England and Wales.
MSOAs are exact aggregations of one or more LSOAs. Births and deaths for MSOAs have been
calculated by summing the published data (see above) for LSOAs. This aggregation was undertaken
using the lookup table published by ONS Geographyvii.
The calculations and analysis described above for LSOAs have been repeated, on aggregated
numbers of births and deaths, for MSOAs.
Zero population estimates
Aggregating over three years there are no MSOAs that have age groups with zero populations when
the 90+ upper age group is used. However there remain a relatively small number when the older,
95+ age band is used (Table 5).
Table 5: Number of MSOAs with zero population in a quinary age
group
2010 to 2012, by sex and oldest age used
Males
Females
90 +
95+
-
285
25
Source: Office for National Statistics
Most of these zero populations are in the 95+ age group, however 3 MSOAs have zeroes in the 90 to
94 age group for males (no MSOAs have equivalent zero estimates for females).
ASR for deaths can still be calculated for these MSOAs. Where an age group has zero population, a
crude age specific death rate for the age-group cannot be calculated (this would involve a division by
zero). Instead the local authority (LA) average rate for the relevant age group has been used in the
calculations. This issue does not occur where there are zero deaths, as a rate of zero can be used in
the calculation of the ASR for deaths.
Summary statistics on MSOA age standardised rates for deaths
Tables 6 and 7 show some key summary statistics for ASRs for deaths for these areas, calculated
using upper age groups of (separately) 90+ and 95+, and the difference between the two.
Although there are relatively few MSOAs with zero population estimates, for completeness the table
has been replicated for only those MSOAs where there are no zero population estimates (Table 7).
Table 6: Age standardised death rates (per 1,000 population) of MSOAs in England and Wales, summary data
by sex, based on upper age groups of 90+ and 95+, using revised European Standard Population
Average1 SMR
Average 1 standard error
Average 1 Relative Standard Error Number of
90+
95+
Change 90+
95+
Change 90+
95+
Change
MSOAs
Males
10.6
12.4
1.8
1.2
1.5
0.3
0.14
0.13
-0.01
7,201
Females
7.4
8.7
1.3
0.9
0.9
0.1
0.12
0.11
-0.01
7,201
Source: Office for National Statistics
Notes
1 Avera ges quoted a re s i mpl e unwei ghted mea ns , a nd therefore wi l l di ffer from ra tes ca l cul a ted a t the na ti ona l l evel .
Table 7: Age standardised death rates (per 1,000 population) of MSOAs in England and Wales, summary data
by sex, based on upper age groups of 90+ and 95+, using revised European Standard Population
Excluding MSOAs where the population for one or more age groups is estimated as zero
Average1 SMR
Average 1 standard error
Average 1 Relative Standard Error Number of
90+
95+
Change 90+
95+
Change 90+
95+
Change
MSOAs
Males
10.6
12.4
1.8
1.2
1.5
0.3
0.11
0.12
0.00
6,917
Females
7.4
8.7
1.3
0.8
0.9
0.1
0.12
0.11
-0.01
7,177
Source: Office for National Statistics
Notes
1 Avera ges quoted a re s i mpl e unwei ghted mea ns , a nd therefore wi l l di ffer from ra tes ca l cul a ted a t the na ti ona l l evel .
Key points on age standardised rates for deaths and standard errors
Increasing the upper age range to 95+ tends to increase the size of the ASR. This occurs because the
England and Wales population has a lower proportion (by sex) of those aged 95+ than in the new
ESP; thus the higher death rate in the 95+ age group is given a greater weight in the calculation. An
implication of this is that it matters whether the 95+ age group is used or not. Further, when
comparing rates they should be compared on the same basis, i.e. all using the same upper age band.
The average standard error increases a little when calculated using the 95+ age group. However, this
is somewhat misleading as the ASR for deaths also increases. Instead the relative standard error is a
better indicator. The relative standard error is virtually unchanged, with differences of ±0.01 when
comparing the use of the 90+ to 95+ upper age band; thus using the upper age band does not affect
the average relative variability of the ASR.
The use of LA level averages has little impact on conclusions drawn about MSOAs. However some
care needs to be taken when drawing conclusions on rates with and without the use of LA level data,
particularly when considering MSOAs at an individual level where LA averages are used. The RSE for
males is slightly higher for MSOAs with no zero populations: MSOAs with zero populations in some
age bands are likely to be smaller, with less deaths, and therefore higher relative standard errors.
Only 11 MSOAs have fewer than 20 male deaths over three years, and 25 have fewer than 20 female
deaths. Care should be used if individual MSOAs with fewer than 20 deaths are considered.
Averaging over fewer than the three years used will increase this number of MSOAs, as well as
increasing the standard errors, and is therefore not recommended.
On average, MSOAs have relative standard errors for the ASR for deaths of around 12%. Natural
variation in the number of deaths will therefore typically cause the rate to vary by about ± 24% (with
some small variation by sex and which upper age group is used). At this level natural variation is still
an issue that needs to be considered carefully when considering the rates; however a range of useful
analyses becomes plausible.
Stability of MSOAs to the upper age band
The previous section shows that using the upper age band tends to increase the ASR for deaths. It
also shows that there is no indication that the relative variability of the ASR changes. However, this
does not show that individual MSOAs show a stable pattern of change when the upper age band is
used. The following charts (Figures 3 and 4) show, for males and females respectively, the range of
change to the ASR when the upper age band is used, compared to those LSOAs where LA level data
are not used. The same horizontal axis is used as for LSOAs facilitating a distributional comparison;
however the vertical axis is changed as there are fewer MSOAs than LSOAs.
Figure 3: Increase in ASR for deaths when the upper age band is increased from 90+ to 95+, males,
MSOAs where no age groups have a population estimate of zero
Figure 4: Increase in ASR for deaths when the upper age band is increased from 90+ to 95+,
females, LSOAs where no age groups have a population estimate of zero
These charts show that there is some distribution of the increase in the ASR rates for deaths, when
moving to the 95+ age group. However, particularly for females, most MSOAs are in a relatively
narrow band. Thus there is a degree of stability in moving from the 90+ to 95+ age band. However,
there is no tight relationship between the rate calculated for 90+ and that for 95+, therefore it is not
sensible to mix rates calculated for 90+ and 95+. For any discrete piece of work rates should be
calculated based either the 90+ or the 95+ age band, and these should not be mixed. ‘Conversion’
from one to another at MSOA level is not possible.
As shown above, ASR for deaths can be used, with some caution, at MSOA level. Further, there is no
additional caution needed when using the higher 95+ age band (other than for a relatively small
number of MSOAs where there is zero population in some age bands). Given there is additionally
some stability in moving from the use of 90+ to 95+ as the upper age band, from the perspective of
natural variability in deaths, there is no reason to prefer the usage of either the 90+ or 95+ upper
age-group, providing these are not mixed within the same work. However, there is a degree of
judgement in this conclusion – individual users may not consider there to be enough stability in the
move to the 95+ age band.
Significance and multiple testing
We have observed above that increasing the upper age group from 90+ to 95+ tends to increase the
ASR for deaths. It is therefore reasonable to ask the questions ‘is the increase for this area
significant?’ and ‘is the increase for this area significantly different from the national average?’
Given there are 7,201 MSOAs a number of them are likely to have a ‘significant’ difference due to
chance alone. Sophisticated analysis can be undertaken to deal with the issue of multiple testing.
However, as a crude starting point, sophisticated consideration would only be required if the
number of ‘significant’ differences across all MSOAs starts to approach 5% of areas (if using a 95%
confidence interval), that is 360 areas.
Over all of the MSOAs, 1,125 areas for males and 1,617 areas for females have an apparently
significant change in ASR for deaths when moving from 90+ to 95+. These numbers are considerably
more than 5% of areas. However, only 89 areas for males, and 59 areas for females, show a change
that is apparently significantly different from the national change in moving from 90+ to 95+. This is
much less than 5%. Consequently any apparently significant change when compared to the national
increase should be considered with caution, as chance alone may well be the reason for the
apparent significance of the change. Further, moving from 90+ to 95+ does have a significant impact,
reinforcing the recommendation that analysis should not mix results from usage of the 90+ and 95+
upper age.
Population denominators
As set out above there is uncertainty in the population denominators used to calculate these rates,
this uncertainty is higher for smaller areas and for the upper age groups. It is not currently possible
to quantify this uncertainty well. However, this uncertainty adds further weight to the
recommendation that care should be taken in the analysis of data at this level, particularly when
comparing results at the individual MSOA level.
Population estimates, splitting the upper age group into 90 to 94 and 95+, are still experimental:
they have not yet achieved National Statistics status. Work is continuing on their evaluation. Given
uncertainty over the reliability for these estimates, a practical recommendation is therefore that the
90+ age group should be used, however it is safe to use rates based on the 95+ upper age-group if
there is a sufficient reason, provided the additional uncertainty in the population denominator is
taken into consideration. The different upper age bands should however, not be mixed within the
same piece of work. As work continues on the population estimates at the upper age-range, it is
likely that a point may be reached where there is sufficient confidence in the quality of the
population denominators to facilitate a change in this recommendation to using the 95+ age group.
This is in line with EU guidance that the 95+ age group should be used where the data are available.
MSOA Summary



ASR death rates for MSOAs are subject to natural variation and care must be taken in their
usage
Provided due consideration is taken of the impact of natural variation, a range of analysis of
ASR death rates for MSOAs is plausible
Natural variation and the implications of multiple testing mean caution should be used in
interpreting results, particularly at the individual MSOA level









Some additional caution is needed when using the 95+ upper age band, as some MSOAs
have zero population estimates in the upper two age bands, though relatively few MSOAs
have zero estimates
A few MSOAs have low (under 20) numbers of deaths and additional care should be taken
with these MSOAs
Averaging over fewer than three years is not recommended
Using the 95+ age group tends to increase the calculated ASR rate for deaths
Comparisons of ASRs should be made only if the same (upper) age bands are used
There is no indication that use of the higher upper age group (95+) makes the ASRs more
unreliable in relative terms as a result of natural variation in the number of deaths
The increase in ASR for deaths, in moving to the 95+ age group, is relatively stable across
MSOAs, particularly for females; however there is no direct correlation and ‘converting’ a
90+ based estimate to a 95+ based estimate is not possible
Uncertainty in measurement of population estimates (particularly at the higher ages) means
additional caution should be taken, particularly when drawing conclusions at the individual
MSOA level
Because work is continuing on the estimation of the population at the upper ages, we
currently recommend using the 90+ upper age limit, but we will change this
recommendation to using the 95+ age group when the population estimates for these upper
age-groups are considered to be sufficiently reliable
Overall summary
There is too much natural variation in the number of deaths for ASR for deaths to be used (for
general purposes) at the LSOA level (Lower level Super Output Areas).
ASRs for deaths may be used, with some appropriate caution, for a range of purposes at the MSOA
level (Middle level Super Output Area).
Currently the upper age band of 90+ should be used. This recommendation may later be changed to
95+ following further work on population estimates at these ages.
Jonathan Page-Swan
March 2014
Office for National Statistics
i
Eurostat, Revision of the European Standard Population: Report of Eurostat's task force, 2013 Edition,
http://epp.eurostat.ec.europa.eu/cache/ITY_OFFPUB/KS-RA-13-028/EN/KS-RA-13-028-EN.PDF
ii
ONS, A Beginners Guide to Geography, web pages: http://www.ons.gov.uk/ons/guidemethod/geography/beginner-s-guide/index.html
iii
P. Boyle and D.M. Parkin, Cancer Registration: Principles and Methods, Chapter 11. Statistical methods
for registries, http://www.iarc.fr/en/publications/pdfs-online/epi/sp95/
iv
This issue is discussed here: Department of Health (New York), Rates Based on Small Numbers - Statistics
Teaching Tools, http://www.health.ny.gov/diseases/chronic/ratesmall.htm
v
ONS, 2012 single year of age super output area mid-year population estimates:
http://www.ons.gov.uk/ons/rel/sape/soa-mid-year-pop-est-engl-wales-exp/mid-2012/stb---superoutput-area---mid-2012.html
ONS, 2011 mid-year LSOA estimates by single year of age: http://www.ons.gov.uk/ons/aboutons/business-transparency/freedom-of-information/what-can-i-request/published-ad-hocdata/pop/april-2013/mid-2011-lsoa-syoa-population-estimates-england-and-wales.zip
ONS, Revised LSOA estimates by single year of age:
http://www.ons.gov.uk/ons/publications/re-reference-tables.html?edition=tcm%3A77-285154
vi
ONS, LSOA Population Estimates of the Very Old, England and Wales: Research Paper,
http://www.ons.gov.uk/ons/guide-method/method-quality/specific/population-and-migration/pop-ests/lsoapopulation-estimates-of-the-very-old--research-paper.zip
vii
The geography lookup table is published as a zip file:
https://geoportal.statistics.gov.uk/Docs/Lookups/Output_areas_(2011)_to_lower_layer_super_output_areas_
(2011)_to_middle_layer_super_output_areas_(2011)_to_local_authority_districts_(2011)_E+W_lookup.zip
available from this page: https://geoportal.statistics.gov.uk/geoportal/catalog/content/filelist.page
Annex 1: Technical Annex
European Standard Population – weights and age groups
Table 1: European standard population ages and weights
Age Group
(years)
Standard
Population
0,0
1-4
5-9
10-14
15-19
1,000
4,000
5,500
5,500
5,500
20-24
25-29
30-34
35-39
40-44
6,000
6,000
6,500
7,000
7,000
45-49
50-54
55-59
60-64
65-69
7,000
7,000
6,500
6,000
5,500
70-74
75-79
80-84
85-89
90-94
5,000
4,000
2,500
1,500
800
95+
Total
200
100,000
Source: Eurostatvii
Where an upper age band of 90+ is used, the 90-94 and 95+ age groups are combined with a weight
of 1,000.
Calculating Age Standardised Death Rates
The European Standard Population (ESP) is used to calculate direct standardised rates, in this case
specifically direct age standardised death rates (ASRs) for deaths.
Sex
Rates are calculated separately for males and females. The same standard population is used for
both sexes.
Population at risk
Calculations of incidence rates require an estimate of the population at risk. For this work calendar
year data are used for the number of deaths, so the mid-year population estimate is used to
estimate population at risk – this is a common approach. In this document the term ‘estimate of
population’ is then used when expressing the formulæ.
Crude age specific death rates
For each age group, i, (separately by sex) calculate:
Weighted age specific death rate
For each age group, i, (separately by sex) calculate:
The standard population (weight) is given in Table 1.
Age standardised rate (ASR) for deaths
Calculate, separately for each sex:
This gives the rate per thousand population – the conventional expression of this rate for small
areas.
is the total of the standard population; for the new ESP this is equal to
100,000, as shown in Table 1, so:
Where a maximum age of 90+ is used there are 20 instead of 21 age-groups, so
becomes
. The standard weight, population, and deaths, are then combined for the upper two groups,
thus the standard weight for this 90+ age group is 800+200=1,000. The overall total for the standard
weights remains changed at 100,000.
Zero population estimates
It is possible for the population of an age/sex group to be estimated as zero. This may be a ‘genuine’
zero or as a result of the uncertainties in the estimation method. This happens frequently at LSOA
level, and occasionally at MSOA level.
Where a zero occurs, the calculation of an ASR would involve division by zero.
Therefore the standard approach to this situation, which was adopted for this work, is to use the
rate calculated at a higher geographical level. In this case the age-specific death rate for the local
authority (LA) containing the MSOA or LSOA is used in the calculation.
As the use of LA level data has an impact on the calculation, this work has paid particular attention
to this issue, examining results (across areas) with and without areas with zero populations (and
therefore LA level rates.
Zero deaths (events) in a specific age/sex group are permitted within the calculation and these occur
frequently. In this case the result is an age-specific death rate of zero, which then gets included in
the overall calculation of the age-standardised death rate.
Calculating standard errors
There is natural variation in the number of deaths in a particular age group for a particular area.
Thus, even if an area was to have the same ‘underlying death rate’ from year to year, chance alone
would mean that there were differing amounts of deaths. The standard error provides a measure of
the natural variability. These standard errors are not a measure of how much error there is in the
number of deaths recorded, nor do they provide a measure of error in the estimate of population
used in the rates; they are a measure of the natural variation expected in the death rate.
There are two main methods of formulaically calculating standard errors for ASRvii. The conventional
approach, used for the standard errors quoted in this report, is to use the Poisson approximation for
the standard error. The main alternative is to use a binomial approximation. These approximations
have been found to give similar resultsError! Bookmark not defined..
For the ESP
.
Because of the structure of the calculations file for this work this has been implemented as:
Confidence interval
The standard error (SE) is approximately normally distributed – N (0, 1).
The 95% confidence interval for an ASR is therefore given by
Relative standard error
The impact of the standard error, what it tells you about how good an estimate is, that is how much
you can expect a rate to change as a result of natural variation is dependent on the size of the ASR it
relates to. The relative standard error, RSE, provides a way of comparing the impact the standard
error will have, irrespective of size of the ASR. Thus the RSEs can be compared for different rates –
even if the size of the rate is different.
The RSE is calculated as:
. This may be expressed as a proportion or a percentage.
Rates over a number of years
It is common practice to ‘average’ rates over a number of years.
In particular for death rates this can lessen the impact of the changing timing of the peaks in the
excess winter deaths. Calendar year deaths data are used. In the UK context there is an increase in
deaths over the winter period. In some years this may start, or be higher, ‘earlier’ than in others, if it
starts before December it will have an impact in the ‘old’ year as well as the ‘new’ year. This
changing timing can cause variation in the ASR, even if overall there are no more or less extra deaths
over the winter period than is usual.
For LSOAs and MSOAs it is also necessary to ‘average’ over a number of years in order to ensure
sufficient events (deaths) to enable calculation to a degree of reliability for these small areas.
It is typical to ‘average’ over three years, and this has been done for this work.
In practice the calculation is undertaken by simply adding the number of deaths over a three year
period, and (separately) adding the corresponding three mid-year population estimates together. It
is then these three year totals that are used in the calculation. No further adjustment is required.
The resultant ASR remains the rate death rate per year (expressed as per thousand population).
However it is calculated (‘averaged’) over a three year period.
Annex 2: Suggestions for further work
Binomial method for calculating standard error
This paper has been prepared using the Poisson approximation for the Standard Error to measure
the variation inherent in the number of deaths (from year to year). This is the conventional approach
to standardised rates. The main deterministic alternative to this is to use a binomial approximation.
As referred to above these tend to produce very similar values. However a useful check would be to
calculate the standard error using the binomial approximation and compare the values produced.
Assessing the impact of uncertainty in population estimates and
computational methods
There is uncertainty in the population estimates. This uncertainty is higher for the more elderly age
bands. Further the age split for the 90+ age group (into 90-94 and 95+) is currently experimental.
With estimates of uncertainty it is possible to apply computational methods (such as bootstrapping)
to look at the impact of these uncertainties on the calculation of ASRs. These methods also provide
an alternative approach to looking at the impact of natural variation.
Formal estimates of the degree of uncertainty in population estimates are the subject of research
within ONS. Nevertheless it might be possible to derive either some indicative or conservative
assumptions about the size of uncertainty in the population estimates that would permit the
consideration of the impact of this uncertainty on ASRs.