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Journal of Public Health Advance Access originally published online on January 25, 2006
Journal of Public Health 2006 28(1):71-81; doi:10.1093/pubmed/fdi068
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© The Author 2006, Published by Oxford University Press on behalf of Faculty of Public Health. All rights reserved.

Estimating diabetes prevalence by small area in England



Peter Congdon
Peter Congdon, Research Professor of Quantitative Geography & Health Statistics, Department of Geography, Queen Mary University of London, Mile End Road, London E1 4NS, UK

Address correspondence to Peter Congdon. Email: p.congdon{at}qmul.ac.uk

Background Diabetes risk is linked to both deprivation and ethnicity, and so prevalence will vary considerably between areas. Prevalence differences may partly account for geographic variation in health performance indicators for diabetes, which are based on age standardized hospitalization or operation rates. A positive correlation between prevalence and health outcomes indicates that the latter are not measuring only performance.

Methods A regression analysis of prevalence rates according to age, sex and ethnicity from the Health Survey for England (HSE) is undertaken and used (together with census data) to estimate diabetes prevalence for 354 English local authorities and 8000 smaller areas (electoral wards). An adjustment for social factors is based on a prevalence gradient over area-deprivation quintiles. A Bayesian estimation approach is used allowing simple inclusion of evidence on prevalence from other or historical sources.

Results The estimated prevalent population in England is 1.5 million (188 000 type 1 and 1.341 million type 2). At strategic health authority (StHA) level, prevalence varies from 2.4 (Thames Valley) to 4 per cent (North East London). The prevalence estimates are used to assess variations between local authorities in adverse hospitalization indicators for diabetics and to assess the relationship between diabetes-related mortality and prevalence. In particular, rates of diabetic ketoacidosis (DKA) and coma are positively correlated with prevalence, while diabetic amputation rates are not.

Conclusions The methodology developed is applicable to developing small-area-prevalence estimates for a range of chronic diseases, when health surveys assess prevalence by demographic categories. In the application to diabetes prevalence, there is evidence that performance indicators as currently calculated are not corrected for prevalence.

Keywords: diabetes, ethnic risks, mortality, performance indicators, prevalence, small area, social gradient


   Introduction
TOP
 Introduction
Materials and methods
 Results
 Discussion
 Appendix 1: Assessing...
 Appendix 2: Assessing the...
 Appendix 3: Poisson regression...
 Acknowledgements
 References
 
Diabetes is a risk factor for cardiac disease and stroke and has complications, such as blindness, kidney failure and nerve damage leading to amputation. Diabetes prevalence has been rising in developed countries across all age and ethnic groups.1,2 For England, the 2003 Health Survey for England (HSE) showed 4.3 per cent of adult males (16 and over) to have the disease, as do 3.4 per cent of adult females – this compares to 2 per cent for both sexes in 1991 (Fig. 1). Further rises in prevalence are forecast.3 Most of the expected increase is in type 2 diabetes, attributable in part to an ageing population (diabetes risk rises with age), growth in the ethnic elderly (with higher diabetes rates), but also to rising levels of obesity and other risk factors for diabetes.4,5 There is also evidence of increased type 1 diabetes in children.6


Figure 1
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  		Figure 1 Prevalence of diagnosed diabetes in adults, 1991–2003, England. Note: Self-reported diagnosis of either type 1 or 2 diabetes. Source: Joint Health Surveys Unit Health Survey for England 2003. London: The Stationery Office, 2003.

 

The future burden of diabetes care is therefore set to increase due to increased prevalence across all age and ethnic groups. However, in some areas in England, especially certain metropolitan areas, national trends are compounded by the impact of deprivation – especially important for the more common type 2 diabetes7 – and by large ethnic minority populations with high diabetes risk. The 1999 HSE found major variation in diabetes prevalence by ethnic group8 (Fig. 2). Estimating current prevalence and extrapolating prevalence by small area is important both in providing and targeting diabetes care and in assessing the quality of diabetes health care.


Figure 2
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  		Figure 2 Diagnosed diabetes prevalence, relative risks to white population by ethnic group and gender (1999 Health Survey for England).

 

The question of appropriate treatment in appropriate settings involves questions, such as appropriate therapy in primary care,9,10 avoidance of emergency hospitalizations related to diabetes and lessening the rate of adverse outcomes. For example, Fig. 3 shows wide variations between English strategic health authorities on two hospital outcomes (based on data for two financial years, 2000–2001 and 2001–2002): namely, a twofold variation in the persons rate for diabetic ketoacidosis (DKA) and coma and nearly threefold variation in lower limb amputation rates. Such variation in health performance may be due in part to genuine variations in morbidity, but may also reflect variations in care effectiveness, or imbalances between resourcing, provision and need that suggest inverse care in diabetes.9,11


Figure 3
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  		Figure 3 Variations in adverse hospitalizations.

 

The analysis here provides small area estimates of both types of diabetes based on recent evidence of age-, sex- and ethnic group-prevalence differences, with an additional adjustment for the impact of social deprivation. It demonstrates how prevalence estimates may be used in assessing variations in health performance indicators and explaining geographic variations in diabetes-related mortality. The application to performance indicators (e.g. rates of diabetic amputation) is based on comparing the level of adverse outcomes to an estimated prevalent population as well as (or possibly instead of) to the ‘expected’ cases based on demographic standardization taking account of age–sex variations in the adverse outcome itself. An excess of adverse outcomes in relation to prevalence is suggestive of deficiencies in health care (beyond the effect of what can be attributed to morbidity); it may also indicate inadequate funding in relation to need.


   Materials and methods
TOP
 Introduction
 Materials and methods
Results
 Discussion
 Appendix 1: Assessing...
 Appendix 2: Assessing the...
 Appendix 3: Poisson regression...
 Acknowledgements
 References
 
Data from the 1999 and 2003 HSE are used here to provide benchmark rates of diabetes by age, sex, ethnic group and specific for diabetes types 1 and 2. The 2003 HSE provides prevalence data by age, sex and social group. However, the 1999 survey was the last designed to provide reliable information on prevalence by ethnicity, especially on ethnic subgroups with varying prevalence. The ethnic groups on which the 1999 HSE provides information are whites, black Caribbeans, Indians, Pakistanis, Bangladeshis and Chinese; this was achieved via a weighted follow-up survey that, inter alia, achieved sufficient coverage of South Asian subgroups to provide estimated relative risks.

As a first step in making the area prevalence estimates, age–sex–ethnic group prevalence rates obtained from the 2003 and 1999 HSE are applied to small area census data (age–sex–ethnic group populations from the 2001 census ST101 tables) to give initial estimates of ward-level prevalent populations. Specifically, gender-specific relative risks for the major ethnic groups from the 1999 HSE are applied uniformly across age–sex group prevalence rates from the 2003 HSE to produce ethnic-/age-/sex-specific rates. The assumption of proportionality in the impact of age and ethnicity on relative risks underlying this procedure was confirmed by analysis of data from the 1999 HSE (Appendix 1).

In line with the 1999 HSE prevalence data, the prevalence of diagnosed type 2 diabetes in black Caribbean men is assumed to be 2.5 times greater than for white men, while for women the relative risk is 4.2. As in Goyder et al.,12 it is assumed that other black ethnic groups have the same relative risks as black Carribeans. Chaturvedi et al.13 also found the prevalence of type 2 diabetes for black males to be about twofold that of white males and a prevalence for black females fourfold that of white females. Type 1 diabetes is assumed to have the same prevalence across all ethnic groups. Type 1 diabetes rates for under 16s are based on Scottish data from Rangasami et al.,6 averaging 24 per 100 000. Type 2 diabetes among children in England is still rare as compared with that of the United States,14 but there is some evidence of its recent emergence, partly due to child obesity. Recent work by Ehtisham et al.15 has suggested a prevalence of 2.1 per million for ages under 16.

Adjusting for area deprivation
Variations in diabetes prevalence by socioeconomic status and area category (both by region and by small area) are also important. Table 1 summarizes the gradient in diabetes from the 2003 HSE by equivalized household income (household income adjusted for the number of people in a household), as well as regional contrasts, with highest prevalence in London and lowest in the South West (men) and North East (women).


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  		Table 1 Doctor-diagnosed diabetes, per cent of prevalence, 2003 Health Survey for England (HSE), income group and region aged 16 and over with diagnosed diabetes

 

To convert individual survey evidence to small area prevalence requires equivalent variables in both the census (or some other area based information source) and the individual survey. Because the census does not report personal income, socioeconomic impacts are represented by using small-area-deprivation categories.

This is possible because the HSE for 2003 includes the official index of multiple deprivation (IMD) for the small area of residence for each survey respondent – specifically the IMD score for census 2001 super-output area (SOA) of residence, there being circa 32500 SOAs in England. The IMD includes factors such as income, education and employment status, and also reflects regional differences in income and socioeconomic status.

Deprivation is especially important in explaining individual and area variation in the more common type 2 diabetes. As Riste et al.16 note, poverty has been under-recognized as a contributory factor to varying diabetes prevalence, and standard mortality from reported diabetes (which is under-recorded) is strongly correlated with area deprivation.17 Individual and area deprivation also impacts on diabetes complication rates.18

Suitable adjustment factors for the impact of deprivation on prevalence are gender specific and obtained via regression techniques that control for the impact of other risk factors. Specifically, separate logit regressions for males and females of diabetes-prevalence probabilities are carried out using HSE 2003 data (Appendix 2) and adjusting for age and ethnicity. It may be noted that (as compared with the 1999 HSE) ethnicity is broadly recorded in the 2003 HSE and here aggregated to white, black, Asian and other. The resulting gradient in prevalence over the IMD quintiles, expressed as a ratio to average prevalence, is 0.76, 0.84, 0.91, 1.13 and 1.37 for males and 0.80, 0.84, 0.93, 1.07 and 1.36 for females. An excess prevalence in the top quintile is apparent for both sexes, though the female deprivation gradient is slightly shallower.

These ratios are applied within the quintile bands defined by the SOA scores: the lowest quintile set of areas (least deprived) has IMD scores between 0.55 and 9.015, the next quintile has scores between 9.016 and 14.148 and so on. The 8000 electoral wards are allocated to the relevant band, and their male/female prevalence on the basis of age structure and ethnicity alone is further adjusted by one of the five ratios above. Then prevalence is aggregated to local authorities and strategic health authorities.


   Results
TOP
 Introduction
 Materials and methods
 Results
Discussion
 Appendix 1: Assessing...
 Appendix 2: Assessing the...
 Appendix 3: Poisson regression...
 Acknowledgements
 References
 
The pattern of area diabetes type 1 and 2 estimates
The total England diabetes prevalent population (all ages) using the methods just described is estimated as 1.529 million, with the all persons all ages rate being 3.1 per cent (males 3.4 per cent, females 2.8 per cent). The over 16 prevalent population estimate is 1.511 million, with the adult rate being 3.85 per cent (4.3 per cent males, 3.5 per cent females). The two type estimates are 188 000 type 1 and 1.341 million type 2. At strategic health authority (StHA) level, total diabetes prevalence varies from 2.4 per cent (Thames Valley) to 4 per cent (North East London) (Table 2).


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  		Table 2 Estimated diabetes prevalence, Type 1 or 2, England and Strategic Health Authorities

 

At local authority level, the prevalence rates vary from 5 per cent in Tower Hamlets to 2 per cent in Bracknell Forest. The former is located in the North East London StHA and is an area with 49 per cent non-white ethnicity (compared with an England figure of 9 per cent) and has high deprivation also (an IMD of 45.2 compared with the England average of 21.7). The latter is an affluent commuter area in the Thames Valley StHA with an IMD of 9 and 5 per cent non-white ethnicity. The estimated ward level prevalence rates range from 7.4 per cent (Latimer ward in Leicester with majority South Asian population and high deprivation) to 0.7 per cent in Hipswell ward in the affluent rural Richmondshire district of north Yorkshire.

One way of depicting the resulting prevalence estimates is in terms of household income estimates for the 354 English local authorities in 1999.19 So a gradient in estimated prevalence over local authority areas grouped by income (specifically income deciles) can be obtained. Table 3 summarizes the estimated prevalence (cases and percents) of both diabetes types combined by area income decile. The estimated percent prevalence varies from 2.6 to 3.6 per cent with a virtually monotonic gradient over the income deciles. Such a gradient at area level is consistent with the individual level evidence in Table 1.


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  		Table 3 Prevalence estimates by local authority income decile

 

Estimates produced by the procedure here relate to doctor diagnosed diabetes and can be compared with another recent prevalence analysis for England (including both diagnosed and undiagnosed diabetes) by the Yorkshire & Humber Public Health Observatory, Brent Primary Care Trust, and University of Sheffield School of Health and Related Research; this is known as the PBS model.20 The model applies age-/sex-/ethnic group-specific estimates of diabetes-prevalence rates, derived from epidemiological population studies, to 2001 census resident populations. There is no correction for socioeconomic effects in the PBS model. Also unlike the estimates derived by the procedure in this article, female prevalence under the PBS model is higher than male prevalence (which is not consistent with the HSE data in Table 1). Despite this there is a broad agreement in terms of rankings of prevalence by StHA (Table 2). The main difference is the high PBS estimated prevalence of the South West peninsula, an area with relatively low ethnic minority populations; this is not in line with the regional contrasts in Table 1.

Mortality and prevalence
One assessment of the predictive validity of the prevalence estimates obtained in this study considers male and female diabetes mortality over 1999–2001 for the 354 local authorities in relation to prevalence categories. A smaller area analysis (for the circa 8000 electoral wards) is prevented by boundary inconsistencies between the 2001 census wards and the wards used to report deaths till 2002. A Poisson regression is used to compare mortality between prevalence categories (Appendix 3).

The mortality gradient as prevalence increases is more regular for females (Fig. 4A and B). However, the top prevalence quintile for males has a higher mean Standard mortality ratio (SMR) of 121, which compares to 87 in the lowest prevalence quintile; for females, the SMR contrast between extreme prevalence quintiles is less pronounced, namely 111 versus 88.


Figure 4
Figure 4
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  		Figure 4 (A) Male diabetes SMRs by prevalence quintile and (B) female diabetes SMRs by prevalence quintile.

 

Diabetic hospitalization outcomes and prevalence
A second validation exercise (and application) of prevalence estimates is in the analysis of health-performance indicators. Performance initiatives relating to health delivery and patient outcomes have been motivated and justified in terms of concepts, such as effectiveness, patient safety, health improvement, efficiency, equity and access.21 In the English National Health Service (NHS), a performance assessment framework based on a set of around 60 high-level performance indicators was introduced in the late 1990s with each indicator justified under one or more of six performance domains: health improvement, fair access, effective delivery, efficiency, patient experience and health outcome of care.22 Diabetes care indicators relate especially to provision of effective primary and community care; the goal is then to reduce hospitalizations for (i) DKA and coma and (ii) lower limb amputations in diabetic patients. The basis for this at patient level is through a planned programme of care and appropriate early intervention.

In the official NHS approach, these outcomes are assessed by age-standardized hospitalization or operation rates without reference to the influence of social or ethnic structure on prevalence. Such a procedure may overstate both the performance deficiencies of high-prevalence areas and the apparently effective performance of low-prevalence areas. To assess such effects, we here compare rankings of the 28 StHAs based on (i) age-standardized rates (ASR) of DKA–coma and amputation and (ii) ratios of DKA–coma episodes and amputation operations to estimated prevalent populations.

Another criterion for the validity of official diabetes performance indicators, as measures of performance per se, is that they should be uncorrelated with prevalence rates (in more technical terms, the 95% confidence interval (CI) for the correlation should straddle zero). If performance indicators in fact are positively correlated with prevalence, the implication is that they are not simply measuring performance but also reflect prevalence. A more appropriate measure of performance in this case is the residual from a regression of the outcome (e.g. diabetic coma rate) on prevalence.

The analysis is based on diabetes indicators in the 2002 Compendium of Clinical and Health Indicators, with pooling of data over the years 2000/2001 and 2001/2002. Table 4 compares the official ASR (columns 6 and 7) with rates that compare event totals to prevalent population estimates (rates per prevalent population or RPP, columns 8 and 9).


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  		Table 4 Comparison of Adverse Outcomes to Prevalence

 

There is in fact a reasonable consistency between the top ASR and RPP rankings, especially for amputation rates. The rank correlation between the ASR and RPP series for amputation is 0.78 and for DKA–coma is 0.62. So for amputation, inferences from rates that take account of age structure alone are not dramatically changed when the full-prevalence pattern is taken account of. Some changes in rank do occur: for instance, the top ranking StHA (28th of 28) on amputation ASR is County Durham & Tees Valley, but this area has rank 25 on the amputation RPP. For DKA and coma, by contrast, there are some major changes in rank: the rank of Birmingham & the Black Country (with high prevalence) falls from 24th among ASR to 11th among RPP, while that of low prevalence Hampshire/Isle of Wight rises from 14th to 24th.

Viewed in terms of the other criterion (the correlation between ASR and prevalence rates), the DKA–coma ASR indicators are positively correlated with prevalence rates. There is a correlation of 0.41 (95% CI = 0.35–0.47) between the DKA–coma ASR and the population prevalence rates in column 3, whereas the corresponding correlation for the amputation ASR is –0.06 (95% CI = –0.135 to 0.015). So the DKA–coma indicators are less clearly a true performance measure than the amputation ASR. A linear regression of the DKA–coma ASR on the population prevalence rate (columns 7 and 3, respectively, in Table 4) is undertaken and ranks on the residual shown in the last column of Table 4. This shows large changes in rank (as compared with rankings on the DKA–coma ASR itself); e.g. the rank of North East London is lowered (from 18 to 8 or from 10th highest to 20th highest) since its high rank on the ASR is partly explained by its high prevalence.


   Discussion
TOP
 Introduction
 Materials and methods
 Results
 Discussion
Appendix 1: Assessing...
 Appendix 2: Assessing the...
 Appendix 3: Poisson regression...
 Acknowledgements
 References
 
This article has set out a procedure for prevalence estimation that can be taken to an area level for which populations are available by age, sex and ethnicity and for which measures of area deprivation are calculated. This is applied to estimating prevalence of diabetes. The first main finding is that the estimated prevalent population in England is around 1.5 million, with a higher rate for males (3.4 per cent) than for females (2.8 per cent). The two type estimates are 188 000 type 1 and 1.341 million type 2. At StHA level, prevalence varies from 2.4 (Thames Valley) to 4 per cent (North East London). It has been demonstrated that prevalence-estimation procedure can assist in evaluating performance rankings: if the worst performing areas are those with high prevalence, this suggests that prevalence, not performance, is being measured (similar issues occur in school-exam rankings that do not take account of catchment area social structure). The analysis showed a clear positive correlation between DKA–coma rates and prevalence, but a zero correlation between amputation and prevalence. This suggests that variation in amputation rates is more clearly a matter of performance and quality of care variation than variation in DKA–coma rates. Among the other main findings of the analysis are that an assumption of proportionality in the impact of age and ethnicity on relative diabetes risk is justified by recent HSE data; this facilitates small-area-prevalence estimation though is not a necessary feature of the method described. There were also clear deprivation effects on diabetes risk (using the recently developed IMD). Finally, a categorization of areas according to prevalence estimates based on age, ethnicity and deprivation explains a large element of variation in diabetes mortality.

The study findings generally confirm the existing body of knowledge about social, demographic and area variations in diabetes prevalence. The 1999 HSE found clear ethnicity effects on diabetes risk, and several studies have noted deprivation gradients for diabetes, especially late-onset diabetes type 2.16 However, existing studies have not necessarily controlled for the interplay between risk factors via formal regression methods. Neither have they necessarily explored the population and area level implications of survey findings nor investigated the association between prevalence and performance rankings. This analysis is distinct in considering these broader issues and in adopting a methodology that can be adapted to other chronic diseases. The method has the advantage that with revised population estimates and updated area-deprivation measures (using non-census indicators, as does the IMD), prevalence estimates can be updated outside census years. The method is also potentially extendable to prevalence forecasts by area that would include extrapolated national rates of age–sex–ethnic group prevalence as well as area projections by age, sex and ethnic group. Another advantage of the method is that by using a Bayesian methodology, it is straightforward to include historical knowledge about prevalence risk factors.

Some possible limitations of the approach may be mentioned. For example, it would be preferable to base the estimated prevalence gradient over area-deprivation levels on a finer gradation of deprivation, such as deciles of the IMD score for an analysis of English areas. The most deprived areas (e.g. in the top 5 per cent of IMD scores) may have their prevalence understated by a procedure relying on deprivation quintiles. There may also be scope for including other demographic variables (e.g. marital status) or for more disaggregated ethnicity categories; e.g. there is likely to be variation in diabetes risk within black or south Asian groups. However, reliance on relatively small survey subsamples within highly defined demographic and ethnic groups tends to make prevalence estimates less precise.23 A final caveat is the use of self-reported survey data, that is not diagnostically confirmed. However, there is evidence that self-reported status does correlate well with formally diagnosed diabetes.24


   Appendix 1: Assessing proportionality of age and ethnicity impacts on diabetes prevalence
TOP
 Introduction
 Materials and methods
 Results
 Discussion
 Appendix 1: Assessing...
Appendix 2: Assessing the...
 Appendix 3: Poisson regression...
 Acknowledgements
 References
 
To assess the impact of age and ethnicity on prevalence, counts of diagnosed diabetes cases from the 1999 HSE were obtained by sex, age (18 5-year bands 0–4, 5–9,..., 80–84, 85+) and ethnic group (seven groups: white, black, Indian, Pakistani, Bangladeshi, Chinese, other). The counts, denoted yijk (i = 1, 2; j = 1, 18; k = 1, 7), are modelled as Poisson variables with means µijkEijk, where µijk models the impact of sex, age and ethnicity, and Eijk is the expected count in subgroup (i, j, k) based on applying the overall diabetes prevalence rate of 2.3 per cent to the sampled population totals Pijk.

A fully Bayesian modelling strategy was employed with the WINBUGS package; this involves specifying prior densities on the parameters and updating these densities using the observed data via Markov Chain Monte Carlo (MCMC) techniques. Model comparison is based on the deviance information criterion (DIC) of Spiegelhalter et al.,25 with lower DIC representing a better-fitting model after taking account of model complexity. A complex model might give a slightly better fit, but at the expense of a large increase in parameters and model complexity (summarized in a complexity measure).

For the model terms Formula, we assume two options: a model with proportional effects

Formula
and one with age–ethnic group interactions

Formula

In both models, the age effect is modelled using a random walk prior that assumes diabetes rates for successive age groups will tend to be similar. This is a smoothing prior26 in contrast to one that retains the possibly jagged age schedule resulting from sampling fluctuations. Specifically, it is assumed that

Formula
for j = 2,...,18, where N(m, V) denotes a normal density with mean m and variance V, where the initial value {gamma}1 is assigned a diffuse N(0, 1000) prior, and the precision Formula is assigned a Ga(1, 1) prior. The gender and ethnic parameters ßi and {delta}k are assigned fixed effects priors, with corner constraints: ß1 = {delta}1 = 0, with ß2 ~ N(0, 1000) and {delta}k ~ N(0, 1000) (k = 2, 7). The interaction parameters are assumed random but unstructured. Thus {varepsilon}jk ~ N(0, 1/Formula), where Formula is assigned a Ga(1, 1) prior. To assess sensitivity to priors on Formula and Formula, Ga(1, 0.1) and Ga(1, 0.001) priors were also investigated.

We find that the model without interactions has a lower DIC than the model including interactions; the latter has a lower average deviance (namely 558 as compared with 580 for the no interaction model), but the complexity measure rises from 20 to 50, so the DIC increases from 600 to 608. To assess the ‘significance’ of the interactions, we consider the probability that {varepsilon}jk > 0 for a particular age–ethnic group.27 We find that the highest posterior probability for a positive effect is 0.96 for Pakistanis aged 55–59, but no other such probabilities exceed 0.95 (the next highest is 0.93 for Bangladeshis aged 55–59). There is one probability below 0.05, in line with an age–ethnic combination at relatively low risk, namely whites aged 50–54 with Pr({varepsilon}11,1 > 0) = 0.02. Conclusions regarding the choice between a proportional model and one including interactions are not affected by using different priors on Formula and Formula: the simpler model is still preferred. The Ga(1, 0.1) and Ga(1, 0.001) priors led to fewer interactions being judged significant.


   Appendix 2: Assessing the prevalence gradient over deprivation categories
TOP
 Introduction
 Materials and methods
 Results
 Discussion
 Appendix 1: Assessing...
 Appendix 2: Assessing the...
Appendix 3: Poisson regression...
 Acknowledgements
 References
 
The 2003 Health Survey for England (HSE) included a five-level category according to the quintile of the index of multiple deprivation of the respondent’s super-output area (SOA) (a 2001 census subdivision), with quintile 5 for the highest deprivation SOAs. The HSE of 2003 did not include a weighted follow-up survey to assess disease risk by ethnicity, and so ethnicity is recorded broadly. Here a four-way ethnic categorization is used: white, black, Asian and other. Ages are grouped into 19 5-year bands: 0–4, 5–9, 10–14,...,85–89, 90 and over.

Then for each sex separately, logistic regressions are carried out including impacts of age, ethnicity and deprivation quintile. In this way, the effects of deprivation are corrected for any impacts of age and ethnicity on prevalence. As in the Appendix 1 analysis, a fully Bayes approach is used, with a random walk prior on the age effects to smooth irregularities in the observed schedules of diabetes prevalence by age. Thus for 8439 males, let yi = 1 if the subject has doctor diagnosed type 1 or 2 diabetes and 0 otherwise. Then yi ~ Bern({pi}i) (where Bern denotes Bernoulli density) and for ethnic group Ei, age group Ai and deprivation quintile Di, let

Formula

Viewed in terms of the ranges of the categories, j = 1,...,4 (ethnic groups), k = 1,...,19 (age groups) and m = 1,...,5 (deprivation quintiles), the model can be written

Formula

As in Appendix 1, the random walk prior on age effects has the form

Formula
with {gamma}1 ~ N(0, 1000), and the effects centred to zero at each Markov Chain Monte Carlo (MCMC) iteration. The deprivation effects are assumed to follow an incremental gradient, in line with well-documented positive deprivation effects on diabetes prevalence. Thus

Formula

Formula

Formula
where I(a, b) means the interval from a to b, so that sampling is constrained to produce a monotonic gradient. Possible alternatives would be a simple random walk prior or a linear term in deprivation, especially if the division of small areas was more disaggregated [e.g. by index of multiple deprivation (IMD) decile]. For ethnic effects, a normal prior (with a corner constraint for identifiability) is assumed: ß1 = 0, ßj ~ N(0, 1000), j = 2, 4.

As outlined in the main text of the article, IMD quintile-specific ratios to average prevalence, denoted {rho}k, are used to scale ethnic-/age-prevalence rates. These are obtained (at each MCMC iteration) by calculating prevalence probabilities {pi}k = exp({delta}k)/[1 + exp({delta}k)] by quintile, then comparing {pi}k to the average Formula, namely

Formula

The posterior means and 95% confidence intervals (CI) for the male ratios are (starting with the least-deprived quintile) 0.76 (0.65–0.86), 0.83 (0.73–0.94), 0.91 (0.80–1.04), 1.13 (0.97–1.30) and 1.37 (1.19–1.62). For the 10 073 females, the corresponding figures are 0.80 (0.67–0.90), 0.84 (0.70–0.94), 0.93 (0.81–1.04), 1.07 (0.93–1.26) and 1.36 (1.14–1.64).


   Appendix 3: Poisson regression for diabetes mortality
TOP
 Introduction
 Materials and methods
 Results
 Discussion
 Appendix 1: Assessing...
 Appendix 2: Assessing the...
 Appendix 3: Poisson regression...
Acknowledgements
 References
 
Let Yi1 denote male deaths, and Ei1 denote expected deaths (using England 2000 rates), where i = 1,...,354; Yi2 and Ei2 are the same quantities for women.

Then a Poisson regression is used with

Formula
where QMi is the male-prevalence quintile to which area i belongs and ßj, j = 1, 5 are fixed effects. A similar regression is made for female diabetes mortality:

Formula
where QFi is the female-prevalence quintile to which area i belongs. The SMR according to quintile is then 100exp(ßj). A Poisson regression is satisfactory as there is no overdispersion (the mean deviance for males is 326 and for females is 345, whereas N = 354).


   Acknowledgements
TOP
 Introduction
 Materials and methods
 Results
 Discussion
 Appendix 1: Assessing...
 Appendix 2: Assessing the...
 Appendix 3: Poisson regression...
 Acknowledgements
References
 
The analysis in this paper is based on the 1999 and 2003 Health Survey for England Data held at the ESRC Data Archive. Neither the survey depositors nor the UK data archive bear any responsibility for the analysis presented in the paper.


   References
TOP
 Introduction
 Materials and methods
 Results
 Discussion
 Appendix 1: Assessing...
 Appendix 2: Assessing the...
 Appendix 3: Poisson regression...
 Acknowledgements
 References
 

  1. Office for National Statistics. Health Survey for England, 2003. London: The Stationery Office, 2004.
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