Modeling the need for hip and knee replacement surgery. Part 2. Incorporating census data to provide small-area predictions for need with uncertainty bounds

Authors


  • The opinions expressed by the authors are theirs alone and do not represent the opinions of supporting organizations. The developers and funders of the English Longitudinal Study of Ageing and the UK Data Archive do not bear any responsibility for the analyses or interpretations presented here.

Abstract

Objective

To develop methods to produce small-area estimates of need for hip and knee replacement surgery to inform local health service planning.

Methods

Multilevel Poisson regression modeling was used to estimate rates of need for hip/knee replacement by age, sex, deprivation, rurality, and ethnic mix using a nationally representative population-based survey (the English Longitudinal Study of Ageing, n = 11,392 people age ≥50 years). Estimates of need from the regression model were then combined with stratified census population counts to produce small-area predictions of need. Uncertainty in the predictions was obtained by taking a Bayesian simulation-based approach using WinBUGS software. This allows correlations in parameter estimates to be appropriately incorporated in the credible intervals for the small-area predictions.

Results

Small-area estimates of need for hip/knee replacement have been produced for wards and districts in England. Rates of need are adjusted for the sociodemographic characteristics of an area and include 95% credible intervals. Need for hip/knee replacement varies geographically, dependant on the sociodemographic characteristics of an area.

Conclusion

For the first time, small-area estimates of need for hip/knee replacement surgery have been produced together with estimates of uncertainty to inform local health planning. The methodologic approach described here could be reproduced in other countries and for other disease indicators. Further research is required to combine small-area estimates of need with provision to determine whether there is equitable access to care.

INTRODUCTION

Health care planners require estimates of service use and need at a small-area level in order to provide services equitably. For example, in England, primary care trusts (PCTs) are responsible for the planning, commissioning, and delivery of National Health Service services to ensure they are responsive to the needs of the local communities (1). PCT service planning is informed by health equity audits (2) so that evidence of inequalities can be used to inform decision making (3, 4) and identify how fairly services or other resources are distributed in relation to the health needs of different groups and areas.

In both England and Canada, a number of small-area population-based studies have been carried out in an attempt to estimate the population requirement for joint replacement surgery (5–12). However, these studies are conducted in geographically small areas, and estimates of need will vary according to the demographic characteristics of an area. Methods are therefore required to produce small-area estimates of need to inform local health planning.

In the literature, a number of different approaches have been used to generate small-area predictions (13–18). They are all essentially very similar in that estimates of prevalence are obtained from population-based surveys according to different sociodemographic groups (such as age, sex, ethnicity, and deprivation). The prevalence estimates are then applied to small-area ward-level population counts obtained from census data in order to generate prevalence estimates in small areas. Although similar, each method of estimation is slightly different: the PBS (Public Health Observatory, Brent Primary Care Trust, and School of Health and Related Research [University of Sheffield]) diabetes prevalence model developed by the Yorkshire and Humber Public Health Observatory (13) uses estimates of prevalence from various small-area surveys; Twigg et al and Twigg and Moon (14, 15) use a multilevel modeling approach that was possible by assuming that the areas (census wards) for which prevalence estimates are needed are actually recorded as survey variables; whereas Congdon uses Bayesian modeling that allows the incorporation of prior evidence (i.e., evidence of ethnic gradients in coronary heart disease risk) on model covariates that will increase the precision of the prevalence estimate for that variable (16–18).

The aim of this analysis was to use a methodologic approach based on those used by Twigg et al (14), Twigg and Moon (15), and Congdon (16–18) to produce, for the first time, small-area estimates of need for hip and knee replacement surgery in England together with estimates of uncertainty around the predicted rates to inform local health planning. The methods are general and can be used in other health care settings to provide small-area estimates of need for health care services.

MATERIALS AND METHODS

We have previously described how a 2-stage cross-cohort approach can be used to identify people in need of hip and knee replacement and explored inequalities in the need for surgery (19). Briefly, the English Longitudinal Study of Ageing (ELSA) is a nationally representative population-based sample of 11,392 people age ≥50 years living in private households in England. Because the health module of the ELSA contains information on the severity of hip and knee pain and activities of daily living, we were able to assign patients a simplified version of the New Zealand score to assess the severity of their joint disease and identify those in need of surgery.

Although the ELSA data set is a large nationally representative sample, it is not detailed enough in itself to predict need for joint replacement in small areas of England. To generate small-area predictions of need, we fit a multilevel Poisson regression model to the ELSA data set, and then combined the estimates from the model with stratified population counts from the 2001 census. In order to combine estimates from the ELSA with the 2001 census population counts, variables in the 2 data sets must be exactly the same.

Census data set.

For the census data set, we had population counts by 5-year age groups and sex for each of the 7,969 census area statistics (CAS) wards in England. We also had the following indicator variables estimated at the CAS ward level: Index of Multiple Deprivation 2004 deprivation quintiles (weighted to the ward population because each census ward varies in size: 1 [least deprived], 2, 3, 4, and 5 [most deprived]) (20), rurality (urban [population ≥10,000], town and fringe, and village/isolated), and ethnic mix of the area (white [≥10% white and ≤0.5% African American, Asian, and other] and nonwhite [all remaining groups]). For each census ward, we knew which deprivation, rurality, and ethnic group it belonged to. Because wards are nested within districts, this later allowed us to generate district-level predictions of need.

ELSA data set.

The outcome of interest was a binary/dichotomous variable of whether or not the patient was in need of joint replacement. Exposure variables consisted of age, sex, Index of Multiple Deprivation 2004 deprivation quintiles, rurality, and ethnic mix of the area. We only included variables available in the census data set. Other important predictor variables such as obesity or individual social class could not be included because they were not available as ward-level population counts. Variables in our census and ELSA data sets were therefore equivalent. A multivariable Poisson regression model was fitted in WinBUGS (MRC Biostatistics Unit, Cambridge, UK) to examine the association between rates of need for joint replacement and each of the sociodemographic variables. Separate models were fitted for hip and knee replacement (see Supplementary Appendix A, available in the online version of this article at http://www3.interscience.wiley.com/journal/77005015/home). Analyses were weighted to control for bias from nonrandom nonresponse in the ELSA sample. Where evidence of effect modification was observed, interaction terms were included. The hierarchical structure of the data consists of 11,392 individuals nested within 2,913 wards within 348 districts. Because there was no evidence of clustering across either wards or districts for hip and knee models, the simpler fixed-effects regression model was used.

Generating small-area predictions.

The method of generating small-area predictions of need in each district is summarized in Figure 1. The estimation process is outlined below.

Figure 1.

Procedure to generate district-level predictions. ELSA = English Longitudinal Study of Ageing; CAS = census area statistics; IMD = Index of Multiple Deprivation.

Step 1: manipulate the ELSA data set.

Having fitted the ELSA models, the first step was to add up the estimates to work out the predicted log rates in each possible age, sex, deprivation, rurality, and ethnic group (there are 300 such groups) and their associated standard errors. This formed our ELSA data set, which produced predictions Pj for group j (see Appendix B, available in the online version of this article at http://www3.interscience.wiley.com/journal/77005015/home).

Additional step if the multilevel model was used.

If evidence of district-level variation was observed (overall rates of need varied across districts over and above that explained by the variables in the regression model), then we could incorporate this extra variation into the predictions process as follows: from the multilevel model we would have had a data set of district residuals Dk for district k. For each district, we would add the district residual to each of the 300 predicted log rates. The log rates were then exponentiated to convert them into rates.

Step 2: manipulate the census data set.

The next step was to reshape the census data set so that we had the estimated population count in each of the 300 age, sex, deprivation, rurality, and ethnic groups for each of the 7,969 CAS wards, forming a (300 × 7,969) data matrix (see Appendix B, available in the online version of this article at http://www3.interscience.wiley.com/journal/77005015/home). For each ward, we could also identify which district it belonged to in the data set. This formed the census data set.

Step 3: generate ward-level predictions.

We now needed to apply the predicted rates in each of the 300 groups in the ELSA data set to the population counts in each of the 300 groups in the census data set. We then summed across the rows to get the total expected numbers of people in need in each census ward. From the census data set, if we summed across the rows, we got the total number of people in the population in each census ward. The expected counts were then divided by the overall total population count in each ward to get a predicted rate of need for joint replacement in each ward (see Appendix B, available in the online version of this article at http://www3.interscience.wiley.com/journal/77005015/home).

Step 4: generate district-level predictions.

If we wanted to generate a predicted rate of need in each district, because we knew which district each census ward belonged to, we simply summed the expected counts in each district. Then we summed the total number of people in the population in each district. Dividing the expected count over the total population count in each district, we got the predicted rate in each district (see Appendix B, available in the online version of this article at http://www3.interscience.wiley.com/journal/77005015/home).

Generating estimates of precision around district-level predictions.

It was important to ensure that we could produce an estimate of precision around the predicted small-area rates of need. Unfortunately, we could not just add up the estimates from the regression model because they were estimated jointly and hence correlated. A way around this problem was to use the simulation environment available in the statistical software WinBUGS. When fitting the regression model in WinBUGS, all of the parameters were sampled from a joint distribution that incorporated the joint uncertainty in, and correlation between, model variables. We could then form any function of the parameters at each iteration, capturing this joint uncertainty between model parameters.

Implementation.

A fixed-effects Poisson model was fitted in WinBUGS, version 1.4.3 (21, 22), to generate log rates of need for joint replacement using the ELSA data (see Supplementary Appendix A, available in the online version of this article at http://www3.interscience.wiley.com/journal/77005015/home). Each variable in the model was given a prior distribution. In a Bayesian analysis, the distribution of the model parameters is obtained by combining a likelihood function with the prior distribution for the parameters to obtain the posterior distribution. In this case, flat uninformative priors were used, so the posterior density was dominated by the likelihood function, and hence provided very similar inference to likelihood-based classic methods. Markov chain Monte Carlo methods were implemented using Gibbs sampling in WinBUGS to evaluate the posterior distribution, which simulated a new value for each parameter in the model from its conditional distribution, assuming the current values of the other parameters were the true values. Convergence was assessed using the Brooks and Gelman diagnostic tool (23) and considered adequate after running 10,000 iterations in all models. For each model, a further sample of 4,000 simulations was then run, on which the results are based. Summary statistics for the model variables were obtained based on 4,000 iterations run after convergence had occurred, which formed a posterior distribution for each variable.

In order to generate the predicted rates of need in each district, we extended the model code in WinBUGS to generate the predicted rates in each of the 300 possible age, sex, deprivation, rurality, and ethnic groups (step 1). This was done using logical expressions to create new variables that summed the betas in the model to estimate the 300 predicted rates. The 300 predicted rates were then applied to population counts from the census (step 2) to get the expected number of people in need in each of the 300 age, sex, deprivation, rurality, and ethnic groups for each of the 354 districts (step 3). The expected counts were then summed together to get the total number of people in need in each of the 354 districts. Then the expected count was divided by the total number of people in the population in each district to get the predicted rate of need in each district (step 4).

This can all be run in the same WinBUGS simulation, enabling us to generate the predicted rate of need for joint replacement together with credible intervals for each district that captured the correlations imposed by joint estimation of the betas. WinBUGS produced 4,000 iterations (predicted rates) for each of the 354 districts, forming a posterior distribution. The overall predicted rate for each district was therefore the mean of the posterior distribution of that district, along with the 2.5% and 97.5% centiles, forming a 95% credible interval for the predicted rates. Due to the large number of logical calculations required, we exported the WinBUGS model-simulated values (Convergence Diagnostic and Output Analysis) into the statistical software package R (R Foundation for Statistical Computing, Vienna, Austria) and performed the logical operations on a high-powered computer cluster.

RESULTS

Separate models of need for both hip and knee replacement have been fitted in WinBUGS and the predicted rate of need in each of the 354 districts in England has been generated. Geographic variation across districts in the rates of need for hip and knee replacement has been displayed on maps of England (Figures 2 and 3). District rates have been split into 5 equally sized groups (quintiles) in order to display areas with the highest and lowest rates of need. Need for joint replacement is higher in urban areas such as London, Birmingham, and the South West peninsula. Need is also higher in Northern areas such as Liverpool, Manchester, and Newcastle-upon-Tyne, as may be expected in industrialized areas. Generally, need for joint replacement is lower in the South than in the North of England. Rates are also lower in a circle of affluent areas in England, Home Counties, areas that border or surround London. The geographic distribution of rates of need across districts of England is similar for both hip and knee replacement.

Figure 2.

Rate of need for hip replacement per population of 1,000 (quintiles) across the 354 districts in England. This work is based on data provided through EDINA UK BORDERS, with the support of the Economic and Social Research Council and the Joint Information Systems Committee, and uses boundary material that is copyright of the Crown.

Figure 3.

Rate of need for knee replacement per population of 1,000 (quintiles) across the 354 districts in England. This work is based on data provided through EDINA UK BORDERS, with the support of the Economic and Social Research Council and the Joint Information Systems Committee, and uses boundary material that is copyright of the Crown.

The overall rate of need in those age ≥50 years in England for hip replacement was 46.8 per 1,000; for knee replacement it was 63.5 per 1,000. Table 1 shows the top 10 highest and lowest rates of need for hip and knee replacement across the 354 districts in England. For hip replacement, the lowest rate of need was in Wokingham (23.0 per 1,000), with the highest rate in Hackney (75.6 per 1,000). For knee replacement, need was lowest in Wokingham (31.1 per 1,000) and highest in Easington (116.5 per 1,000). For hip replacement, there is a 3-fold difference between rates of need across districts, but there is greater geographic variation in rates of need for knee replacement, with a 5-fold difference in the highest and lowest rates of need in districts across England.

Table 1. Overall rate and top 10 highest and lowest rates of need for hip and knee replacement, adjusted for sociodemographic variables
DistrictAdjusted rate per 1,000 (95% credible interval)
Ten lowest 
 Hip replacement 
  Wokingham (00MF)22.98 (17.43–29.22)
  Hart (24UG)23.06 (17.42–29.37)
  East Hertfordshire (26UD)24.55 (19.10–30.61)
  Uttlesford (22UQ)24.71 (18.61–31.73)
  South Northamptonshire (34UG)24.94 (18.81–32.07)
  South Cambridgeshire (12UG)25.00 (18.49–32.65)
  Mid Sussex (45UG)25.34 (19.44–32.01)
  Rutland (00FP)25.37 (18.82–33.05)
  Surrey Heath (43UJ)25.49 (20.04–31.61)
  West Oxfordshire (38UF)25.75 (19.51–32.95)
 Knee replacement 
  Wokingham (00MF)31.08 (24.09–38.64)
  Hart (24UG)31.24 (24.31–38.80)
  East Hertfordshire (26UD)33.14 (26.43–40.34)
  Uttlesford (22UQ)33.53 (26.10–41.87)
  South Cambridgeshire (12UG)33.62 (25.68–42.80)
  South Northamptonshire (34UG)33.81 (26.22–42.37)
  Surrey Heath (43UJ)33.97 (27.31–41.30)
  Rutland (00FP)34.70 (26.68–44.10)
  Chiltern (11UC)34.73 (28.43–41.61)
  Mid Bedfordshire (09UC)34.77 (28.65–41.56)
Ten highest 
 Hip replacement 
  Sandwell (00CS)68.67 (59.12–78.80)
  Nottingham (00FY)68.68 (59.17–78.81)
  Kingston upon Hull, City of (00FA)69.16 (58.61–80.70)
  Liverpool (00BY)70.12 (59.85–81.21)
  Tower Hamlets (00BG)72.78 (60.87–85.83)
  Manchester (00BN)74.06 (61.99–87.28)
  Newham (00BB)75.32 (62.18–89.77)
  Easington (20UF)75.43 (60.42–93.18)
  Islington (00AU)75.56 (62.45–90.04)
  Hackney (00AM)75.60 (62.42–90.12)
 Knee replacement 
  Stoke-on-Trent (00GL)96.83 (85.72–108.90)
  Liverpool (00BY)98.25 (86.16–110.92)
  Kingston upon Hull, City of (00FA)98.99 (86.37–112.59)
  Tower Hamlets (00BG)102.89 (88.75–117.97)
  Wear Valley (20UJ)103.34 (86.77–122.42)
  Manchester (00BN)104.60 (90.22–119.86)
  Islington (00AU)107.15 (91.78–124.02)
  Newham (00BB)107.25 (91.71–124.00)
  Hackney (00AM)107.31 (91.82–124.30)
  Easington (20UF)116.54 (95.87–139.97)

Sensitivity analyses.

To identify whether or not a person is in need of joint replacement surgery in the ELSA data set, we used the New Zealand score out of 80, with a cutoff of 48 (19). Different choices of threshold will classify those with more/less severe disease as being in need of surgery. We therefore conducted a sensitivity analysis, repeating the analyses to generate small-area predictions in each district of England using both higher and lower choices of threshold (scores of 43 and 53, respectively) in the ELSA regression model. Although the overall rate of need for hip and knee replacement surgery differed depending on the cutoff used, the geographic pattern remained unchanged (results not shown). Regardless of the choice of threshold, the same districts are identified as having high or low rates of need.

DISCUSSION

To our knowledge, this is the first time small-area estimates of need for hip and knee replacement surgery have been produced for a national population, and the information should be of use to health care planners and to inform local health equity audit. Rates of need have taken into account the sociodemographic profile of each district and include estimates of precision (95% credible intervals). In our analysis, there was no evidence of clustering across districts, but by using a multilevel modeling approach, the methods presented here could incorporate any additional district variation (beyond that explained by variables in the regression model) into the predictions process. The methodologic approach described here can be used to produce small-area estimates of need in other countries if population-based data on need and small-area population counts are available, as well as for other important conditions.

In this study, the overall rate of need in those age ≥50 years in England for hip replacement was 46.8 per 1,000, and for knee replacement was 63.5 per 1,000. Respectively, this compares with 13.5 per 1,000 and 20.4 per 1,000 in those age >55 years in the North Yorkshire study (5, 6), 15.2 per 1,000 and 27.4 per 1,000 in those age ≥35 years in the Somerset and Avon Survey of Health (7, 8), and 34 per 1,000 and 51 per 1,000 in those age ≥65 years in the Wiltshire and Sheffield study (9, 10). There are a number of reasons as to why the overall rates of need for joint replacement vary between studies. First, rates of need will vary geographically, depending on the sociodemographic characteristics of an area. Each of the other studies has been conducted in different areas of the country, whereas this study uses a nationally representative sample. Second, the different scoring systems used to identify people in need of joint replacement and different choices of threshold will lead to different estimates of need for surgery. Third, prior studies have excluded patients with comorbidities from the estimate of need that may preclude them from receiving surgery. We included all of the patients, because due to improvements in modern anesthesia and surgical techniques, more people may now be eligible for surgery; hence, our overall estimate of prevalence is higher.

The benefit of using the ELSA to estimate need for joint replacement surgery is that it is a large nationally representative sample that allows us to explore geographic variation in rates of need, but there are a number of limitations, as previously described elsewhere (19). An important limitation of this analysis is that our estimates of need were not adjusted for willingness and fitness for surgery. Data on comorbidities that may make a person unfit for surgery are available in the ELSA, but it is unclear what would make a patient an unsuitable candidate for surgery, given improvements in modern anesthesia, surgical techniques, and prosthesis survival. We had no information on patient willingness. There are arguments for and against excluding those unwilling for surgery from the estimates of need. On one hand, there is a need to know patient preference for surgery if attempting locally based health needs assessment in order to know how many people would accept the operation if offered, so that in the short term, local health planners can allocate adequate levels of provision. On the other hand, local planners are meant to assess population needs in order to provide services equitably, and because willingness is a determinant of why inequity exists, providing only for those who would accept surgery if offered will not tackle inequity.

The methodologic approach to generating small-area predictions outlined in this study could be performed using conventional statistical software such as Stata (StataCorp, College Station, TX), or in data management packages such as Microsoft Access (Microsoft, Redmond, WA). It is just a case of data manipulation to generate overall rates of need in small areas. The difficulty is in creating estimates of precision around the predicted rates. For example, in stage 1 of the methodologic approach, we add up the estimates from the ELSA regression model to work out the predicted log rates of need in each of 300 possible age, sex, deprivation, rurality, and ethnic groups, which raises the question of how to calculate the standard errors of these 300 predicted log rates. Although the ELSA regression model provides standard errors for each model coefficient, we have no estimate of the covariance between each of the model parameters. A naive approach that ignores this covariance would overestimate the standard errors of the 300 predicted log rates. This is why we chose to use the Bayesian analysis software WinBUGS, because all of the parameters are sampled from a joint distribution that incorporates the joint uncertainty in, and correlation between, model variables. However, it is important to note that computation time is an issue due to the high dimension of calculations required to form all of the predictions, and the feasibility of the methods will be challenged because of the number of districts and wards that predictions require for increase. However, once the calculations have been carried out, then the predictions are available for all of the small areas in the country, and effort does not need to be duplicated by each local health care planner (PCTs in England). A central government body or academic unit could be commissioned to do the work and then disseminate the results, making them accessible to the public. Although the methods may be complex, the results are relatively easy to interpret.

A limitation of the maps shown in this study is that they do not display the precision with which the rates of need have been estimated. Finding a solution to this problem is an area for future research to address. Possible approaches would be to display a second parallel map of precision next to the map of disease rates, such as a map of standard errors; a cartogram (24), where the size of the district is proportional to the coefficient of variation (a normalized measure of dispersion defined as the ratio of the SD to the mean), where higher values indicate greater dispersion; a contour map, where higher areas have greater precision; or even a spatially smoothed map that allows areas with high reliability to retain their real value while areas with low reliability are smoothed, either toward the national/regional mean or toward a more local mean, perhaps of surrounding areas. However, such proposed methods are difficult to either implement or interpret, or both.

In this study, we have demonstrated that it is possible to produce maps displaying small-area estimates of need for hip and knee replacement surgery that can be used to inform local health planning. The methodologic approach we describe could be reproduced in other countries if data on need and small-area population counts are available, and for other important clinical indicators. The results of this study should be of use to local health planners in monitoring inequalities in the need for hip and knee replacement surgery, but note that inequality does not necessarily imply inequity. Further work is required to determine whether estimated provision of joint replacement (25) matches need across sociodemographic groups to assess whether there is evidence of inequity.

AUTHOR CONTRIBUTIONS

All authors were involved in drafting the article or revising it critically for important intellectual content, and all authors approved the final version to be submitted for publication. Dr. Judge had full access to all of the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis.

Study conception and design.Judge, Sandhu, Ben-Shlomo.

Acquisition of data.Judge, Sandhu, Ben-Shlomo.

Analysis and interpretation of data.Judge, Welton, Ben-Shlomo.

Acknowledgements

We would like to thank Dr. Mary Shaw at the Department of Social Medicine, University of Bristol, for support and advice throughout the project, Dr. Richard Harris for help and advice with the Geographical Information Systems software, and Professor Kelvyn Jones for statistical advice on multilevel modeling, both from the Department of Geographical Sciences, University of Bristol.

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