Health Care Management Science

, Volume 14, Issue 3, pp 253–261

Modelling catchment areas for secondary care providers: a case study

Authors

    • Centre for Workforce Intelligence
  • Jessica Wardlaw
    • Department of Civil, Environmental and Geomatic EngineeringUniversity College London
  • Susan Crouch
    • Dr Foster Intelligence
  • Michelle Carolan
    • Dr Foster Intelligence
Article

DOI: 10.1007/s10729-011-9154-y

Cite this article as:
Jones, S., Wardlaw, J., Crouch, S. et al. Health Care Manag Sci (2011) 14: 253. doi:10.1007/s10729-011-9154-y
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Abstract

Hospitals need to understand patient flows in an increasingly competitive health economy. New initiatives like Patient Choice and the Darzi Review further increase this demand. Essential to understanding patient flows are demographic and geographic profiles of health care service providers, known as ‘catchment areas’ and ‘catchment populations’. This information helps Primary Care Trusts (PCTs) to review how their populations are accessing services, measure inequalities and commission services; likewise it assists Secondary Care Providers (SCPs) to measure and assess potential gains in market share, redesign services, evaluate admission thresholds and plan financial budgets. Unlike PCTs, SCPs do not operate within fixed geographic boundaries. Traditionally, SCPs have used administrative boundaries or arbitrary drive times to model catchment areas. Neither approach satisfactorily represents current patient flows. Furthermore, these techniques are time-consuming and can be challenging for healthcare managers to exploit. This paper presents three different approaches to define catchment areas, each more detailed than the previous method. The first approach ‘First Past the Post’ defines catchment areas by allocating a dominant SCP to each Census Output Area (OA). The SCP with the highest proportion of activity within each OA is considered the dominant SCP. The second approach ‘Proportional Flow’ allocates activity proportionally to each OA. This approach allows for cross-boundary flows to be captured in a catchment area. The third and final approach uses a gravity model to define a catchment area, which incorporates drive or travel time into the analysis. Comparing approaches helps healthcare providers to understand whether using more traditional and simplistic approaches to define catchment areas and populations achieves the same or similar results as complex mathematical modelling. This paper has demonstrated, using a case study of Manchester, that when estimating the catchment area of a planned new hospital, the extra level of detail provided by the gravity model may prove necessary. However, in virtually all other applications, the Proportional Flow method produced the optimal model for catchment populations in Manchester, based on several criteria: it produced the smallest RMS error; it addressed cross-boundary flows; the data used to create the catchment was readily available to SCPs; and it was simpler to reproduce than the gravity model method. Further work is needed to address how the Proportional Flow method can be used to reflect service redesign and handle OAs with zero or low activity. A next step should be the rolling out of the method across England and looking at further drill downs of data such as catchment by Healthcare Resource Group (HRG) rather than specialty level.

Keywords

Proportional FlowFirst Past the PostGravity modelCatchment areasCatchment populationsSecondary care providersProviders

1 Introduction

The modelling of hospital catchment areas is important for both Primary Care Trusts (PCTs) and Secondary Care Providers (SCPs) i.e. hospitals, for many reasons. Firstly they are useful planning tools because hospitals serve more than one administrative area and catchment areas can be used for resource allocation for beds, operating theatres and nurses [11] (Flowers [7, 8]). Secondly, they can be used in needs assessments to compare, for example, beds per capita and activity rates. Thirdly, Foundation Trusts are legally required to ensure that the membership of any public constituency is “representative of those eligible for such membership” [15]; for this they need to understand the origin of their patients, which can only be achieved by modelling their catchment.

Apportioning populations to hospitals is not trivial because catchments are not coterminous with the administrative areas used for population estimates. Furthermore, multiple factors influence where people are admitted to hospital; people often use services outside of their catchment area, resulting in poorly-defined catchment boundaries [30]. Catchment areas can be defined as follows: “For a given hospital or unit and for a particular specialty the catchment population is that group of persons who would attend the hospital or unit were they to require treatment under that specialty” [30], hence catchment populations are also called “population at risk” [31]. A catchment population is distinctively different to a catchment area, which is defined as “the region from which the clients of a particular health facility—or a service within it—are drawn” [31].

Modelling catchment populations requires allocating administrative populations (e.g. OAs) to SCPs. Accordingly, the minimum data requirements are: patient admission data referenced to place of residence (e.g. postcode) and the admitting health care provider [31]; resident population estimates, and geographical unit. Simplistic approaches have been used to model catchments thus far (using both elective and non-elective admissions) e.g. PCT boundaries or the area within 30 minutes’ drive time of the SCP. In reality, SCPs need to understand the origin of their service demand, which requires more sophisticated approaches. Two methods commonly used by the National Health Service (NHS) in England are: ‘First Past the Post’ (FPTP) and the Proportional Flow “Norris-Bailey” (PF) model [1, 24]. This paper aims to compare these methods to a spatial interaction or gravity model which is more sophisticated and accounts for travel time, which is an increasingly important criterion on which patients decide which hospital to attend. These methods will now be described in more detail.

FPTP attributes the whole population of an area to the SCP admitting the most patients from that area [5, 31]. The dominant SCP is assigned according to the SCP with the greatest proportion of activity. This calculation provides a simple estimate of the probability of attendance at each SCP. Variance in calculations can be smaller than using other methods, although catchment populations may be underestimated if there is zero flow in some areas. In this case, catchment populations must be assigned based on proximity.

PF allocates populations to a SCP based on the proportion of admissions to that SCP [31]. This method is potentially more accurate than FPTP because the calculation is more detailed. However, like FPTP, areas with zero flow must be assigned a SCP based on proximity. This method assumes that admission rates within areas are constant but admission rates between areas do not have to be constant [30]. This assumption is more valid where small units of population are used, thus increasing the variance of results. PF is recommended in the literature but its use for resource allocation and planning purposes has been criticised [9]; districts with small populations may erroneously appear to be adequately served and, furthermore, it does not account for the age-sex profile of patients admitted compared to the district population, unless analysis concerns specialties relating to specific population subsets such as Geriatrics and Gynaecology. This method also assumes that resources can be allocated to SCPs in the same proportions as historical admissions [34].

In the last 20 years, several gravity models have been constructed to model hospital catchments because patients are increasingly choosing hospitals based on their accessibility [3, 14, 18, 20, 34]. The name ‘gravity’ model arises from their equivalence with Newton’s law of gravity: force of attraction is proportional to the product of the masses (or size) of the two bodies involved and inversely proportional to a power of the distance between them [2, 28]. Gravity models were first used to examine patient flows to health care facilities in the United States in the late 1960s [2123].

A gravity model might estimate the number of patients who visit hospital j from region i as
$$ {E_{{i,j}}} = g\frac{{{M_i}{B_j}}}{{D_{{i,j}}^{\lambda }}}, $$
(1)
where Mi is a measure of the ‘mass’ or level of health need for region i. Population, number of hospital visits and number of people with a specific condition have all been used for Mi. Bj is the ‘mass’ of hospital j and is often the number of hospital beds. Di,j is the distance between the region and hospital. Straight line distance and car travel times are commonly used measures of distance (for example, [4, 10, 17]). The constants, g and λ, need to be estimated from historical data on patients flows. The reader is referred to Bailey and Gatrell [2, 4] for methods used to estimate these constants.

Simply explained, these models assume that the flow of patients from an area of residence (region), i, to a hospital (destination), j, is proportional to the demand for services (i.e. relative morbidity of the population, based on their age and social structure), the capacity of hospital j to treat patients, and is inversely proportional to a power of the accessibility of hospital j (i.e. distance or travel time) for the residents of region i [4, 33].

These assumptions tend not to predict patient flows satisfactorily because supply and demand rarely match due to the absence of formally defined catchment areas. In metropolitan areas, where patients have more choice between SCPs, the boundaries are highly permeable. Gravity models account for this by modelling and parameterising factors that constrain cross-boundary flow, until the observed number of patients being admitted has been modelled [2]. Constraints could include a certain total number of people who must flow from each origin or a particular number of patients who must flow to each destination; the total ‘cost’ of travel in the whole system may also be fixed.

Gravity models attempt to capture the pattern of flow resulting from unconstrained patient choice and assume that the probability of patients choosing a particular hospital is independent of other possible destinations. While health applications have tended to use unconstrained gravity models, origin-constrained gravity models may be used to model changing impacts of supply at destinations [4]. Gravity models have also been adapted to investigate the hierarchical structure of hospital services and the influence of the many sources of variation that result from the complex nature of patient flows at different geographical scales, drawing comparisons to Central Place Theory [5, 19]. In more recent years location-allocation models have also been developed, which use the principles of gravity models to locate facilities on a network rather than in continuous space (e.g. [1114]) and have been used to explore different concepts of equity of access by modelling redistribution of hospital supply using varying assumptions about patients’ behaviour [27].

Huff [16] proposed a model to estimate the probability of a consumer travelling from a region to a particular shopping centre. Huff argued that a catchment area for a shopping centre should be all regions with a probability of purchasing a product from that shopping centre greater than zero. Adapting Huff’s model, the probability of a patient from region i visiting hospital j is
$$ {p_{{i,j}}} = \frac{{\frac{{{B_j}}}{{D_{{i,j}}^{\lambda }}}}}{{\sum\limits_{{k = 1}}^b {\frac{{{B_j}}}{{D_{{i,k}}^{\lambda }}}} }}, $$
(2)
and the number of patients from region i visiting hospital j is estimated as
$$ {E_{{i,j}}} = {p_{{i,j}}}\bullet {C_i}, $$
(3)
where Ci is the number of patients from region i. Huff’s approach was used by Gu et al. [10] to identify optimal locations for preventive health care facilities so as to maximise participation.

Other methods have been used to model catchment populations, such as the Resource Allocation Working Party Net Flow formula, which was used by the Department of Health and Social Security in England for their regional allocations [30, 34] but it has already been sufficiently scrutinised and is no longer widely in use [29]. Cooper et al. [6] used an adaptive radius; however this method was rejected for this paper as its estimation was believed to be too complex for this application. A very simple approach is to define a catchment area as the mid-point between two trusts. Whilst this is easy to understand and implement, it was rejected as it generates a simple boundary. This boundary is unlikely to follow the geographic units (e.g. OAs) used in the analysis, forcing an arbitrary decision of whether or not to include geographical units in the catchment area.

The aim of this paper is to compare the three methods described, to determine whether the detail and granularity provided by the more comprehensive catchment models are worth the additional work involved. We ask the question, “Do more complex methods provide further insight or do more simplistic and reproducible approaches suffice?”

2 Method

The methods outlined above are now applied to a case study of hospital admissions in the Manchester metropolitan area in England where there is a large urban population who have access to a variety of hospital trusts.

All three methods were calibrated using routine administrative data from 2005/06 to 2008/09 to create their catchment areas. Data was obtained from the Secondary Uses Service (SUS), which is the single source of comprehensive data to enable a range of reporting and analyses for the English NHS. The data is derived from the commissioning datasets, which providers of NHS care must submit and make available to commissioners. Two different surgical/specialty areas were chosen to model the catchment areas. It was important to look at both elective (pre-booked) and non-elective (emergency, transfer or maternity) admissions to account for the effect upon the size and shape of the catchment areas. One might expect the non-elective catchment boundary to extend farther than the elective catchment boundary due to the nature of an elective pre-booked admission and the ability to plan for it with many decisions based on travel time.

Analysis was carried out at the OA level to achieve highest potential accuracy in the results. OAs are the smallest unit of geography at which the Office for National Statistics (ONS) collect Census data, each one representing a minimum of 40 resident households and 100 residents, although the recommended size was 125 households [25]. The increased accuracy and spatial resolution achieved by using small areas must however be weighed against the error introduced by small numbers and admission rate variability. To account for this, elective admissions for the specialty Trauma and Orthopaedics was the first topic area chosen for comparison due to its high volumes and large percentage of planned activity. The second area chosen for comparison was all non-elective surgery. Again, to ensure high volumes, all procedural admissions were analysed.
  1. 1.

    First Past the Post Method

    ONS population estimates for 2008 at OA level were assigned to a SCP if they had the highest number of unique patients.

     
  2. 2.

    Proportional Flow Method

    The number of unique patients from each OA visiting each SCP was divided by the total number visiting all SCPs to create a proportion, which was then assigned to each SCP.

     
  3. 3.

    The Gravity Model

    The gravity model was implemented using Huff’s [16] approach described in Eqs. 2 and 3. The statistical package R version 2.10.1 was used to estimate the parameters. The number of general and acute beds was used to represent the mass of a hospital Bj and travel time in minutes was used as a measure for distance, Di,j.

     

The hospital catchment area could be defined as the collection of regions where the probability of someone visiting the hospital exceeds some critical value. The choice of this value would depend on the application. Huff [16] would argue that this critical value should be zero.

The gravity model estimates them in such a way that predicted flows reproduce exactly the total observed flow from each region to each destination. In this way, doubly constrained models describe rather than explain observed flows. However, the distance parameter d quantifies the relative ability of distance (and by implication, cost of travel) to be an obstacle to spatial interaction, and this can be useful information. These kinds of models can be used to predict what flows will result if certain changes are made in the system (e.g. [4]).

3 Results and analysis

Figure 1 shows the results of the FPTP method for elective Trauma and Orthopaedic admissions in the Manchester region. The map shows the region split into different shaded blocks (i.e. SCPs) with many areas neatly fitting to PCT boundaries; though there is some erosion. It can be seen that Manchester PCT is nearly evenly split into thirds by the three main local SCPs. In a couple of areas private SCPs can be seen.
https://static-content.springer.com/image/art%3A10.1007%2Fs10729-011-9154-y/MediaObjects/10729_2011_9154_Fig1_HTML.gif
Fig. 1

Catchment boundaries for elective Trauma and Orthopaedic admissions produced by the ‘First Past the Post’ method

Figure 2 shows a similar, yet neater picture to Fig. 1. Again, similar to the catchment areas produced for elective Trauma and Orthopaedic admissions, a number of SCPs’ catchments follow the PCT boundary line; however there is less erosion than in Fig. 1. The transition between SCPs is much clearer and defined in the non-elective surgery map (Fig. 2) than in the elective Trauma and Orthopaedic map (Fig. 1); there is less cross-boundary flow.
https://static-content.springer.com/image/art%3A10.1007%2Fs10729-011-9154-y/MediaObjects/10729_2011_9154_Fig2_HTML.gif
Fig. 2

Catchment boundaries for non-elective surgery admissions produced by the ‘First Past the Post’ method

Figures 3 and 4 show the catchment area for South Manchester NHS Foundation Trust for elective Trauma and Orthopaedic admissions and non-elective surgery using the PF method. It can be clearly seen in both maps that this method captures cross-boundary flows unlike the simplistic FPTP method which very nearly follows PCT boundaries (Figs. 1 and 2). The maps show a very similar concentration of admissions to FPTP, with the highest levels of concentration between 75% and 100% of admissions. It is interesting to see just how far reaching and more concentrated the non-elective catchment area is compared to the elective. The non-elective surgery map (Fig. 4) shows Proportional Flows are considerably more widely dispersed than the elective Trauma and Orthopaedic map (Fig. 3). The hospital site in the non-elective surgery map (Fig. 4) appears to be surrounded by significantly more OAs of high concentration than the elective Trauma and Orthopaedic map shown in Fig. 3, which had varying levels of concentration. Figure 3 shows that there is not a linear relationship between the proportion of elective admissions and distance from the SCP. This may suggest that referrals are in fact based on habit and not on distance, a major assumption of the gravity model.
https://static-content.springer.com/image/art%3A10.1007%2Fs10729-011-9154-y/MediaObjects/10729_2011_9154_Fig3_HTML.gif
Fig. 3

Catchment boundaries for elective Trauma and Orthopaedic admissions produced by the Proportional Flow Method

https://static-content.springer.com/image/art%3A10.1007%2Fs10729-011-9154-y/MediaObjects/10729_2011_9154_Fig4_HTML.gif
Fig. 4

Catchment boundaries for non-elective surgery admissions produced by the Proportional Flow Method

The gravity model was used to forecast the market share for both the elective Trauma and Orthopaedic admissions and non-elective surgery data. Figure 5 combines these forecasts to show an overall market share for the University of South Manchester NHS Foundation Trust as calculated by the gravity model. This market share would be combined with actual or expected number of admissions, for each OA, to produce a forecast of actual numbers of patients who attend the hospital. In any particular direction, the gravity model produces forecasts that steadily decline as travel time increases. Therefore, it does not show the anomalies present in the Figs. 1, 2, 3 and 4. This is both a strength and weakness. Its strength is that it reduces the statistical fluctuations that we would expect to find when dealing with small areas. On the other hand, it masks important anomalies, which may be due to GPs or patients with a strong preference for a particular hospital in a particular area.
https://static-content.springer.com/image/art%3A10.1007%2Fs10729-011-9154-y/MediaObjects/10729_2011_9154_Fig5_HTML.gif
Fig. 5

Market share % for University of South Manchester NHS Foundation Trust for elective T&O and all non-elective surgery admissions

Root Mean Square (RMS) error, also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. This value was calculated for each method for comparative purposes. The results are presented in Table 1.
Table 1

Root of the mean square error for catchment boundary models

Root of the mean square error

First Past the Post

Proportional Flow

Gravity model

Elective Trauma and Orthopaedics

3.13

1.00

1.31

Non-elective surgery

2.69

0.86

2.48

In order to compare the accuracy of each model, their performance was evaluated against SUS data from 2009 for activity to South Manchester NHS Foundation Trust, for both elective Trauma and Orthopaedics and non-elective surgery, which was held back from the creation of the catchment area models. Each model was then used to predict patient flows to the Trust for that year. Table 1 shows the RMS error of the results of the forecasted activity produced by each model against the actual activity flows to the Trust. Of the three methods, the Proportional Flow method produced the smallest RMS error for both elective Trauma and Orthopaedic activity and non-elective surgery (1.00 and 0.86 respectively) and therefore the most accurate result. FPTP had the greatest RMS error for both areas analysed (3.13 and 2.69), suggesting this to be the least accurate measure.

4 Discussion

Each method was evaluated against assessment criteria as presented in Table 2.
Table 2

Evaluation of model results

 

First Past the Post

Proportional Flow

Gravity model

Simplicity—is the method easy to reproduce?

Yes

More detailed than FPTP

More detailed than PF

What is the coverage like?

Clear geographical boundaries created

Catchment area can be quite widespread

Catchment area can be quite widespread

Does the method address cross-boundary flows?

No

Yes

Yes

Can you easily map more than one SCP on one map?

Yes

No

No

Can it be used to predict catchment areas for new SCPs?

No

No

Yes

The chosen model must be simple so that it can be easily understood by SCP Boards. FPTP is the simplest of the three models assessed, with the PF and gravity models providing increased detail. Gravity models also use drive time (from region to destination) which adds further uncertainty into the results; the further the distance from region to destination, the greater the potential for the drive time to be inaccurate.

The usefulness of the model’s outcome should also be assessed, with respect to whether the model generates clearly defined boundaries or boundaries that cover a large area. FPTP creates very clearly defined boundaries that match those of administrative areas surrounding the SCP; the PF and gravity models cover much larger areas. Once calibrated, it is clear that the gravity model takes into account only the mass of the hospital and the distance between a hospital and a region. Therefore, it could be most useful for estimating the potential catchment area for a new hospital.

The model should also account for cross-boundary flows. FPTP simply allocates each OA to one hospital trust whereas the PF and gravity models allow for modelling of patients being referred across PCT boundaries.

The catchments generated should also be easy to visualise. FPTP is easy to map because it simply allocates each OA to one SCP. PF is more difficult to map because it shows the percentage of OA admissions going to each SCP, and it is difficult to visualise more than one SCP on the same map. It is possible to apply transparencies to the colours but this mixes the colours, rendering the legend difficult to interpret. Choropleth maps such as these can also be biased because different methods may be used to calculate the data intervals used for shading, with each method producing slightly different visualisations. The shading should represent the distribution of the dataset as accurately as possible.

An important limitation of all three methods is that they require relatively large amounts of data to drive them. In order to have sufficient volumes, we have used 5 years’ data. However, during this time, a hospital’s catchment area may change due to a range of factors including service redesign or even damage to a hospital’s reputation due to adverse media coverage. Alternative methods would be needed to detect such changes (e.g. [26]).

The area surrounding Manchester was chosen for the area of analysis as it has a mixture of urban and rural regions. It also has three NHS SCPs competing in a relatively small area, which enables the strengths and weaknesses of the methods to be illustrated without generating over-complicated maps. Whilst we assume the model performance will be indicative of very rural areas, or areas with many more competing hospitals like London, this has not been proven. In some areas, such as London, it may be more appropriate to use public transport travel times rather than drive times as a measure of hospital accessibility.

5 Conclusion

This paper has demonstrated that when estimating the catchment area of a planned new hospital, the extra level of detail provided by the gravity model may prove necessary. However, in virtually all other applications, the Proportional Flow method produced the optimal solution to model catchment populations in Manchester, based on several criteria: it produced the smallest RMS error, addresses cross-boundary flows, the data used to create the catchment is readily available to SCPs and it is simpler to produce than the gravity model method. That said catchment populations should be one of many management tools used when allocating resources [32]. It should be combined with other relevant information such as patient travelling times, economic viability and current service provision.

Further work is needed to address how the Proportional Flow method can be used to reflect service redesign and handle OAs with zero or low activity. These must be assigned based on proximity and the result is affected by the geographical scale of the analysis. The results are also difficult to visualise, particularly when analysis utilises small geographical units. Further work would include rolling out the method across England and looking at further drill downs of data such as catchment by Healthcare Resource Group (HRG) rather than specialty level.

Copyright information

© Springer Science+Business Media, LLC 2011