6.2 Spatial interaction models

Perhaps the most complex method for making decisions about health facility locations is spatial interaction modelling. Spatial interaction models are a means of deciding where to locate a new health facility, or understanding the effects of moving or closing an existing facility. A spatial interaction model is a mathematical model that predicts the movement of people between origins (usually their homes) and destinations (health facilities) by examining the distance between them. A spatial interaction model also takes into account the likely demand for health services among the population and the quality of service provision at health centres. An alternative name for many of these spatial interaction models is the term ‘gravity model’ (see Box 1). Such models are one of the more complex ways of deciding where to locate a new health facility.

 

How do spatial interaction models work?

Spatial interaction models generally draw on three types of data:

• Distances between facilities and population: distance often explains much of the observed pattern of facility use, with patients showing a marked preference for nearby facilities. Often, straight-line distances are used in spatial interaction models, although some more sophisticated models use travel times.
• Service characteristics: There is a trade-off between the level of service available and the distances that people are prepared to travel for healthcare, with patients travelling further to what are perceived to be better quality facilities. Although quality ratings and measures of the range of services available at a facility could potentially be used to assess its attractiveness, in practice many spatial interaction models use measures of a facility’s capacity or size. For example, Congdon (1996) used bed capacity and total emergency admissions to describe accident and emergency (A & E) unit characteristics in his study of A & E unit closures.
• Demand characteristics describe the potential uptake of health services by the population living in a given study area. Demand estimates can be derived from a population’s age-sex structure, from measures of population health, or from socio-economic characteristics. For example, Congdon (1996) describes how emergency admissions are typically greater among those living in more deprived neighbourhoods.

Spatial interaction models use these three types of data to predict the number of trips made to each facility in a health service network. Spatial interaction models can be expressed mathematically in many different ways, but may include several parameters. For example, there is typically a ‘friction of distance’ parameter that describes how the number of trips to health facilities declines as distance decreases and there may be an ‘attractiveness’ parameter that describes how much further people are prepared to travel to facilities that offer a wider – or better quality – range of services.

For a spatial interaction model to produce meaningful results, it is important that it is properly calibrated – in other words, the parameters such as friction of distance and attractiveness are carefully selected and not just chosen at random. This is normally done by looking at the actual uptake of health facilities within a given region. If records are kept of patients attending a given health centre, their addresses can be geocoded and linked to census tracts throughout its catchment. The three parameters described above in the spatial interaction model can be chosen, so that the number of visits from each census tract to each facility estimated by the model closely matches those observed in reality.

Making decisions with spatial interaction models

Once a spatial interaction model has been properly calibrated, it can be used to support decisions about health facility locations. Such decisions might include opening a new facility, closing an existing facility, or moving an existing facility to a new location. These decisions normally involve optimisation – such as the identification of the optimal (best) location for a new health centre. A related set of techniques called mathematical programming can be used to solve such problems. Mathematical programming makes use of a set of rules to decide where best to place a new facility. There are normally two types of rule used (see Tables 10.1 – 10.6 of the course text book Cromley and McLafferty for further examples):

• One or more objective function(s): An objective function describes the main goal of a health service network in quantitative terms. For a private facility, the objective function may be to maximise the number of patients seen in a year. For a publicly-funded, welfare-driven network, it may be to minimise the overall distance travelled across all sectors of the population. In a few instances, health-based objective functions have been used. With a health-based objective function, the overall aim of the system is to reduce the number of disease cases or mortality. For example, deaths from road traffic accidents (RTAs) are likely to be lower when travel times to the nearest emergency unit are low. Rather than focusing on distance, a health-based objective function for RTAs would minimise mortality from such accidents instead – a subtle, but important, distinction.
• Constraints: Constraints are upper or lower limits that can be placed on particular properties of the model. For example, there may be a capacity constraint, which sets an upper limit on the number of patients who can be admitted overnight to a given health facility (e.g. based on number of beds available). Similarly, there may be a lower limit for patient numbers, below which a given unit is no longer economically viable. There may also be constraints in terms of minimum standards. For example, under government targets, there may be a maximum distance beyond which no household should have to travel to obtain healthcare.

Mathematical programming is used to maximise the objective function, whilst ensuring that any constraints specified are met at the same time. A detailed review of mathematical programming techniques is beyond the scope of this course, but for those interested, a useful starting point is Oliveira and Bevan (2006).

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