Letters

# Use of “population served” distorted findings

BMJ 1996; 313 (Published 23 November 1996) Cite this as: BMJ 1996;313:1329
1. Barry Tennison,
2. Alison Frater,
3. Keith Baker
1. Director of public health Assistant director of public health West Hertfordshire Health Authority, Welwyn Garden City AL8 6JL
2. Assistant director of public health East and North Hertfordshire Health Authority, Welwyn Garden City AL8 6JL

EDITOR,—M A Richards and J C Parrott raise important issues about tertiary cancer services.1 Sadly, their paper does not contribute to our understanding of benchmarking for tertiary cancer centres because the calculation of population denominators is seriously flawed. The standard method of calculating catchment populations for specific services uses the proportions of current activity provided by different providers to allocate a district's resident population to those providers.2 The key principle is that the catchment populations of all providers add up to the total populations of the districts considered.

Instead, Richards and Parrott use the concept of “population served,” which involves classifying districts as local or distant and exclusive or shared and then allocating the populations of shared districts by relating activity for them to activity for the host population.

This definition of population served seriously distorts the findings.

Visualise three districts, X, Y, and Z. Each has a population of one million. Cancer centres A and B are located in districts X and Z, respectively. All the activity for the population of X and Z takes place at A and B, respectively, while half of the activity for the population of Y takes place at A and half at B. Under these conditions, whatever the actual levels of activity for the populations of X, Y, and Z, the catchment populations of A and B are each 1.5 million. In contrast, the population served by A and B, as defined in the paper, depends on levels of activity for each population. Table 1 shows this, with four scenarios for activity. Only if the activity for each district is the same will the figure for the population served be the same as that for the catchment population. In scenario 2 the total population served is four million when the total population of the three districts is only three million. Similarly, in scenario 3 (which is possibly more likely) the total population served is only 2.5 million. In scenario 4 the centre that provides most activity looks as though it serves a smaller population.

Table 1

Population served in four possible scenarios of activity at two cancer centres, assuming that all activity for populations of X and Z takes place at A and B, respectively, and that half of activity for population of Y takes place at A and half at C

View this table:

This is not simply an arithmetical quibble. Multiplying the rate of new referrals contrived from the authors' method by a local population could seem to indicate, out of the blue, a need for more activity. While this may be the situation in many districts, this method will not elucidate which ones to target.

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