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# Statistics and Its Interface

## Volume 2 (2009)

### Number 2

### Applying the Lorenz curve to disease risk to optimize health benefits under cost constraints

Pages: 117 – 121

DOI: http://dx.doi.org/10.4310/SII.2009.v2.n2.a1

#### Author

#### Abstract

This paper shows how the Lorenz curve can be used, together with models of disease risk, to allocate scarce resources so as to optimize a health benefit. Consider the example of breast cancer mortality. If there were sufficient resources to provide all women with mammograms, a certain maximal number of lives could be saved. Suppose, however, that only a fraction of that amount of money is available for prevention activities. Suppose that a questionnaire could be given to assess a woman’s risk of dying of breast cancer. Depending on the amount of money available, on the ratio of the cost of a questionnaire to the cost of a mammogram, and on the Lorenz curve of the distribution of risks of breast cancer mortality, I calculate the proportion of women who should be given questionnaires, the proportion of women given the questionnaires who should be given mammograms because they have high risks, and the proportion of women not given questionnaires who should be assigned to receive mammograms at random so as to maximize the number of lives saved.

#### Keywords

absolute risk, cost constraints, constrained optimization, cumulative incidence, disease prevention, Lorenz curve, risk prediction model