# The impact of the use of multiple risk indicators for fracture on case-finding strategies: a mathematical approach

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## Abstract

The value of bone mineral density (BMD) measurements to stratify fracture probability can be enhanced in a case-finding strategy that combines BMD measurement with independent clinical risk indicators. Putative risk indicators include age and gender, BMI or weight, prior fracture, the use of corticosteroids, and possibly others. The aim of the present study was to develop a mathematical framework to quantify the impact of using combinations of risk indicators with BMD in case finding. Fracture probability can be expressed as a risk gradient, i.e. a relative risk (RR) of fracture per standard deviation (SD) change in BMD. With the addition of other continuous or categorical risk indicators a continuous distribution of risk indicators is obtained that approaches a normal distribution. It is then possible to calculate the risk of individuals compared with the average risk in the population, stratified by age and gender. A risk indicator with a gradient of fracture risk of 2 per SD identified 36% of the population as having a higher than average fracture risk. In individuals so selected, the risk was on average 1.7 times that of the general population. Where, through the combination of several risk indicators, the gradient of risk of the test increased to 4 per SD, a smaller proportion (24%) was identified as having a higher than average risk, but the average risk in this group was 3.1 times that of the population, which is a much better performance. At higher thresholds of risk, similar phenomena were found. We conclude that, whereas the change of the proportion of the population detected to be at high risk is small, the performance of a test is improved when the RR per SD is higher, indicated by the higher average risk in those identified to be at risk. Case-finding strategies that combine clinical risk indicators with BMD have increased efficiency, while having a modest impact on the number of individuals requiring treatment. Therefore, the cost-effectiveness is enhanced.

## Keywords

Case finding Fractures Mathematical model Osteoporosis Risk## Notes

### Acknowledgements

We are grateful to the Alliance for Better Bone Health, Hologic, IGEA, Lilly, Lunar, Novartis, Pfizer, Roche, Wyeth, and the EU (FP3/5) for supporting this study and the International Osteoporosis Foundation, the International Society for Clinical Densitometry, and the National Osteoporosis Foundation for their unrestricted support of this work.

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