The use of clinical risk factors enhances the performance of BMD in the prediction of hip and osteoporotic fractures in men and women

Abstract

Summary

BMD and clinical risk factors predict hip and other osteoporotic fractures. The combination of clinical risk factors and BMD provide higher specificity and sensitivity than either alone.

Introduction and hypotheses

To develop a risk assessment tool based on clinical risk factors (CRFs) with and without BMD.

Methods

Nine population-based studies were studied in which BMD and CRFs were documented at baseline. Poisson regression models were developed for hip fracture and other osteoporotic fractures, with and without hip BMD. Fracture risk was expressed as gradient of risk (GR, risk ratio/SD change in risk score).

Results

CRFs alone predicted hip fracture with a GR of 2.1/SD at the age of 50 years and decreased with age. The use of BMD alone provided a higher GR (3.7/SD), and was improved further with the combined use of CRFs and BMD (4.2/SD). For other osteoporotic fractures, the GRs were lower than for hip fracture. The GR with CRFs alone was 1.4/SD at the age of 50 years, similar to that provided by BMD (GR = 1.4/SD) and was not markedly increased by the combination (GR = 1.4/SD). The performance characteristics of clinical risk factors with and without BMD were validated in eleven independent population-based cohorts.

Conclusions

The models developed provide the basis for the integrated use of validated clinical risk factors in men and women to aid in fracture risk prediction.

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Acknowledgements

We are grateful to the principal investigators of the cohorts studied and the investigators of the Women’s Health Initiative (http://www.whi.org/about). We would like to thank the Alliance for Better Bone Health, Hologic, IGEA, Lilly, Lunar, Merck Research Laboratories, Novartis, Pfizer, Roche, Servier and Wyeth for their unrestricted support of this work. We are also grateful to the EU (FP3/5), the International Osteoporosis Foundation, the International Society for Clinical Densitometry and the National Osteoporosis Foundation for supporting this study.

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Correspondence to J. A. Kanis.

Appendix

Appendix

Relationship between area under the ROC curve and gradient of risk for a normally distributed risk variable

Let X be a risk variable with the frequency function f0 among the not diseased and f1 among the diseased. Furthermore, assume that the probability of being diseased among the studied individuals is p. Then the conditional probability of belonging to the diseased group given the that X=x is

$$ 1 \mathord{\left/ {\vphantom {1 {{\left[ {1{\text{ }} + {\text{ }}{\left( {{{\left( {1 - p} \right)}} \mathord{\left/ {\vphantom {{{\left( {1 - p} \right)}} p}} \right. \kern-\nulldelimiterspace} p} \right)} \cdot {\left( {{f_{0} {\left( x \right)}} \mathord{\left/ {\vphantom {{f_{0} {\left( x \right)}} {f_{1} {\left( x \right)}}}} \right. \kern-\nulldelimiterspace} {f_{1} {\left( x \right)}}} \right)}} \right]}}}} \right. \kern-\nulldelimiterspace} {{\left[ {1{\text{ }} + {\text{ }}{\left( {{{\left( {1 - p} \right)}} \mathord{\left/ {\vphantom {{{\left( {1 - p} \right)}} p}} \right. \kern-\nulldelimiterspace} p} \right)} \cdot {\left( {{f_{0} {\left( x \right)}} \mathord{\left/ {\vphantom {{f_{0} {\left( x \right)}} {f_{1} {\left( x \right)}}}} \right. \kern-\nulldelimiterspace} {f_{1} {\left( x \right)}}} \right)}} \right]}} $$

We assume that f0 and f1 are frequency functions corresponding to normally distributed variables with the same standard deviation σ and the difference between means of diseased and not diseased equal to Δ. Then the conditional probability can be written as

$$ 1 \mathord{\left/ {\vphantom {1 {{\left[ {1 + \exp {\left( { - {\left( {\beta _{0} + \beta _{1} \cdot x} \right)}} \right)}} \right]}}}} \right. \kern-\nulldelimiterspace} {{\left[ {1 + \exp {\left( { - {\left( {\beta _{0} + \beta _{1} \cdot x} \right)}} \right)}} \right]}} $$

where β1 = Δ/σ2. If individuals are followed for a short period so that the proportion of diseased are low, then the beta coefficients for a risk variable obtained by Cox regression, Poisson regression or logistic regression will be approximately the same and the standard deviation of the risk variable X in the population as a whole will be approximately as among the not diseased, σ. The gradient of risk per 1 standard deviation, GR, is exp(β1·σ)=exp(Δ/σ), and thus

$$ \ln {\left( {GR} \right)} = \Delta \mathord{\left/ {\vphantom {\Delta \sigma }} \right. \kern-\nulldelimiterspace} \sigma $$
(1)

Let Y denote the value of the risk variable of a randomly chosen individual among the diseased individuals and let X be the corresponding quantity among not diseased individuals. We assume that Y tends to be larger than X. The area under the ROC curve is equal to the probability P(Y>X) = 1−P(Y−X ≤ 0). If Y and X have normal distributions with the same standard deviation σ and the difference Δ between the means, then the area under the curve is \( 1 - \Phi \left( {{ - \Delta } \mathord{\left/ {\vphantom {{ - \Delta } {{\left( {\sigma \cdot {\sqrt 2 }} \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {\sigma \cdot {\sqrt 2 }} \right)}}} \right. = \Phi {\left( {\Delta \mathord{\left/ {\vphantom {\Delta {\sigma \cdot {\sqrt 2 }}}} \right. \kern-\nulldelimiterspace} {\sigma \cdot {\sqrt 2 }}} \right)} \), where Φ is the standardised normal distribution function. When we use the relationship (1), the area under the ROC curve can be represented as the following function of gradient of risk per 1 standard deviation, GR, \( Area\,under\,the\,ROC\,curve = \Phi {\left( {{\ln {\left( {GR} \right)}} \mathord{\left/ {\vphantom {{\ln {\left( {GR} \right)}} {{\sqrt 2 }}}} \right. \kern-\nulldelimiterspace} {{\sqrt 2 }}} \right)} \).

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Kanis, J.A., Oden, A., Johnell, O. et al. The use of clinical risk factors enhances the performance of BMD in the prediction of hip and osteoporotic fractures in men and women. Osteoporos Int 18, 1033–1046 (2007). https://doi.org/10.1007/s00198-007-0343-y

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Keywords

  • Bone mineral density
  • Hip fracture
  • Meta-analysis
  • Osteoporotic fracture
  • Risk assessment