Estimating the prevalence of low-lumbar spine bone mineral density in older men with or at risk for HIV infection using normal mixture models

Abstract

Bone mineral density decreases naturally as we age because existing bone tissue is reabsorbed by the body faster than new bone tissue is synthesized. When this occurs, bones lose calcium and other minerals. What is normal bone mineral density for men 50 years and older? Suitable diagnostic cutoff values for men are less well defined than for women. In this paper, we propose using normal mixture models to estimate the prevalence of low-lumbar spine bone mineral density in men 50 years and older with or at risk for human immunodeficiency virus infection when normal values of bone mineral density are not generally known. The Box–Cox power transformation is used to determine which transformation best suits normal mixture distributions. Parametric bootstrap tests are used to determine the number of mixture components and to determine whether the mixture components are homoscedastic or heteroscedastic.

Keywords:

• bone mineral density
• Box–Cox power transformation
• EM algorithm
• HIV infection
• normal mixture
• parametric bootstrap

Acknowledgement

The author wish to thank the referees for very helpful comments and suggestions that improved the presentation of this paper.