Modelling of age-related bone loss using cross-sectional data

Background: Current applications of bone mineral density (BMD) data in age studies are not free of certain drawbacks. Since it is well established that age-related patterns of BMD changes involve three distinct periods (bone acquisition in youth, stabilization at maturity, and decrease with ageing), adjusting for age via an inappropriate mathematical function may lead to inconsistencies and wrong conclusions. Hypothesis: The piecewise model, which encompasses the above three periods, will accurately describe the BMD dependence on age. Objective: To examine age-related patterns of BMD changes using a number of possible mathematical functions and to find among them the best-fitting function. Next, to test whether the chosen function is universally applicable or if there are diverse population-specific functions. Material and methods: Thirteen ethnic samples from various regions of Europe and Asia, assigned into five ethnic-geographic groups, were examined. The total sample included 2430 males and 2515 females. Compact BMD of hand phalanges was measured by photodensitometry from plain radiographs of each individual studied. Statistical software was developed for the purposes of the present study; this software gave a maximum likelihood of the parameter estimates for various statistical models (functions). Results: In all samples of sufficient size and representative age range, a two-interval function was found as the best fitting and most parsimonious model to describe the BMD age-related changes. This two-interval function was characterized by age-related bone mass increase, positive slope β_1s in young age or a plateau (β_1s = 0, i.e. no age-related changes) until a sex-specific age threshold, T₀, after which annual bone loss ensued with a slope coefficient β_2s. Threshold of BMD loss in women of different ethnic groups ranged between 37.85 and 47.77 years, and roughly coincided with perimenopausal age. In males, the age T₀ varied between 27.85 and 49.07 years. The ensuing cortical bone loss appeared to be linear in both sexes, averaging between 0.51% and 1.15% in men and between 0.74% and 1.77% per year of young age BMD value in females. Conclusions: The change of phalangeal BMD with age may be best described by a two-interval function, regardless of sex and ethnic background. However, specific parameter estimates depend both on gender and ethnic affiliation. This study has yielded a well-fitted model of BMD dependence on age suitable for further use in population studies.