Sources of variability in bone mineral density measurements: implications for study design and analysis of bone loss

Measurement of bone mineral density (BMD) is a useful tool for monitoring efficacy in osteoporosis therapy. However, the ability to detect true change for a subject as well as for a group of subjects is dependent on the precision of the measurement. In this paper, short-term and long-term reliability of bone mass measurements were examined at the spine and femoral neck using dual-photon and dual-energy X-ray absorptiometry and related to guidelines for study design. The concepts involved in these analyses are relevant to a study for any therapy involving a quantitative trait. Short-term reliability was assessed by repeated measures in 60 subjects aged 46 +/- 9 years (mean +/- standard deviation [SD]), and in 32 elderly subjects (aged 75 +/- 5 years), on the same day with repositioning. Long-term variability in the rate of linear changes in BMD was assessed in a cohort of 293 women and 184 men, aged 60+, each having BMD measured on three separate occasions over an average interval of 2 years. Short-term variability in BMD was assessed using the coefficient of reliability (R) and standard deviation (SD) of measurement error. Long-term variability in BMD was modeled by linear regression. In the younger sample, the SD of measurement error for the lumbar spine and femoral neck was 14 and 25 mg/cm2, respectively, yielding coefficients of reliability for short-term measurements of 0.99 and 0.97, respectively. In the elderly sample, the coefficient of reliability was 0.96 and 0.77 for lumbar spine and femoral neck, respectively. For long-term variability, for which a linear rate of change in BMD was assumed, the SD of intrasubject variation in the women was 42 mg/cm2 at both the lumbar spine and femoral neck and in men 57 and 42 mg/cm2, respectively. The between-subject SD of the rates of change was higher in males than females (21 and 14 mg/cm2/year, respectively; p = 0.037). Importantly, intrasubject estimation error contributed about 90% of the variability component. These sources of variability lead to reduction in the power of a study and underestimation of the relative risk in logistic regression relating BMD and fracture risk in population studies. At the individual level, they increase the false-positive and false-negative error rates of diagnostic BMD and present major difficulties in the assessment of bone loss. The measurement error can be reduced by taking multiple measurements per visit. However, long-term intrasubject variation can be reduced by increasing the length of follow-up and/or increasing the frequency of measurements and, in a study, by increasing the number of subjects. Modeling of these errors, study duration, and frequency of measurements indicates that studies with a duration of 3-5 years appear to have the optimum "cost-benefit," and making measurements more than twice a year does not improve the precision appreciably. These modeling approaches can be extended to other clinical studies involving quantitative measurements with measureable errors within and between individuals and contributes to rational selection of the duration and frequency of measurements.