Setting Up a Precision Assessment and Judging a 6-Month Change
A community clinic has installed a new DXA scanner and hired a second technologist. Before starting follow-up scanning, the lead technologist performs an in vivo precision assessment: 15 patients are scanned twice each with repositioning between scans, and the duplicate L1–L4 results are used. The root-mean-square standard deviation of the 15 pairs is 0.011 g/cm², and the group mean L1–L4 BMD is 0.905 g/cm². Six months later, a 68-year-old woman returns. She has been on alendronate for three years and reports taking it regularly. Her baseline L1–L4 BMD was 0.880 g/cm²; today it is 0.845 g/cm² on the same scanner, same technologist, same software version, with satisfactory positioning and identical region-of-interest placement. Her femoral neck changed from 0.700 to 0.690 g/cm². The ordering physician asks whether the spine change is "real" and whether the patient is losing bone despite adherence.
1. Calculate the L1–L4 precision error as a coefficient of variation and the least significant change at the 95% confidence level. Show the arithmetic.
Read the worked answer
Precision error as %CV
%CV = (RMS SD ÷ mean BMD) × 100 = (0.011 ÷ 0.905) × 100 ≈ 1.22%
The RMS SD comes from the duplicate pairs with repositioning - repositioning is the part that matters, because it captures the error a real follow-up visit will contain.
Least significant change at 95% confidence
LSC = 2.77 × %CV = 2.77 × 1.22% ≈ 3.4%
The 2.77 multiplier is the 95% confidence factor for a precision assessment with approximately 30 degrees of freedom, which is what 15 patients scanned twice provides. Using 1.81 (80% confidence) here would be too permissive for a clinical monitoring decision.
Convert to absolute units for this patient
LSC(g/cm²) = 0.034 × 0.880 ≈ 0.030 g/cm²
Note that %CV drifts with BMD level, so the absolute LSC in g/cm² is the safer number to apply to an individual whose BMD differs from the precision cohort mean of 0.905.
2. Is the spine change statistically significant? Can the same reasoning be applied to the femoral neck?
Read the worked answer
Spine: change = 0.845 − 0.880 = −0.035 g/cm², or −0.035 ÷ 0.880 = −4.0%.
Compare with the LSC: 4.0% > 3.4%, and 0.035 g/cm² > 0.030 g/cm². The loss exceeds the least significant change, so at 95% confidence it is not attributable to measurement error. It should be reported as a statistically significant decrease.
Femoral neck: change = 0.690 − 0.700 = −0.010 g/cm², or −1.4%. This cannot be judged against a spine-derived LSC. Precision is site-specific: hip precision must be established with duplicate hip scans, and hip precision is generally poorer than spine precision because of rotation and soft-tissue variability. A 1.4% hip change would almost certainly fall inside the hip LSC, so the correct statement is "no significant change at the femoral neck" - not "stable bone density everywhere" and certainly not "hip loss of 1.4%."
Keep the two sites separate in the report; a single LSC applied to every region is a common and consequential error.
3. What conditions must hold for this comparison to be valid, and what non-measurement explanations would you raise with the physician?
Read the worked answer
Validity conditions (all were met here, which is why the conclusion is defensible): same densitometer, same software version and reference database, same acquisition mode, consistent positioning and analysis, identical region-of-interest placement, no new artifact or contrast material, and comparison of BMD in g/cm² rather than T-scores. Both scans must also be technically adequate; a comparison is only as good as its weaker image.
Non-measurement explanations worth raising:
- A 6-month interval is early. Treatment response is usually judged over 1–2 years; a change beyond the LSC at 6 months can be real but is a weak basis for declaring treatment failure.
- New or progressive degenerative change, a new vertebral fracture, or aortic calcification superimposed on the region of interest can move BMD in either direction.
- True bone loss from nonadherence that the patient does not report, malabsorption, a new medication (glucocorticoid, aromatase inhibitor, proton-pump inhibitor), or an unrecognized secondary cause.
The technologist's job is to certify that the measurement comparison is valid and to flag confounders; the therapy decision belongs to the physician. A reasonable report language is: "Statistically significant decrease at L1–L4 exceeding the facility LSC; confirm with clinical correlation."