Device-specific weighted T-score for two quantitative ultrasounds: operational propositions for the management of osteoporosis for 65 years and older women in Switzerland

Abstract.

The World Health Organization (WHO) criteria for the diagnosis of osteoporosis are mainly applicable for dual X-ray absorptiometry (DXA) measurements at the spine and hip levels. There is a growing demand for cheaper devices, free of ionizing radiation such as promising quantitative ultrasound (QUS). In common with many other countries, QUS measurements are increasingly used in Switzerland without adequate clinical guidelines. The T-score approach developed for DXA cannot be applied to QUS, although well-conducted prospective studies have shown that ultrasound could be a valuable predictor of fracture risk. As a consequence, an expert committee named the Swiss Quality Assurance Project (SQAP, for which the main mission is the establishment of quality assurance procedures for DXA and QUS in Switzerland) was mandated by the Swiss Association Against Osteoporosis (ASCO) in 2000 to propose operational clinical recommendations for the use of QUS in the management of osteoporosis for two QUS devices sold in Switzerland. Device-specific weighted "T-score" based on the risk of osteoporotic hip fractures as well as on the prediction of DXA osteoporosis at the hip, according to the WHO definition of osteoporosis, were calculated for the Achilles (Lunar, General Electric, Madison, Wis.) and Sahara (Hologic, Waltham, Mass.) ultrasound devices. Several studies (totaling a few thousand subjects) were used to calculate age-adjusted odd ratios (OR) and area under the receiver operating curve (AUC) for the prediction of osteoporotic fracture (taking into account a weighting score depending on the design of the study involved in the calculation). The ORs were 2.4 (1.9–3.2) and AUC 0.72 (0.66–0.77), respectively, for the Achilles, and 2.3 (1.7–3.1) and 0.75 (0.68–0.82), respectively, for the Sahara device. To translate risk estimates into thresholds for clinical application, 90% sensitivity was used to define low fracture and low osteoporosis risk, and a specificity of 80% was used to define subjects as being at high risk of fracture or having osteoporosis at the hip. From the combination of the fracture model with the hip DXA osteoporotic model, we found a T-score threshold of –1.2 and –2.5 for the stiffness (Achilles) determining, respectively, the low- and high-risk subjects. Similarly, we found a T-score at –1.0 and –2.2 for the QUI index (Sahara). Then a screening strategy combining QUS, DXA, and clinical factors for the identification of women needing treatment was proposed. The application of this approach will help to minimize the inappropriate use of QUS from which the whole field currently suffers.

Appendix

Global analysis

In the following paragraph, we describe the methodology used to weight the odds ratio, the area under the curve, and to define the weighted T-score for a given specificity and sensitivity.

The average weighted odds ratio (OR_w) is defined as follows for one standard deviation decrease:

$$OR_w = {{\sum\limits_{i = 1}^n {W_i \times e} ^{ - SD_i \times \beta _l } } \over {\sum\limits_{i = 1}^n {W_i } }}$$

(1)

where i represents each study included in the analysis, and SD_i the corresponding standard deviation over the population. β_i is the estimate extracted from the logistic regression for a given study and W_i is the weighted score which could be either 0.5, 1, 2, or 3 depending on the design of each study. Similarly, the 95% confidence interval of the OR_w (95% CI OR_w) is:

$$95\% .CI.OR_w = {{\sum\limits_{i = 1}^n {W_i \times e} ^{\left( { - SD_i \times \beta _i } \right) \pm \left( {1.96 \times SD_i \times SEE_i } \right)} } \over {\sum\limits_{i = 1}^n {W_i } }}$$

(2)

with SEE _i being the standard error of estimate of the logistic regression for a given study.

Based on the same approach, the area under the curve was weighted and averaged as follows:

$$AUC_w = {{\sum\limits_{i = 1}^n {W_i \times AUC_i } } \over {\sum\limits_{i = 1}^n {W_i } }}$$

(3)

where i represents each study included in the analysis, AUC _i the corresponding area under the curve, and W _i the weighted score which could be either 0.5, 1, 2, or 3 depending on the design of each study.

Once a threshold was calculated for each study based on the 90% sensitivity and 80% specificity, the weighted average was then calculated for the raw data (using the ROC analysis) and the corresponding T-score. As such, the weighted T-score, for example, is the following:

$$T.score_w = {{\sum\limits_{i = 1}^n {W_i \times T.score_i } } \over {\sum\limits_{i = 1}^n {W_i } }}$$

(4)

where i represents each study included in the analysis, T.score_i the threshold corresponding T-score at either 90% sensitivity or 80% specificity, and W _i the weighted score which could be either 0.5, 1, 2, or 3 depending on the design of each study.

Individual-level meta-analysis vs the "meta-like" analysis

To check if our developed approach gives results in the expected range, we compared the average weighted odds ratio and area under the curve with the one calculated from an individual-level meta-analysis. As an example for the hip fracture study, the results are given in Table 6. The results are very close to our approach. The small difference observed as compared with our model is that the individual-level meta-analysis does not take into account the different design of the study, thereby giving the same weight for a small cross-sectional study as for a large prospective study.

Table 6. Results of hip and fracture study. OR odds ratio, AUC area under the curve

Other thresholds

Besides the 80% specificity threshold, we also calculated the 90% specificity in both models (hip-fracture and DXA osteoporosis-based, respectively). Comparative results are given in Table 7.

Table 7. Comparative results of study models

It was decided that threshold based on the 90% specificity would be too selective for screening purposes; thus, we used the 90% sensitivity and 80% specificity for our model.