ASSESSMENT OF THE ROLE OF QUANTITATIVE COMPUTED TOMOGRAPHY IN PREDICTING OSTEOPOROTIC VERTEBRAL FRACTURES
Kemerovo State Medical Academy,
Kemerovo State University,
Kemerovo, Russia
Osteoporosis is a metabolic skeletal disease, which is marked by decreasing bone strength and increasing risk of fractures [1]. The important characteristics of osteoporotic changes are decreasing bone mineral density and changes in microstructural architectonics of bone tissue. Incidence of such pathology increases with aging [2]. For estimation of risk of osteoporotic changes and fractures the priority area is development of predictive models on the basis of modern statistical methods. Estimation of probability of fractures will allow decreasing the burden of material and financial costs relating to treatment and rehabilitation.
There are various ways for estimation of risk of osteoporotic changes and incurrence of fractures. The Fracture Risk Assessment Tool (FRAX) is a wide-spread method, which is based on estimation of such factors as age, sex, body mass index, previous history of fractures, fractures in first-degree relatives, smoking, administration of glucocorticoids, rheumatoid arthritis, other causes of secondary osteoporosis, alcohol abuse and level of mineral density in neck of the femur [3]. The advantages of the above mentioned technique are availability, relative simplicity of estimation, and the economic aspect. On the other hand, some authors give the evidence about low sensitivity and specificity of the predictive tool. A retrospective study of risk of fractures showed the sensitivity of the Russian model of FRAX at the level of 42 %, the specificity – 74 % [4]. Another study showed ROC-curve of FRAX at the level of 0.63 [0.56; 0.69]. It means mean quality of the predictive model [5].
The level of bone mineral density (BMD) is a key parameter (75-80 %) of mechanical strength of the bone. Decreasing BMD results in increasing risk of fractures [6, 7].
The radial diagnostic techniques play the leading place in estimation of BMD: dual energy X-ray absorptiometry (DXA) and quantitative computer tomography (QCT) [8, 9]. The important advantage of CT osteodensimetry is a possibility for separate estimation of BMD of trabecular and cortical bone tissue.
Increasing rate of osteoporotic fractures requires search of new methodical solutions relating to development of the predictive model.
One of the perspective methods of statistical prediction in medicine is the logistic regression technique, which estimates the relationship between the dependent variable and several independent variables. Binary logistic regression allows estimation of the probability of an event according to combination of several factors, for example, risk of developing osteoporosis and occurrence of a fracture.
Objective – based on the method of binary logistic regression to assess the role of bone densitometry conducted by means of quantitative computed tomography in predicting postmenopausal osteoporotic vertebral fractures.
MATERIALS AND METHODS
The study presents estimation of bone mineral density of lumbar vertebrae 2-4 by means of quantitative computer tomography for the postmenopausal women. CT osteodensimetry was conducted for 72 patients with compression fractures of vertebral bodies and for 210 patients without fractures. Diagnostics was made with the computer scanner Somatom Emotion (Siemens, Germany) with Osteo mode.
The predictive model was developed on the basis of the received results of three-dimensional osteodensimetry. The selected parameters included the values of mineral density of trabecular and cortical bone tissue and the indices of bilateral asymmetry of bone mineral density of the lumbar vertebrae 2-4. The regression coefficients were calculated for each factor. ROC-analysis [10] was used for estimation of quality of the model on the basis of area under the curve.
The regressive equation was used for development of the predictive model:
where y – the dependent variable possessing two values: 0 – no fracture; 1 – presence of a fracture; a – the constant; bi – regression coefficients; Õi – variables.
The probability of occurrence of a fracture was calculated according to the formula:
where P – predictive probability, e – the exponent, with 2.718 as its approximate value.
RESULTS AND DISCUSSION
The results of CT osteodensimetry were analyzed. The regression coefficients were calculated (the table 1), ROC-curves for each factor were designed. On the basis of the results in the table 1 one can conclude that the probability of fractures increases under the conditions of decreasing mineral density in trabecular and cortical bone tissue and increasing indices of bilateral asymmetry of BMD.
| Table 1 | ||||
| The indices of binary logistic regression | ||||
| Note: | ||||
| Trabecular and cortical BMD - mineral density of trabecular and cortical bone tissue; | ||||
| Trabecular and cortical IA - indices of bilateral assymetry of mineral density in trabecular and cortical bone tissue of lumbar vertebrae. | ||||
After the calculation of the regression coefficients the formula of predictive probability of vertebral fracture occurrence has been developed:
The results of the statistical examination were processed with ROC-analysis with construction of ROC-curves. The area under ROC-curve was 0.894 [0.855; 0.932] that indicates high predictive capacity (Fig. 1).
Figure 1
ROC–curve of the predictive model
The classification threshold was chosen on the basis of ROC-analysis. This threshold was associated with sensitivity of the model at the level of 77.8 % (Se = 0.778), and specificity 86.7 % (Sp = 0.867).
The estimation of Wald statistic resulted in the following results: the most significant predictor is the index of bilateral asymmetry of BMD in the trabecular bone, the indices with lower significance are indices of BMD in the trabecular bone, BMD in the cortical bone and the index of bilateral asymmetry in the cortical bone (the table 2).
| Table 2 | ||
| Wald statistic values | ||
The estimation of the areas under ROC-curves (AUC) gave the following results: AUC for trabecular bone mineral density – 0.862 [0.819; 0.905], for cortical bone mineral density – 0.848 [0.799; 0.896], for the index of bilateral asymmetry of trabecular bone mineral density – 0.802 [0.741; 0.864], for the index of bilateral asymmetry of cortical bone mineral density – 0.807 [0.752; 0.862] (Fig. 2, 3).
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Figure 2 ROC–curves of BMD in trabecular and cortical bone tissue of the lumbar vertebrae
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Figure 3 ROC–curves of bilateral asymmetry indices of BMD in trabecular and cortical bone tissue of the lumbar vertebrae |
On the basis of the developed model the ranges of qualitative estimation of risk of fractures were calculated. If predictive probability exceeded 0.5, the woman was related to the group of high risk of fracture occurrence, 0.5-0.371 – the group of moderate risk, lower than 0.371 – low risk.
The applied computer software Prediction of risk of vertebral fractures was created for optimizing the activity of the practicing physician (Fig. 4).
Figure 4
The visual appearance of the computer program “Prediction of risk of vertebral fractures”
Administration of the software requires entering such data as full name, age of the patient, results of CT osteodensimetry: bone mineral density (L2, L3, L4), indices of bilateral asymmetry of BMD for trabecular and cortical bone tissue of the lumbar vertebrae. The output data shows predictive probability in view of quantitative and qualitative equivalents. The conclusion is made about the degree of risk of occurrence of osteoporotic vertebral fractures.
CONCLUSION
The method of binary logistic regression allows developing the predictive models for estimating risk of osteoporotic fractures with use of results of CT osteodensimetry. Timely estimation of risk of fractures will favor realization of well-timed preventive and correcting measures.