Logistic regression in estimates of femoral neck fracture by fall
Derer’s University Hospital and Policlinic, Osteological Unit, Bratislava, Slovakia
Abstract: The latest methods in estimating the probability (absolute risk) of osteoporotic fractures include several logistic regression models, based on qualitative risk factors plus bone mineral density (BMD), and the probability estimate of fracture in the future. The Slovak logistic regression model, in contrast to other models, is created from quantitative variables of the proximal femur (in International System of Units) and estimates the probability of fracture by fall.
Objectives: The first objective of this study was to order selected independent variables according to the intensity of their influence (statistical significance) upon the occurrence of values of the dependent variable: femur strength index (FSI). The second objective was to determine, using logistic regression, whether the odds of FSI acquiring a pathological value (femoral neck fracture by fall) increased or declined if the value of the variables (T–score total hip, BMI, alpha angle, theta angle and HAL) were raised by one unit.
Patients and methods: Bone densitometer measurements using dual energy X–ray absorptiometry (DXA), (Prodigy, Primo, GE, USA) of the left proximal femur were obtained from 3 216 East Slovak women with primary or secondary osteoporosis or osteopenia, aged 20–89 years (mean age 58.9; 95% CI: −58.42; 59.38). The following variables were measured: FSI, T-score total hip BMD, body mass index (BMI), as were the geometrical variables of proximal femur alpha angle (α angle), theta angle (θ angle), and hip axis length (HAL).
Statistical analysis: Logistic regression was used to measure the influence of the independent variables (T-score total hip, alpha angle, theta angle, HAL, BMI) upon the dependent variable (FSI).
Results: The order of independent variables according to the intensity of their influence (greatest to least) upon the occurrence of values of the dependent FSI variable was found to be: BMI, theta angle, T-score total hip, alpha angle, and HAL. An increase of one unit of an independent variable was shown, with statistical significance, to either raise or decrease the odds of the dependent FSI variable. Specific findings were as follows: an increase by 1° of the α angle escalated the probability of FSI acquiring a pathological value by 1111 times; an increase by 1° of the θ angle was found to boost these odds 1231 times; an increase by 1 mm of the HAL was found to increase these odds by 1043 times; an increase by 1.0 kg/m2 of the BMI raised the odds 1302 times; an increase by +1 standard deviation of the value of the T-score total hip subsequently decreased these odds 198 times.
Conclusion: The equation of the Slovak regression model makes it possible in praxis to determine the probability or absolute risk of femoral neck fracture by fall at those densitometrical workplaces without a program for measuring the FSI variable.
Keywords: osteoporosis, femoral neck fracture, logistic regression, absolute risk, bone densitometry, bone geometry, biomechanics
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