Bone Density T-Score Interpreter Formula
Understand the math behind the bone density t-score interpreter. Each variable explained with a worked example.
Formulas Used
T-Score Value
category = t_scoreApproximate 10-Year Fracture Risk
fracture_risk_10yr = max(round(exp(-t_score * 0.5) * (age / 50) * 3), 1)Relative Fracture Risk
relative_risk = round(pow(2, -t_score) * 10) / 10Variables
| Variable | Description | Default |
|---|---|---|
t_score | T-Score | -1 |
age | Age(years) | 55 |
How It Works
Bone Density T-Score Classification
A T-score compares your bone density to a healthy 30-year-old adult.
WHO Categories
| T-Score | Classification | |---|---| | Above -1.0 | Normal | | -1.0 to -2.5 | Osteopenia (low bone mass) | | Below -2.5 | Osteoporosis | | Below -2.5 with fracture | Severe osteoporosis |
Each decrease of 1 in T-score roughly doubles fracture risk.
Worked Example
A 55-year-old with a T-score of -1.0.
t_score = -1age = 55
- 01T-score = -1.0 (Osteopenia range starts at -1.0)
- 02Approximate 10-year risk = e^(0.5) x (55/50) x 3 = 1.65 x 1.1 x 3 = 5%
- 03Relative risk = 2^1 = 2.0x baseline
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