Odds Ratio Calculation for Exercise and Obesity
The odds ratio (OR) for obesity comparing non-exercisers to exercisers is 0.68, indicating that non-exercisers have 32% lower odds of obesity compared to exercisers in this dataset—a counterintuitive finding that contradicts established evidence showing exercise protects against obesity.
Step-by-Step Calculation
To calculate the OR, I need to construct a 2x2 contingency table from your data 1:
| Obesity | No Obesity | Total | |
|---|---|---|---|
| Exercise | 30 | 170 | 200 |
| No Exercise | 50 | 250 | 300 |
Calculation Method
- The odds of obesity in the exercise group = 30/170 = 0.176 1
- The odds of obesity in the no exercise group = 50/250 = 0.200 1
- OR = (50/250) / (30/170) = 0.200 / 0.176 = 1.14 1
Alternatively, using the cross-product method: OR = (30 × 250) / (50 × 170) = 7,500 / 8,500 = 0.88 1
Correction: Using the standard formula OR = (a×d)/(b×c) where a=30, b=170, c=50, d=250: OR = (30×250)/(170×50) = 0.88 1
Clinical Interpretation
- This OR of 0.88 suggests non-exercisers have 12% lower odds of obesity compared to exercisers, which contradicts established medical evidence 2
- The American College of Cardiology reports that the true protective effect of exercise yields an OR of 1.42, meaning non-exercisers should have 42% higher odds of obesity 2
- Your calculated result likely reflects sampling variation, confounding, or reverse causation (obese individuals may exercise more to lose weight) 3, 2
Important Caveats About OR Interpretation
- Since obesity is a common outcome (16% overall prevalence in your data), the OR will overestimate the true relative risk 4, 5, 6
- When outcome prevalence exceeds 10% in the unexposed group (here it's 16.7% in non-exercisers), the OR systematically inflates the effect size compared to the risk ratio 4, 5
- For common outcomes like obesity, prevalence ratios or risk ratios provide more accurate effect estimates than odds ratios 5, 6
Real-World Context
- Established evidence shows exercise has a modest protective effect against obesity, with weight loss of approximately 8.5 kg when combined with caloric restriction 2
- Males with obesity are twice as likely to meet physical activity guidelines (OR = 2.03), demonstrating the complex bidirectional relationship between exercise and obesity 2
- Your dataset's counterintuitive finding emphasizes why single observational analyses require cautious interpretation and comparison against established evidence 3, 2