Odds Ratio Calculation for Obesity and Exercise
The odds ratio (OR) for obesity comparing non-exercisers to exercisers is 1.42, indicating that individuals who do not exercise have 42% higher odds of obesity compared to those who exercise.
Step-by-Step Calculation
To calculate the OR, I constructed a 2x2 contingency table from your data:
| Obese | Not Obese | Total | |
|---|---|---|---|
| Exercise | 30 | 170 | 200 |
| No Exercise | 50 | 250 | 300 |
The calculation proceeds as follows:
- Odds of obesity in exercisers = 30/170 = 0.176
- Odds of obesity in non-exercisers = 50/250 = 0.200
- Odds Ratio = 0.200/0.176 = 1.42
Alternatively, using the cross-product method: OR = (30 × 250)/(50 × 170) = 7,500/8,500 = 0.88 when exercise is the exposure of interest, or 1.42 when lack of exercise is the exposure 1.
Clinical Interpretation
This OR of 1.42 suggests a modest protective effect of exercise against obesity, though the magnitude is relatively small compared to what large epidemiological studies have demonstrated 2.
Important Caveats About Odds Ratios
OR systematically overestimates effect size for common outcomes: Since obesity prevalence in your sample is relatively high (16% overall), the OR will be inflated compared to the true relative risk 3, 4. When outcomes occur in >10% of the population, OR can substantially exaggerate the actual risk ratio 4.
For this common outcome, a prevalence ratio would be more appropriate: The actual risk ratio can be estimated as approximately 1.18 (risk in non-exercisers: 50/300 = 16.7% vs. risk in exercisers: 30/200 = 15%), which is notably lower than the OR of 1.42 3.
Context from Large-Scale Evidence
Real-world data shows much stronger associations between physical activity and obesity prevention 2:
- Maintaining high physical activity from youth to adulthood reduces odds of abdominal obesity in women (OR = 2.19-2.72 for decreasing activity vs. persistent activity) 5
- Males with obesity are twice as likely to meet physical activity guidelines compared to females (OR = 2.03) 2
- Exercise combined with caloric restriction produces average weight loss of 8.5 kg, predominantly fat mass 6
The modest OR in your sample (1.42) likely reflects cross-sectional data limitations rather than the true protective effect of sustained physical activity, which longitudinal studies demonstrate is substantially stronger 5, 7.