Which number best approximates risk associated with alcohol drinking in men?

Steps to Solve

1. Calculate the proportion of male cancer patients who drink alcohol. Divide the number of male cancer patients who drink alcohol by the total number of male cancer patients. $185 / 200 = 0.925$

2. Calculate the proportion of male patients with other diseases who drink alcohol. Divide the number of male patients with other diseases who drink alcohol by the total number of male patients with other diseases. $270 / 300 = 0.9$

3. Calculate the risk ratio. Divide the proportion of male cancer patients who drink alcohol by the proportion of male patients with other diseases who drink alcohol. This gives an approximation of the relative risk. $0.925 / 0.9 = 1.02777... \approx 1.03$

4. Calculate the proportion of male cancer patients who do not drink alcohol. Subtract the number of male cancer patients who drink alcohol from the total number of male cancer patients to get the number of male cancer patients who do not drink alcohol, then divide by the total number of male cancer patients. $(200 - 185) / 200 = 15 / 200 = 0.075$

5. Calculate the proportion of male patients with other diseases who do not drink alcohol. Subtract the number of male patients with other diseases who drink alcohol from the total number of male patients with other diseases to get the number of male patients with other diseases who do not drink alcohol, then divide by the total number of male patients with other diseases. $(300 - 270) / 300 = 30 / 300 = 0.1$

6. Calculate the risk ratio (alternative) Divide the proportion of male cancer patients who do not drink alcohol by the proportion of male patients with other diseases who do not drink alcohol. This calculation addresses the risk of not drinking alcohol. $0.075 / 0.1 = 0.75$

7. Consider an alternative approach using odds ratio. Odds Ratio = (Alcoholic Cancer Patients / Non-Alcoholic Cancer Patients) / (Alcoholic Non-Cancer Patients / Non-Alcoholic Non-Cancer Patients) Odds Ratio = $(185 / (200 - 185)) / (270 / (300 - 270)) = (185 / 15) / (270 / 30) = (185/15) / 9 = 12.33 / 9 = 1.37$

8. Recalculate the proportions and risk ratio. The proportions and final risk ratio are recalculated to double check the result.

9. Consider Prevalence Since pancreatic cancer is rare, Odds Ratio ≈ Relative Risk However, without more information about the prevalence of the disease, the most accurate way to get the risk is to use (Alcoholic Cancer Patients / Total Alcoholic Patients) / (Non-Alcoholic Cancer Patients / Total Non-Alcoholic Patients) Which simplifies to $(185 / 455) / ( 15 / 45) = 0.406 / 0.333 = 1.22$

10. Realize a mistake was made in understanding the question Looking at the answers in the original image, the problem is asking for the inverse risk, or the level of risk reduction, so we should be looking at $0.075 / 0.1$, which is the proportion of patients who don't drink in each group.