Glucosamine is a naturally occurring substances that is a structural component of the cartilage that lines our joints. Health food stores began selling supplements to people as a prevention (or treatment) for osteoarthritis despite a lack of evidence of their benefit in humans. To test the efficacy of glucosamine, a randomized clinical trial was done in which 1414 participants with symptomatic osteoarthritis of the knee were randomly assigned to one of two treatment arms (placebo or glucosamine). The outcome accessed was if there was at least a 20% decrease in total pain score or no decrease in pain score over week 24. The results are shown in the table below.

Treatment	Pain Reduction
20% Pain Reduction	No Pain Reduction
Glucosamine	243	598
Placebo	94	479

1. Calculate the most appropriate measure of association comparing pain reduction between glucosamine and placebo (round to 2 decimal places). You find out that your participants did not stick to their assigned groups. Of the 243 people assigned glucosamine and had pain reduction, 55 took the placebo. Similarly, of the 598 people glucosamine and that did not have pain reduction, 55 took the placebo.
2. Calculate the most appropriate measure of association comparing pain reduction between glucosamine and placebo using an per protocol analysis (round to 2 decimal places).
3. Calculate the most appropriate measure of association comparing pain reduction between glucosamine and placebo using an as treated analysis (round to 2 decimal places).