Problems:
A placebo controlled clinical trial of a new treatment for chronic pain was performed on 200 patients in a pain clinic. 100 patients were given the new treatment and 100 patients were given placebo. A pain questionnaire was administered to all 200 patients 1 week later. Based on the questionnaire, patients were classified as having moderate to severe pain (pain = 1) or mild to no pain (pain = 0). The data are attached below.
(1) Summarize the data relating to pain by treatment.
(2) Calculate the risk difference. Formally test whether the proportion of patients with moderate to severe pain is the same across treatment groups based on this effect measure. Does the treatment work?
(3) Perform a logistic regression with treatment as the only explanatory variable. Formally test if the odds of having pain are the same between the treatment groups. Include the odds ratio for treatment and the associated 99% confidence interval based on the modelin your summary and interpret this value. What is the c-statistic for this model?
(4) Perform a multiple logistic regression predicting pain from treatment, age, and severity at baseline score. Summarize briefly the output from this model. Give the odds ratio for treatment, age (for a 10 year increase), and severity at baseline. What is the c-statistic of this model?
(5) Which model fit the data better? Support your response with evidence from your output. Present the ROC curve for the model you choose.
(BONUS) Did the odds ratio for treatment change once you adjusted for age and severity at baseline? What explains the change?