7.6 In Exercise 6.8, an arthritis clinical trial was described.

(a) Assume the patients represent a random sample from a population of possible patients and refit the data using an appropriate logistic mixed effects model (be sure to argue whether a model with random intercepts, random slopes, or both should be used). In fitting the logistic model, let y = liftheself-assesmentwas'good'andy = 0 if'good' was not indicated.

(b) Determine if there is a significant treatment effect.

(c) Determine if there is a significant treatment by time interaction.

(d) Suppose we would like to estimate the difference in the proportion of patients who felt "poor" at baseline and those who felt "poor" after 3 months in the study. Fit an appropriate mixed effects model for estimating this difference.

(e) Provide a 90% confidence interval on the difference in the proportion of patients who felt "poor" at baseline and those who felt "poor" after 3 months in the study.