Table shows results of a randomized clinical trial conducted at five centers. The purpose was to compare an active drug to placebo for treating fungal infections (1 = success, 0 = failure). For these...

Table shows results of a randomized clinical trial conducted at five centers. The purpose was to compare an active drug to placebo for treating fungal infections (1 = success, 0 = failure). For these data, let y = response, x = treatment (1 = active, 0 = placebo), and z = center.

a. For the model logit[P(Y = 1) = α + βx + βz k, explain why quasi-complete separation occurs in terms of the effects of center.

b. Using a “no intercept” option so that {βzk} refer to the individual centers rather than contrasts with a baseline center, fit the model and report βˆz 1 and βˆz 3 and their standard errors. What are the actual ML estimates?

c. The counts in the 2 × 2 marginal table relating treatment to response are all positive, so the empty cells do not affect the treatment estimate. Report the estimated treatment log odds ratio and show that it does not change when you delete Centers 1 and 3 from the analysis. (When a center has outcomes of only one type, it provides no information about the treatment effect.)