For the clinical trial in Table 9.16, let π_it= P(Y_it= 1 | u_i) denote the probability of success for treatment t in center i.

a. The random intercept model (12.11) has β̂ = 1.52 (SE = 0.70) and σ̂ = 1.9. Interpret.

b. From Section 9.8.3, the fixed effects analog of this model (replacing α + u_i by α_i) has α̂₁ = α̂₃ = €“ ˆž, corresponding to π̂_1t = π̂_3t = 0 for each treatment. By contrast, the random effects model has α̂ + uÌ‚₁ = €“3.78 (using NLMIXED in SAS) and π̂₁₁ = 0.047 and π̂₁₂ = 0.011 in center 1. Explain how this model can have π̂_it > 0 in centers having successes.

Table 9.16:

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Clinical Trial Relating Treatment to Response with XY and YZ Marginal Tables" YZ Marginal Response Success Center Failure Success Failure Treatment Active drug Placebo 5 1 14 2 Active drug Placebo 12 22 10 Active drug 3 12 Placebo 5 Active drug 4 3 6. Placebo 2 5 Active drug Placebo 5 21 2 12 XY Active drug Placebo 12 36 marginal 4 42 "X, Treatment; Y, response; Z, center. 9.