The name is absent

16

In other words , the modification of the algorithm consists on sampling from p(θ ∣ z, /3)
instead of from p(θ ∣ z,v,β'). A Metropolis-Hasting algorithm (see, Cowles, 1996;
Johnson and Albert 1999, p. 135) is used to simulate from the former distribution.

Once a posterior sample (∕3¹,θ¹),..., (∕3^m,0^m) from p(β,θ ∣ z) is obtained the
Monte Carlo estimate of cell probability τ⅛ ≡ Pr[zf = k] for a future observation
with covariate Xf is

1    ^M

^π* ≈ 77 = Σ K W^m - ‰) - Φ^¹(∙τJ∕3^m - f^)} for к = O,..., K - 1.

IVl          ¹

m=l

Finally, we note that Albert and Chib’s model for more than two categories re-
quires the “parallel regression assumption,” the probit version of the proportional
odds assumption of the logistic model. That is,

Pr[z ≤ к I τ] =Pr[x^tβ + e ≤ 0_fc+1]

=Pr[e ≤ θ_k+1 - x^tβ] = Φ(0_fc+1 - x^tβ)

and, therefore,
f_k(x) := Φ~¹(-Pφ ≤ к I x]) = θ_k+1 - x^tβ.

In other words, the assumption is that the functions f_k for к — 0,...,7^-1 are
parallel lines.

2.3 A Phase III Clinical Trial

Studies have suggested that retinoid chemoprevention may help control second pri-
mary tumors, disease recurrence, and mortality for stage I non-small-cell lung cancer
(NSCLC) patients. A National Cancer Institute (NCI) intergroup phase III trial of
1166 patients with pathologic stage I NSCLC was conducted to validate the efficacy
of isotretinoin, a retinoid hypothesized to have chemopreventive properties. Patients
were randomly assigned to receive either placebo or isotretinoin (30 mg∕day) for 3
years in a double-blinded study. Patients were stratified at randomization by tumor

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