The name is absent

26

(J = 4) ordinal outcomes labeled ¾ = (z_iχ,..., z_ii) with four (K = 3) possible values,
i.e., z_ij ∈ {0,1,2,3}. The observations z_i were generated according to the model
defined by (2.2)-(2.4) but with r_i generated from a mixture of normal distributions,
r_i ~ 0.75 N (0,1) ÷ 0.25 7V(4,1). In (2.2) we fixed the values of the cutpoints, θjk,
as (0ofc, θik, ∙ ∙ ∙, ^4fc) — (—∞, —3,1,2, ∞) for all j. We deliberately chose cutpoints
different from the default cutpoints that are used in the analysis model. In (2.3) we
set Xi — — 1 for group A and x_i = 1 for group B. The slope parameters in the probit
regression were set to (∕3j,,...,/З4) = (0,0.5,1,1.5)^τ. In (2.4) we set the variance
σ∣ = 1, the number of components in the normal mixture G = 3, the normal means
(μ_jι,μ_j∙2>Mj2) ⁼ (—5,0,3) and the mixture weights (p_j1,Pj2,Pj3) = (0.9,0.05,0.05) for
all j. The true cell probabilities are reported in Table 2.2.

We fit model (2.2)-(2.5) with priors for the parameters as described in Section 4.
More specifically, we assume that the probit parameters in (2.3), βj, follow the normal
distribution specified in (2.10) with τ∏β_j = 0 and = 1. In (2.4) we assume G = 2,
and weights distributed according to (2.5) with c⅛_jι = o_j2 = 1 for all j. The normal
means are assigned conjugate priors, μ_js ~ N{φ,σ²_fl = 16) and φ ~ N(0,σψ = 10⁴).
We use the default choices σ∣ = 1,   = 4 and σ²_μ — 16. The values of the cutpoints

in (2.2), θjk, were set to (0_j∙_o, ∙ ∙ ■, ⅛4) = (—∞, —4,0,4, ∞) for all j.

We simulated a total of 110,000 iterations of the posterior MCMC scheme. Af-
ter an initial burn-in of 10,000 iteration, the imputed parameters were saved after
each 10^th iteration, yielding to a posterior Monte Carlo sample size of 10,000. The
marginal posterior probabilities for each combination of toxicity type and grade were
estimated and compared with the true cell probabilities in Table 2.2. The model
reports reasonable estimates of the cell probabilities; in 26 out of 32 cells the true cell
probability is within the reported 95% central credible interval.

For comparison we also implemented an ordinal probit regression with random
cutpoints, but a (single) normal distribution for the latent probit scores (Albert and
Chib, 1993). For a fair comparison we included patient-specific random effects as

<<   35   36   37   38   39   40   41   >>

More intriguing information