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List of Figures

2.1 Distribution of the latent random variable vι ~ N(x^t_iβ, 1) according to Al-
bert and Chib’s model considering four categories, K = 3. The cutpoints Θ2
and Θ3 are random. The observed value ¾ is indicator of the interval where
Vi falls.................................... 15

2.2 Illustration of the distribution of the latent variable υ_iι in the model
described in (2.2)-(2.4) when the covariate takes values —1 and 1. Here
we consider: J — ∖ type of toxicity, no patient-specific random effect
r_i, G = 2 components in the mixture of normals and three, K =
2, possible ordinal outcomes. In both mixtures, the darkly shaded,
lightly shaded and white areas correspond to the probabilities ττγι- of
the ordinal outcome taking the values 0, 1 and 2, respectively. ....   22

2.3 Boxplots of the simulated posterior samples of the ordinal probit model
parameters (χ3_j^,s). Boxes corresponding to samples of βj^,s with 0.01-
quantile greater that zero are shaded................... 29

2.4 Estimated mixture of normal distribution of the latent variable vʊ
conditioned on η = 0 for j = 1,...,7. Shaded curve corresponds
to placebo (x = —1) and dashed to isotretinoin {x = 1). Darkly
and lightly shaded areas represent, respectively, the probability of no
toxicity (π_jo) and toxicity at grade 1 (7r₇1) under placebo........ 30

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