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28

rior sample of size 10,000 was saved to estimate cell probabilities. Table 2.3 displays
the estimated cell probabilities together with central 95% credible intervals. Note the
near zero probabilities for some of the higher toxicity grades. The proposed model
is appropriate to handle sparse tables. The estimates formally confirm and quantify
what is expected from inspection of the data. There were more incidences of cheilitis
and conjunctivitis observed in the isotretinoin group than in the placebo group. Ele-
vated triglyceride levels were found more frequently in the isotretinoin group than in
the placebo group. In contrast, more patients experienced headache in the placebo
group. Posterior inference confirms that adverse event rates under treatment and
placebo differ significantly. Figure 2.3 summarizes posterior inference for the probit
regression parameters. It is 99% certain that the treatment (isotretinoin) had an
undesired (i.e., βj > 0) effect on cheilitis, conjunctivitis and hyp er-triglyceride.

The posterior distribution allows us to report coherent probabilities for any event
of interest. In particular, we can report inference on joint and conditional probabilities
of adverse events across different toxicities. For example, Table 4 reports conditional
probabilities for each adverse event (at any grade) given an adverse event in another
toxicity for the same patient. For comparison the table also reports the marginal
probabilities (in the diagonal). The considerable variation of probabilities in each
row confirms that the toxicities exhibited by the same patient are not independent.
The inclusion of subject specific random effects r⅛ was critical in fitting this data. For
example, the first row reports that the probability that a patient exhibits abnormal
vision is low marginally, but considerably increased when the patient has experienced
fatigue or headache.

Figure 2.4 shows the estimated distribution for the underlying latent variable,
v_ij, in equation (2.3) conditioned on r_i = 0. Let βj = E(βj ∣ z), pj_g = E{p_jg ∣ z)
and μ_jg = E(jj,j_g ∣ z). The figure shows χTβj + ∑_gPj_gN(μj_g, 1), for x — —1,1 and
j = l...,7.

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