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recommendation. Another approach is to make G random by using, for example,
reversible jump. This would greatly complicate inference. Since the parameter G is
not of primary interest we did not pursue this direction. The model has two more
limitations. First, we showed that for any given set of toxicity probabilities under
placebo (ʃ — —1), there exists a mixture of normal densities that can represent
these probabilities as the area under the curve in the (fixed) intervals (‰, 0⅛+ι]. The
model assumes that by a simple shift of this mixture on the horizontal axis we can
represent the toxicity probabilities under treatment (.τ = 1). Second, a univariate
parameter, the patient-specific random effect, models the dependency of the different
toxic grades reported by the same patient. This implies, in particular that toxic
grades are positively correlated. For the particular application this is appropriate.
Nevertheless, in general, a scalar patient-specific random effect may not be sufficient
to model the correlation structure across adverse events. A possible solution is to
consider a multivariate patient-specific random effect. Modifications of the model to
analyze data with different dependence structures could be studied. An example is
mentioned in the discussion section of the second chapter. It considers the analysis
of repeated toxicity measures of the adverse events in the same patient.
In chapter 3, I introduced a semi-parametric model to analyze the outcome of
multistage phage display experiments with humans. The aim of the phage display
experiment is to identify peptides that bind with high affinity to specific tissues. That
is, the objective is a list of peptides binding to specific tissues. The particular ex-
periment considered has three stages. For every peptide-tissue pair, we only have
one observation: the triplet of counts in the three stages. The hierarchical structure
of the model allows borrowing strength across all pairs. The binding behavior of a
peptide is reflected by the event of having increasing mean counts across the three
stages. The model allows a biological interpretation of the parameters and an easy
representation of the event of increasing mean counts. Besides, the model is math-
ematically tractable. The MCMC simulation is straightforward due to the use of