The name is absent

approach based on a utility function that includes explicit weights for the size of the
increase.

In chapter 4, I introduce a non-parametric Bayesian model for phase II clinical
trial with patients presenting different subtypes of the disease under study. The
subtypes are not a priori exchangeable. The lack of a priori exchangeability hinders
the straightforward use of traditional hierarchical models to implement borrowing of
strength across disease subtypes. We introduce instead a random partition model for
the set of disease subtypes. All subtypes within the same cluster share a common
success probability. The random partition model is a variation of the product partition
model that allows us to model a non-exchangeable prior structure. This model is the
categorical covariate version of the more general non exchangeable product partition
model proposed in Mller et al. (2009). In particular the data arises from a phase
II clinical trial of patients with sarcoma, a rare type of cancer affecting connective
or supportive tissues and soft tissue (e.g., cartilage and fat). Each patient presents
one subtype of the disease and subtypes are grouped by good, intermediate and
poor prognosis. The prior model should respect the varying prognosis across disease
subtypes. Two subtypes with equal prognosis should be more likely a priori to co-
cluster than any two subtypes with different prognosis. The practical motivation for
the proposed approach is that the number of accrued patients within each disease
subtype is too small to asses the success rates with the desired precision if we were
to analyze the data for each subtype separately. It would be practically impossible
to carry out a clinical study of possible new therapies. Like a hierarchical model, the
proposed clustering approach considers all observations, across all disease subtypes,
to estimate individual success rates. But in contrast with the standard hierarchical
models, the model considers disease subtypes a priori non-exchangeable. This implies
that when assessing the success rate for a particular type our model borrows more
information from the outcome of the patients sharing same prognosis than from the
others.

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