The name is absent

89

Notice that in general,

K(n)+1

Pr{pⁿ I xⁿ) ≠      ^p'^r(p"'⅜+ι = ^l I ⅛₊ι = q)fk{p_n)

fc=l

where ʌ was defined in (4.5). That is, Pr{p_n ∣ xⁿ) is not obtained when marginalizing
Pr(p",φ_ra+ι I xⁿ,x_n+r = q) with respect to φ_n+1.

4.4 Comparison and Operating Characteristics

In this section we compare via simulation the performance of the proposed model vs.
different alternative models. The comparison is in terms of bias, mean square error
and coverage probability (CP). Later, in Subsection 4.4.2 we continue the comparison
for the best two models by focusing on performance summaries that are relevant for
the clinical trial design. Specifically, we will consider the probability (under repeat
experimentation) of correctly identifying disease subtypes for which the treatment
is not effective. Early identification of such disease subtypes is important to avoid
exposure of patients to unnecessary risks. In the implementation of the proposed
NEPPM model we assume that the parameter a in the definition of in (4.5) is
Gα(5,0.5) distributed. Here Gα(α,6) denotes the gamma distribution with mean a∕b.

4.4.1 Competing Models

We compare the proposed NEPPM (4.1) with the following alternative models. The
first model entirely abandons borrowing strength across subtypes. The second model
borrows strength, but assumes a priori exchangeable subtypes. The third model
respects the lack of exchangeability across sub-types, but goes to the extreme of
grouping the subtypes by the covariate, in our case prognosis, and fixing this grouping
for the rest of the analysis.

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