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91

Table 4.2: Simulation truth pi under five alternative scenarios

scenario

good

intermediate

poor

Ni

6, 6, 8

40, 40, 30, 20, 20,10

7, 7, 6

SO

.59,.55,.47

.45,.4,.36,.34,.3,.26

.23,.19,.17

Sl

.28,.26,.24

.18,.16,.15,.17,.2,.19

.12,.13,.10

S2

.28,.26,.18

.24,.16,.15,.17,.10,.19

.12,.20,.10

S3

.40,.45,.35

.15,.10,.15,.12,.10,.10

.45,.35,.40

S4

.30,.40,.15

.20,.10,.30,.20,.15,.12

.15,.40,.30

The covariate ʃ, is equal to —1,0 or 1 when i indexes a sarcoma subtype with
poor, intermediate or good prognosis, respectively, MVN(μ, Λ) is the multivariate
normal distribution with mean μ and precision matrix Λ; and I2 denotes the 2 × 2
identity matrix. The precision matrix for the vector of regression parameters is chosen
to match the hyperparameter means in (4.1).

In the comparison, we consider n = 12 different experimental units (sarcoma
subtypes) with a categorical covariable xi with values -1 (poor), 0 (intermediate) and
1 (good). Each simulated trial realization consists of n independent observations
yi ~ Bin(7¾,jVi) with success rates fixed at an assumed simulation truth, and fixed
sample size Ni. We use Ni = 6,6,8,40,40,30,20,20,10,7,7 and 6, respectively. The
first three subtypes have poor overall prognosis, xi = — l,i = 1,...,3. The last three
subtypes have good prognosis, xi = 1, i — 10,..., 12. The remaining six subtypes
have xi = 0. The sample sizes Ni are chosen to match the expected accrual under
the 12 sarcoma subtypes in the motivating phase II sarcoma trial. For the simulation
truth on pi we consider five scenarios, SO through S4, summarized in Table 4.2.

Scenarios SO and Sl favor the HLRM model. The grouping by prognosis is perfect
and the monotonicity assumption implicit in the HLRM is satisfied. The remaining
scenarios represent varying levels of mismatch between prognosis and true success



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