ST 520 Statistical Principles of Clinical Trials - NCSU Statistics ...

CHAPTER 7 ST 520, A. TSIATIS and D. Zhang
|Tn34| = |2
� �1/2 640 × 639
(.633 − .715)| = 2.94 ∗ .
640 + 639
Clearly, treatments 2 and 4 are the better treatments, certainly better than control. The only
controversial comparison is treatment 2 versus treatment 3, where, we may not be able to conclude
that treatment 2 is significantly better than treatment 3 because of the conservativeness of the
Bonferroni correction
7.4 K-sample tests for continuous response
For a clinical trial where we randomize patients to one of K > 2 treatments and the primary
outcome is a continuous measurement, then our primary interest may be to test for differences in
the mean response among the K treatments. Data from such a clinical trial may be summarized
as realizations of the iid random vectors
(Yi, Ai), i = 1, . . ., n,
where Yi denotes the response (continuously distributed) for the i-th individual and Ai denotes
the treatment (1, 2, . . ., K) that the i-th individual was assigned. Let us denote the treatment-
specific mean and variance of response by
and
Note:
E(Yi|Ai = j) = µj, j = 1, . . .,K
var(Yi|Ai = j) = σ 2 Y j , j = 1, . . .,K.
1. Often, we make the assumption that the treatment-specific variances are equal; i.e. σ 2 Y 1 =
. . . = σ2 Y K = σ2 Y , but this assumption is not necessary for the subsequent development.
2. Moreover, it is also often assumed that the treatment-specific distribution of response is
normally distributed with equal variances; i.e.
(Yi|Ai = j) ∼ N(µj, σ 2 Y ), j = 1, . . .,K
Again, this assumption is not necessary for the subsequent development.
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