Consider a clinical trial where treatments A and B are assigned to n patients via Efron's (1971) biased coin design. Randomization tests of the null hypothesis H(,0) of no treatment difference are studied. We derive a recursion procedure for obtaining the exact randomization distribution for each member of a class of test statistics. This enables one to perform exact tests of H(,0). In accordance with Cox' (1982) suggestion, the randomization distributions of the test statistics are conditional on the terminal imbalance of the treatment allocation. Letting T(,1), ..., T(,n) be the treatment assignment variables, with T(,i) = 1 if the i('th) patient receives treatment B, = 0 if the i('th) patient receives treatment A, conditional distributional properties of these variables are obtained. Recursive procedures for computing the conditional exact and approximate moments of T(,1), ..., T(,n) are also derived. Based on these results, test statistics are proposed for use in the randomization tests when the sample size is large. The adequacy of the normal approximations to the conditional randomization distributions of these statistics are ascertained via a computer simulation. / Methods for constructing asymptotic simultaneous confidence bands for the survival function under the proportional hazards model of random right-censorship are developed. These bands are based on the maximum likelihood estimator (MLE) of the survival function, rather than the well-known product limit estimator (PLE). In the case where the censoring parameter, denoted by (beta), is known the bands are asymptotically exact, while when (beta) is unknown the bands are asymptotically conservative. For the (beta) unknown case, the proposed bands are shown to be narrower than those proposed by Cheng and Chang (1985). The idea of Csorgo and Horvath (1986) of mixing bands is also employed to obtain even narrower bands. As one would expect, under the more structured model, the PLE-based band of Gillespie and Fisher (1979) is shown to be inferior to the MLE-based bands, and this inferiority is more marked as the degree of censoring increases. / Source: Dissertation Abstracts International, Volume: 47-08, Section: B, page: 3423. / Thesis (Ph.D.)--The Florida State University, 1986.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_75929 |
| Contributors | PENA, EDSEL ALDEA., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 107 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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