Statistical inference under the assumption of monotonic dose-response with applications to animal carcinogenicity studies

This dissertation is concerned with statistical issues involved in dose-response experiments. Several new methods are developed to deal with problems in multiple comparisons and testing for any potential dose-related trend in response. The discussion will be focused on applications to animal carcinogenicity studies although the methodologies are broadly applicable.; First, schemes of sequential testing for multiple comparisons are proposed in order to compare several dose groups with a zero-dose control (Chang, Ahn, and Chen, [7]). The sequential testing is conducted within a closed family of one-sided tests, and some common trend tests are chosen to conduct each individual hypothesis test. The procedures investigated are based on a monotonicity assumption. These closed procedures strongly control the familywise error rate while providing information concerning the shape of the dose-response relationship. Comparisons among the sequential testing procedures and some traditional Bonferroni-type approaches are made via a Monte Carlo simulation study.; Second, methods of isotonic regression are proposed to increase the power of common trend tests in situations where a monotonicity constraint is imposed upon the dose-response function. Isotonic versions of Cochran-Armitage-type trend tests for binary response data are developed, and the bootstrap method is used in finding the empirical distributions of the test statistics and their critical values (Mancuso, Ahn, and Chen, [28]). The isotonic likelihood ratio test with a survival adjustment is also proposed. This survival adjustment can be applied to the likelihood ratio test for the order-restricted and unrestricted parameter cases. To achieve the isotonic modifications, an amalgamation algorithm is applied when the observed dose-response is nonmonotonic. A Monte Carlo simulation study comparing these trend tests shows the advantages of the isotonic modifications and survival adjustment.; When the response consists of a rare event such as the development of a certain type of tumor, sparse data can often occur. It has been recognized in the literature that asymptotic tests may be unreliable in the context of sparse data (Mantel et al., [30]; Ali, [1]), and exact statistical methods are preferred. The exact randomization trend test based on the multivariate hypergeometric distribution is less powerful in the presence of treatment-related risks other than the specified response. Particularly, the loss of power becomes more pronounced when competing risks cause progressively higher mortality rates with increasing dose, which is usual in practice. An age-adjusted form of the exact randomization test is proposed to adjust for this effect (Mancuso et al., [29]). Permutational distribution for Peto's cause-of-death (COD) test is also explored and compared to its asymptotic counterpart by simulation. Such tests that rely on COD information have been criticized for the subjectivity in the pathologists' determinations as well as for economic reasons. The proposed age-adjusted exact test does not require COD, and it is shown to compare favorably to the COD tests via an extensive Monte Carlo simulation.; The methods developed in this dissertation were motivated by analyses of some real data sets originating from sources such as the National Toxicology Program (NTP) and National Center for Toxicological Research (NCTR). The results of these applications will be included for illustration.