Tests for a Simple Tree Order Restriction with Application to Dose–Response Studies

Abstract

We propose 'Dunnett-type' test procedures to test for simple tree order restrictions on the means of p independent normal populations. The new tests are based on the estimation procedures that were introduced by Hwang and Peddada and later by Dunbar, Conaway and Peddada. The procedures proposed are also extended to test for 'two-sided' simple tree order restrictions. For non-normal data, nonparametric versions based on ranked data are also suggested. Using computer simulations, we compare the proposed test procedures with some existing test procedures in terms of size and power. Our simulation study suggests that the procedures compete well with the existing procedures for both one-sided and two-sided simple tree alternatives. In some instances, especially in the case of two-sided alternatives or for nonnormally distributed data, the gains in power due to the procedures proposed can be substantial.

Evaluation of Toxicological Studies Using a Nonparametric Shirley-Type Trend Test for Comparing Several Dose Levels with a Control Group

“…Hothorn (1989) also discussed simulation results on robustness for both the parametric Williams test and the Shirley test. Further simulation results on the Shirley test were presented by Peddada et al (2006). Table 3 demonstrates the slight liberality of the new nonparametric Shirley-type trend tests in the case of k = 2 and extremely small sample sizes.…”

“…Shirley's procedure itself is to some extent robust against downturn effects at high dose due to its pooling of dose groups, see Section 3.3. In a simulation study, Peddada et al (2006) described the tradeoff between the gain in power of Williams/Shirley test compared with Dunnett (1955) /Dunn test (1964) for monotonic dose-response pattern and their nonrobustness for nonmonotonic pattern. A modification of the Williams/Shirley approach can be used, where not only k contrasts p 1 , p 2 , .…”

On the Design of Experiments with Ordered Treatments

“…Hu et al (2005) and Davidov and Peddada (2011)). There are, of course, many other orderings; we briefly mention the simple tree order which arises when comparing several treatments with a control (Dunnett, 1955;Peddada et al, 2006) and the umbrella order which may be used as an alternative to the simple order if high doses, or treatment levels, are associated with reduced efficacy or response.…”

A New Test for Simple Tree Alternative in a 2 x k Table

“…Among the RMLE based approaches, the work on confidence interval estimation subject to order restriction (Hwang and Peddada, 1994) is based on modified generalised isotonic regression estimator (MGIRE). A number of testing procedures are obtained following MGIRE (see, for example, Peddada et al, 2001;Peddada and Haseman, 2006;Teoh et al, 2008). In this paper we choose an MGIRE based test as competitor and is referred to as the MGIRE test.…”