Optimal approximate designs for comparison with control in dose-escalation studies

Abstract

Consider an experiment, where a new drug is tested for the first time on human subjectshealthy volunteers. Such experiments are often performed as dose-escalation studies: a set of increasing doses is pre-selected, individuals are grouped into cohorts, and in each cohort, the dose number i can be administered only if the dose number i − 1 has already been tested in the previous cohort. If an adverse effect of a dose is observed, the experiment stops and thus no subjects are exposed to higher doses. In this paper, we assume that the response is affected both by the dose or placebo effects as well as by the cohort effects. We provide optimal approximate designs for selected optimality criteria (E-, M V -and LV -optimality) for estimating the effects of the drug doses compared with the placebo. In particular, we obtain the optimality of Senn designs and extended Senn designs with respect to multiple criteria.

E- and R-optimality of block designs for treatment-control comparisons

“…, τ v − τ 0 . This interpretation is similar to that of Rosa and Harman [2017] for dose-escalation designs, and is analogous to that of Aor M V -optimality, but based on both the variances and the covariances of the estimators. In the discussion on Hedayat et al [1988a], multiple authors (Bechhofer and Tamhane [1988], Giovagnoli and Verdinelli [1988]) criticized the usually used criteria of A-and M V -optimality on the basis that they deal only with the variances of the estimators of τ i − τ 0 , disregarding the covariances between the estimators.…”

“…We extend the results of Rosa and Harman [2017] by providing all E-optimal approximate designs for comparisons with a control for any number of blocks and treatments, and without the dose-escalation design constraints. We apply this characterization to obtain E-optimal exact block designs for blocks of unequal sizes.…”

“…In this paper, we first provide approximate and exact designs that are optimal with respect to the E-optimality criterion, which minimizes the maximum variance for the linear combinations i>0 x i τ i − ( i>0 x i )τ 0 over all normalized x ∈ R v . The E-optimality received little attention for treatment-control experiments, with some exceptions: see Majumdar and Notz [1983], Notz [1985], Morgan and Wang [2011], Rosa and Harman [2017]. The lower interest resulted from the fact that this criterion was considered to be lacking a natural statistical interpretation (see Majumdar and Notz [1983], Hedayat et al [1988b]).…”

“…He showed that designs in a particular class of E-optimal row-column designs minimize the variance of the estimator of i>0 τ i /v − τ 0 . Rosa and Harman [2017] studied optimal approximate block designs under the presence of some special (dose-escalation) constraints when the number of blocks is v or v + 1. They provided interpretation of the obtained E-optimal approximate designs analogous to that of Notz [1985], and provided an interpretation for the obtained designs by means of variances and covariances for the (τ i − τ 0 )'s.…”

“…As noted by Hedayat et al [1988a], such an experimental objective arises, for instance, in screening experiments or in experiments in which it is desired to assess the relative performance of new test treatments with respect to a standard treatment. Comparisons with a control are also quite natural for medical studies involving placebo (e.g., see Senn [1997], Rosa and Harman [2017]).…”