Augmented p-rep designs

Early generation variety trials are very important in plant and tree breeding programs. Typically many entries are tested, often with very little resources available. Unreplicated trials using control plots are popular and it is common to repeat the trials at a number of locations. An alternative is to use p-rep designs, where a proportion of the test entries are replicated at each location; this can obviate the need for control plots. α-Designs are commonly used for replicated variety trials and we show how these can be adapted to produce efficient p-rep designs.     

Optimal promising zone designs

Clinical trials with adaptive sample size reassessment based on an unblinded analysis of interim results are perhaps the most popular class of adaptive designs (see Elsäßer et al., 2007). Such trials are typically designed by prespecifying a zone for the interim test statistic, termed the promising zone, along with a decision rule for increasing the sample size within that zone. Mehta and Pocock (2011) provided some examples of promising zone designs and discussed several procedures for controlling their type‐1 error. They did not, however, address how to choose the promising zone or the corresponding sample size reassessment rule, and proposed instead that the operating characteristics of alternative promising zone designs could be compared by simulation. Jennison and Turnbull (2015) developed an approach based on maximizing expected utility whereby one could evaluate alternative promising zone designs relative to a gold‐standard optimal design. In this paper, we show how, by eliciting a few preferences from the trial sponsor, one can construct promising zone designs that are both intuitive and achieve the Jennison and Turnbull (2015) gold‐standard for optimality.     

Efficient biokinetic experimental designs

Of the experimental methods available for obtaining data to estimate the biological kinetic parameters μ_m, K_s, and Yeach requires considerable experimental effort, yet often yields somewhat imprecise estimates of the parameters, particularly K_s. Therefore it would be worthwhile to seek ways to get parameter estimates of greater precision using less experimental effort. The precision of parameter estimates is strongly dependent, upon the settings of the independent, variables used in the experiments. This dependence is explained and an attempt made to show how experimental settings can be determined that lead efficiently to precise parameter estimates with minimal effort.     

Retrospective analysis of sequential dose-finding designs

The continual reassessment method (CRM) is a dose-finding design using a dynamic sequential updating scheme. In common with other dynamic schemes the method estimates a current dose level corresponding to some target percentile for experimentation. The estimate is based on all included subjects. This continual reevaluation is made possible by the use of a simple model. As it stands, neither the CRM, nor any of the other dynamic schemes, allow for the correct estimation of some target percentile, based on retrospective data apart from the exceptional situation in which the simplified model exactly generates the observations. In this article we focus on the very specific issue of retrospective analysis of data generated by some arbitrary mechanism and subsequently analyzed via the continual reassessment method. We show how this can be done consistently. The proposed methodology is not restricted to that particular design and is applicable to any sequential updating scheme in which dose levels are associated with percentiles via model inversion.