A study of BIB designs through support matrices

This paper deals with the existence and nonexistence of BIB designs with repeated blocks. The approach is an algebraic one. The concept of a support matrix is introduced and some of its basic properties are noted. Some basic examples of support matrices are given when the block size is 3. The connection between full column rank proper support matrices and irreducible designs is explored and some examples of such matrices are given.     

On the equivalence of two approaches to simplicity in the analysis of block designs and some related results

Two seemingly different approaches to simplicity in the analysis of connected block designs, and their relationship to the concepts of balance are discussed.     

Comparing search and estimation performances of designs based on a compound criterion

Since the introduction of the search design by Srivastava [Designs for searching non-negligible effects. In: Srivastava, editor. A survey of statistical design and linear models. Amsterdam: North-Holland, Elsevier; 1975. p. 507–519], construction of such designs has been considered by many researchers. The efficient performances of constructed search designs in terms of parameter estimation and search ability of parameters have also been investigated by several authors. They have proposed suitable optimality measures such as DD- and AD-optimality for estimation in the early stage of search design construction. Moreover, since 1990s, some criteria have been developed to evaluate search performance of a design. Although these criteria are useful none of them is able to evaluate both estimation and search efficiency of a design simultaneously. In this paper, we propose dual-task criteria to deal with searching and estimating performances of search designs. These compound criteria are weighted multiplication of estimation and search suitable criteria. They will be used for design comparison and the results will be presented.     

An Empirical Analysis of Some Nonparametric Goodness-of-Fit Tests for Censored Data

In this article, we consider some nonparametric goodness-of-fit tests for right censored samples, viz., the modified Kolmogorov, Cramer–von Mises–Smirnov, Anderson–Darling, and Nikulin–Rao–Robson χ² tests. We also consider an approach based on a transformation of the original censored sample to a complete one and the subsequent application of classical goodness-of-fit tests to the pseudo-complete sample. We then compare these tests in terms of power in the case of Type II censored data along with the power of the Neyman–Pearson test, and draw some conclusions. Finally, we present an illustrative example.     

Some new constructions of circular balanced repeated measurements designs

Repeated measurements designs are widely used in medicine, pharmacology, animal sciences, and psychology. In this article, some infinite series are developed to generate the balanced repeated measurements designs for p (periods) even. For p odd, construction procedures are also described. Catalogues of the proposed designs are also presented for p = 5, 7, 9, when v ≤ 100.     

Optimal designs for multivariate logistic mixed models with longitudinal data

This paper considers the optimal design problem for multivariate mixed-effects logistic models with longitudinal data. A decomposition method of the binary outcome and the penalized quasi-likelihood are used to obtain the information matrix. The D-optimality criterion based on the approximate information matrix is minimized under different cost constraints. The results show that the autocorrelation coefficient plays a significant role in the design. To overcome the dependence of the D-optimal designs on the unknown fixed-effects parameters, the Bayesian D-optimality criterion is proposed. The relative efficiencies of designs reveal that both the cost ratio and autocorrelation coefficient play an important role in the optimal designs.     

The Parshvanath yantram yields a constant-sum partially balanced incomplete block design

Yantrams have been used to generate mixture designs in the interior of a simplex. In this note, we show a connection between Parshvanath yantram and a particular partially balanced incomplete block design. This block design is rather special and somewhat unexpected due to the feature that sum of the treatment symbols in any block is constant.     

Properties of the weighted log‐rank test in the design of confirmatory studies with delayed effects

Proportional hazards are a common assumption when designing confirmatory clinical trials in oncology. This assumption not only affects the analysis part but also the sample size calculation. The presence of delayed effects causes a change in the hazard ratio while the trial is ongoing since at the beginning we do not observe any difference between treatment arms, and after some unknown time point, the differences between treatment arms will start to appear. Hence, the proportional hazards assumption no longer holds, and both sample size calculation and analysis methods to be used should be reconsidered. The weighted log‐rank test allows a weighting for early, middle, and late differences through the Fleming and Harrington class of weights and is proven to be more efficient when the proportional hazards assumption does not hold. The Fleming and Harrington class of weights, along with the estimated delay, can be incorporated into the sample size calculation in order to maintain the desired power once the treatment arm differences start to appear. In this article, we explore the impact of delayed effects in group sequential and adaptive group sequential designs and make an empirical evaluation in terms of power and type‐I error rate of the of the weighted log‐rank test in a simulated scenario with fixed values of the Fleming and Harrington class of weights. We also give some practical recommendations regarding which methodology should be used in the presence of delayed effects depending on certain characteristics of the trial.     

t-Latinized Designs

A variety trial sometimes requires a resolvable block design in which the replicates are set out next to each other. The long blocks running through the replicates are then of interest. A t -latinized design is one in which groups of these t long blocks are binary. In this paper examples of such designs are given. It is shown that the algorithm described by John & Whitaker (1993) can be used to construct designs with high average efficiency factors. Upper bounds on these efficiency factors are also derived.     

Cutting Experimental Designs into Blocks

Most experimental material in agriculture and industry is heterogeneous in nature and therefore its statistical analysis benefits from blocking. Many experiments are restricted in time or space, and again blocking is useful. This paper adopts the idea of orthogonal blocking of Box & Hunter (1957) and applies it to optimal blocking designs. This approach is then compared with the determinant-based approach described in the literature for constructing block designs.