Small Youden Rectangles, Near Youden Rectangles, and Their Connections to Other Row-Column Designs

In this paper we study Youden rectangles of small orders. We have enumerated all Youden rectangles for all small parameter values, excluding the almost square cases, in a large scale computer search. For small parameter values where no Youden rectangles exist, we also enumerate rectangles where the number of symbols common to two columns is always one of two possible values. We refer to these objects as \emph{near Youden rectangles}. For all our designs we calculate the size of the autotopism group and investigate to which degree a certain transformation can yield other row-column designs, namely double arrays, triple arrays and sesqui arrays. Finally we also investigate certain Latin rectangles with three possible pairwise intersection sizes for the columns and demonstrate that these can give rise to triple and sesqui arrays which cannot be obtained from Youden rectangles, using the transformation mentioned above.Comment: 33 pages, 21 Table

Double Arrays, Triple Arrays and Balanced Grids

Triple arrays are a class of designs introduced by Agrawal in 1966 for two-way elimination of heterogeneity in experiments. In this paper we investigate their existence and their connection to other classes of designs, including balanced incomplete block designs and balanced grids

Complete Enumeration and Properties of Binary Pseudo-Youden Designs PYD(9, 6, 6)

A binary pseudo -Youden design PYD(9, 6, 6) is a 6 × 6 array in which each cell contains one element from the set V = {1, 2, . . ., 9}, and each element from V occurs 4 times. Every row of the array contains distinct elements and every column contains distinct elements. The rows and columns, when taken together, are pairwise balanced and form a (9, 12, 8, 6, 5)-BIBD. In Preece (1968) and (1976) a total of 345 species of binary PYD(9, 6, 6) were found. Here we complete this enumeration and find 348 species of binary PYD(9, 6, 6). We give a complete set of invariants for these species based upon the numbers of intercalates and anti-intercalates that they contain; and discuss some of their properties. We also show that there are 696 non-isomorphic binary PYD(9, 6, 6), and give a complete set of invariants for these arrays

Relations among partitions

Combinatorialists often consider a balanced incomplete-block design to consist of a set of points, a set of blocks, and an incidence relation between them which satisfies certain conditions. To a statistician, such a design is a set of experimental units with two partitions, one into blocks and the other into treatments: it is the relation between these two partitions which gives the design its properties. The most common binary relations between partitions that occur in statistics are refinement, orthogonality and balance. When there are more than two partitions, the binary relations may not suffice to give all the properties of the system. I shall survey work in this area, including designs such as double Youden rectangles.PostprintPeer reviewe

Supervised Dimension Reduction for Large-scale Omics Data with Censored Survival Outcomes Under Possible Non-proportional Hazards

The past two decades have witnessed significant advances in high-throughput ``omics technologies such as genomics, proteomics, metabolomics, transcriptomics and radiomics. These technologies have enabled simultaneous measurement of the expression levels of tens of thousands of features from individual patient samples and have generated enormous amounts of data that require analysis and interpretation. One specific area of interest has been in studying the relationship between these features and patient outcomes, such as overall and recurrence-free survival, with the goal of developing a predictive ``omics profile. Large-scale studies often suffer from the presence of a large fraction of censored observations and potential time-varying effects of features, and methods for handling them have been lacking. In this paper, we propose supervised methods for feature selection and survival prediction that simultaneously deal with both issues. Our approach utilizes continuum power regression (CPR) - a framework that includes a variety of regression methods - in conjunction with the parametric or semi-parametric accelerated failure time (AFT) model. Both CPR and AFT fall within the linear models framework and, unlike black-box models, the proposed prognostic index has a simple yet useful interpretation. We demonstrate the utility of our methods using simulated and publicly available cancer genomics data

Optimal Row-Column Designs for Correlated Errors and Nested Row-Column Designs for Uncorrelated Errors

In this dissertation the design problems are considered in the row-column setting for second order autonormal errors when the treatment effects are estimated by generalized least squares, and in the nested row-column setting for uncorrelated errors when the treatment effects are estimated by ordinary least squares. In the former case, universal optimality conditions are derived separately for designs in the plane and on the torus using more general linear models than those considered elsewhere in the literature. Examples of universally optimum planar designs are given, and a method is developed for the construction of optimum and near optimum designs, that produces several infinite series of universally optimum designs on the torus and near optimum designs in the plane. Efficiencies are calculated for planar versions of the torus designs, which are found to be highly efficient with respect to some commonly used optimality criterion. In the nested row-column setting, several methods of construction of balanced and partially balanced incomplete block designs with nested rows and columns are developed, from which many infinite series of designs are obtained. In particular, 149 balanced incomplete block designs with nested rows and columns are listed (80 appear to be new) for the number of treatments, v \u3c 101, a prime power

A computational approach to identify predictive gene signatures in Triple Negative Breast Cancer

Microarray technology has been extensively used to detect patterns in gene expression that stem from regulatory interactions. Seminal studies demonstrated that the synergistic use of microarray-based techniques and bioinformatics analysis of genomic data might not only further the understanding of pathological phenotypes, but also provide lists of genes to dissect a disease into distinct groups, with different diagnostic or prognostic characteristics. Nonetheless, optimism for microarray-based technologies as clinical tools has suffered of both perceptual and real setbacks. Criticism is largely on the ground of general non-reproducibility of gene signatures and the inability to replicate results. The research activity illustrated in this thesis aimed at fulfilling methodological gaps still hampering the identification of gene signatures with proved prognostic and predictive value and, finally, affecting their reliability, reproducibility, and applicability. Specifically, we developed computational methods to efficiently merge gene expression profiles of tumors from multiple, independent, retrospective studies and to construct meta-datasets storing high throughput gene expression profiles and clinical information from thousands cancer patients. Moreover, we expanded on the concept of gene signature and derived consensus signatures, i.e. linear weighted combinations of gene signatures that, singularly, recapitulate independent signaling pathways or specific molecular mechanisms, while intertwined together render a more comprehensive molecular model of tumor progression or chemo-resistance. This approach has been applied to breast cancer, in general, and to triple negative breast cancer (TNBC), in particular, and resulted in the identification of gene signature combinations with increased robustness and power to predict cancer progression or response to therapy over the use of single signatures

Advanced row-column designs for animal feed experiments

Not AvailableInappropriate statistical designs may misinterpret results of animal feed experiments. Thus complete statistical designs can make animal feed research more appropriate and cost effective. Usually factorial row-column designs are used when the heterogeneity in the experimental material is in two directions and the experimenter is interested in studying the effect of two or more factors simultaneously. Attempts have been to develop the method of construction of balanced nested row column design under factorial setup. Factorial experiments are used in designs when two or more factors have same levels or different levels. The designs that are balanced symmetric factorials nested in blocks are called block designs with nested row-column balanced symmetric factorial experiments. These designs were constructed by using confounding through equation methods.Construction of confounded asymmetrical factorial experiments in row-column settings and efficiency factor of confounded effects was worked out. The design can be used in animal feed experiment with fewer resources by not compromising the test accuracy.Not Availabl