A Selection Procedure for Selecting Good Exponential Populations

Consider k independent exponential populations with location parameters μ₁,…, μ_k and a common scale parameter or standard deviation θ. Let μ_(k) be the largest of the μ's and define a population to be good if its location parameter exceeds μ_(k) –Δ₁. A selection procedure is proposed to select a subset of the k populations which includes the good populations with probability at least P*, a pre-assigned value. Simultaneous confidence intervals, that can be derived with the proposed selection procedure, are discussed. Moreover, if populations with locations below μ_(k) –δ₂, (δ₂ > δ₁) are “bad”, a selection procedure is proposed and a sample size is determined so that the probability of omitting a “good” population or selecting a “bad” population is at most 1 – P*.     

A stepdown procedure with feedback for identifying inferiority among three treatments

This paper considers the problem of identifying which treatments are strictly inferior to the best treatment or treatments in a balanced one-way layout with three treatments, which has important applications in screening trials for new product development. A stepdown procedure is constructed that selects a subset of the treatments containing only treatments that are known to be strictly inferior to the best treatment or treatments. This stepdown procedure uses feedback from the first stage to the second stage that improves its operating characteristics. The advantages accruing from this feedback are demonstrated.     

Subset Selection Procedures for Randomized Designs

Starting from the principle that there exists a randomization procedure that assigns treatments to experimental units, four subset selection rules for the problem of selecting the best treatment from a set of different treatments are proposed. Two of these are extensions of already existing subset selection procedures, which were defined for unbalanced designs, and need a separate selection constant for each individual treatment. The other two rules proposed are new and need only one selection constant for all treatments. The various procedures are compared, and illustrated by application to a plant breeding variety trial.     

A testcross procedure for selecting exotic strains to improve pure-line cultivars in predominantly self-fertilizing species

Methods for identifying germplasm carrying alleles with the potential to improve a particular single-cross hybrid have been proposed and discussed in recent years. There is a need for similar methods to be used in breeding crops for which pure-line cultivars, rather than hybrids, are the goal. The objective of this research was to develop a method to identify germplasm lines with the potential to contribute favorable alleles not present in a specified pure line or set of pure lines. Given a set of adapted pure lines (A ₁, A ₂ ..., A _m) to be improved and a set of germplasm lines (P ₁ P ₂ ..., P _f), the procedure consists of producing all f x m possible hybrids and evaluating them along with the parents. The testcross statistic T _ij is defined by T _ij=(F _ij–A _j)+(1–) (F _ij–P _i), where A _j, P _i, and F _ij represent the performance of thej ^th adapted line, the i ^th germplasm line, and their hybrid, respectively. The statistic is the mean value of T _ij over all adapted parents A _j. If =(1/2)(1+d), where d = the mean degree of dominance, then T _ij measures the potential for alleles from P _i to improve A _j and measures the potential for alleles from P _i to improve the set A ₁, A ₂ ..., A _m. Use of data on soybean and peanut hybrids published by other researchers suggests that the value assumed for d has little effect on the P _i chosen. The ability of the T _ij and statistics to identify germplasm strains carrying rare favorable alleles should be assessed in empirical studies.Joint contribution: OARDC (Journal Articale No. 161-94), USDAARS, Iowa Agriculture and Home Economics Expriment Station (Journal Paper No. J-16109; Project 2985), and Agreculture and Agri-Food Canada. Salaries and research support for S. K. St. Martin Provided by state and federal funds appropriated to the Ohio Agricultural Research and Development Center, Ohio State University     

Subset Selection for Exponential Populations: Determination of the Selection Constant

Given are k(≧2) exponential populations differing only in their location parameter. One wishes to choose the best one, that is the population with the largest value of the location parameter. A possible method for solving this problem is to select a subset of the k populations of size at least one which includes the best population with a required confidence P*(k^?1 ≤ P* ≤1). In this paper the required selection constant is determined for different values of k and P*. Also an approximation for the selection constant is derived. A comparison with the exact results is made.     

A parsimonious statistical design and breeding procedure for evaluating and selecting desirable characteristics over environments

The concept of stability as described in the literature does not meet all of the desirable criteria required by growers of cultivars. Various types of possible responses are discussed, and these are divided into those desirable from a grower's viewpoint and those not. Measures of stability appearing in the literature are based on variances, linear regression slopes, and/or deviations from regression. The most desirable response type would be denoted as unstable by current concepts of stability. It is shown how to simulate environments that exceed the ranges found in practice. A statistical design is described which is the height of parsimony and has the advantage that the conditions varied are known. The experimental results can then be interpreted in light of the known conditions. The design is optimally cost effective in terms of funds, material, and personnel. A breeding procedure is presented for such characteristics as desired response, stability under current definitions, tolerance (to pests, cold, drought, etc.), protein, quality, fiber, etc.Technical Report Series No. Bu-960-MA of the Biometrics Unit, Cornell University, Ithaca, N.Y.Liberty Hyde Bailey Professor Emeritus, Biometrics Unit, Department of Plant Breeding and Biometry, Cornell University, Ithaca, NY; Assistant Professor of Vegetable Crops, IFAS, University of Florida, Everglades Research Center, Belle Glade, Fla.     

A new criterion for confounder selection

Summary We propose a new criterion for confounder selection when the underlying causal structure is unknown and only limited knowledge is available. We assume all covariates being considered are pretreatment variables and that for each covariate it is known (i) whether the covariate is a cause of treatment, and (ii) whether the covariate is a cause of the outcome. The causal relationships the covariates have with one another is assumed unknown. We propose that control be made for any covariate that is either a cause of treatment or of the outcome or both. We show that irrespective of the actual underlying causal structure, if any subset of the observed covariates suffices to control for confounding then the set of covariates chosen by our criterion will also suffice. We show that other, commonly used, criteria for confounding control do not have this property. We use formal theory concerning causal diagrams to prove our result but the application of the result does not rely on familiarity with causal diagrams. An investigator simply need ask, “Is the covariate a cause of the treatment?” and “Is the covariate a cause of the outcome?” If the answer to either question is “yes” then the covariate is included for confounder control. We discuss some additional covariate selection results that preserve unconfoundedness and that may be of interest when used with our criterion.     

Simultaneous Comparisons of Multiple Treatments to Two (or More) Control

DUNNETT (1955) developed a procedure simultaneously comparing k treatments to one control with an exact overall type I error of α when all sampling distributions are normal. Sometimes it is desirable to compare k treatments to m≧2 controls, in particular to two controls. For instance, several new therapies (e.g., pain relievers) could be compared to two standard therapies (e.g., Aspirin and Tylenol). Alternatively, a standard therapy could be very expensive, difficult to apply and/or have bad side effects, making it useful to compare each new therapy to both standard therapy and no therapy (Placebo). Dunnett's method is expanded here to give comparisons of mean values for k treatments to mean values for m≧2 controls at an exact overall type I error of α when all sampling distributions are normal. Tabled values needed to make exact simultaneous comparisons at α = .05 are given for m = 2. An application is made to an example from the literature.     

Covariate adjustment in the analysis of microarray data from clinical studies

There is tremendous scientific interest in the analysis of gene expression data in clinical settings, such as oncology. In this paper, we describe the importance of adjusting for confounders and other prognostic factors in order to select for differentially expressed genes for follow-up validation studies. We develop two approaches to the analysis of microarray data in non-randomized clinical settings. The first is an extension of the current significance analysis of microarray procedures, where other covariates are taken into account. The second is a novel covariate-adjusted regression modelling based on the receiver operating characteristic (ROC) curve for the analysis of gene expression data. The ideas are illustrated using data from a prostate cancer molecular profiling study.