The Blind Paper Cutter: Teaching about Variation,Bias, Stability,and Process Control

The intention of this article is to provide teachers with a student activity to help reinforce learning about variation, bias, stability, and other statistical quality control concepts. Blind paper cutting is an effective way of generating tangible sequences of a product, which students can use to address many levels of questions. No special apparatus is required.     

A note on some conditions for optimality of certain ridge estimators

Consider the linear regression model, y = Xβ + ε in the usual notation with X'X being in the correlation form. Galpin(1980) claimed that the ridge estimators of Hoerl, Kennard and Baldwin(1975) and Lawless and Wang(1976) give guaranteed lower mean squared error than the least squares estimator when X'X has at least two very small eigen values. We show that the arguments of Galpin(1980) leading to the above claim are incorrect, and hence the claim itself is unsubstantited. A Monte Carlo study shows that Galpin's claim is not correct in general.     

Direct methods for generating extreme characteristic roots of certain random matrices

Computer generation of extreme characteristic roots of random matrices is considered. The usual approach in Monte-Carlo applications is to randomly generate the matrix and then compute desired characteristic roots. There are, however, theoretical results about the distribution of individual characteristic roots which might be used as a basis for computing algorithms. This alternative approach is considered for the Wishart and Beta matrices.     

An adaptive seamless phase II/III design for oncology trials with subpopulation selection using correlated survival endpoints

Although the statistical methods enabling efficient adaptive seamless designs are increasingly well established, it is important to continue to use the endpoints and specifications that best suit the therapy area and stage of development concerned when conducting such a trial. Approaches exist that allow adaptive designs to continue seamlessly either in a subpopulation of patients or in the whole population on the basis of data obtained from the first stage of a phase II/III design: our proposed design adds extra flexibility by also allowing the trial to continue in all patients but with both the subgroup and the full population as co-primary populations. Further, methodology is presented which controls the Type-I error rate at less than 2.5% when the phase II and III endpoints are different but correlated time-to-event endpoints. The operating characteristics of the design are described along with a discussion of the practical aspects in an oncology setting.     

Evaluating the relative accuracy and significance of net migration estimates

This paper presents the elements of a theory for evaluating the quality of a set of net migration estimates. The total error in a net migration estimate is decomposed into total bias and total variation. The bias is further decomposed into three bias elements-selection bias, estimator bias, and measurement bias. Tables of bounds for measurement and estimator biases in the vital statistics and the forward survival ratio estimates of net intercensal migration are presented. Both net migration levels and net migration ratios are treated, and provision is made for both life table and census survival ratio estimates. Some of the statistical tables are applied illustratively to net migration data for Canadian counties or census divisions during the 1951-61 decade. Tests of significance and confidence intervals are indicated for net migration estimates, and the basic technical notes are presented in appendices.     

When is a seamless study desirable? Case studies from different pharmaceutical sponsors

Background: Inferentially seamless studies are one of the best‐known adaptive trial designs. Statistical inference for these studies is a well‐studied problem. Regulatory guidance suggests that statistical issues associated with study conduct are not as well understood. Some of these issues are caused by the need for early pre‐specification of the phase III design and the absence of sponsor access to unblinded data. Before statisticians decide to choose a seamless IIb/III design for their programme, they should consider whether these pitfalls will be an issue for their programme. Methods: We consider four case studies. Each design met with varying degrees of success. We explore the reasons for this variation to identify characteristics of drug development programmes that lend themselves well to inferentially seamless trials and other characteristics that warn of difficulties. Results: Seamless studies require increased upfront investment and planning to enable the phase III design to be specified at the outset of phase II. Pivotal, inferentially seamless studies are unlikely to allow meaningful sponsor access to unblinded data before study completion. This limits a sponsor's ability to reflect new information in the phase III portion. Conclusions: When few clinical data have been gathered about a drug, phase II data will answer many unresolved questions. Committing to phase III plans and study designs before phase II begins introduces extra risk to drug development. However, seamless pivotal studies may be an attractive option when the clinical setting and development programme allow, for example, when revisiting dose selection. Copyright © 2014 John Wiley & Sons, Ltd.     

Neglected Method of Separating Demand and Supply in Time Series Regression

This article argues that in many markets, quantity is demand determined in the short run but price is supply determined, and that the dynamic restrictions between price and quantity implied by the model have been widely neglected in empirical research. Two examples illustrate our point—the demand and supply relationships between inflation and unemployment and between the terms of trade and the trade balance. In both, specifying quantity as a function of lagged prices in demand and price as a function of lagged quantities in supply (rather than concentrating on exogenous shift determinants) is sufficient to separate demand and supply.