Detecting the interaction of quantity and quality: A study of Fisher's analysis

In Sections 49 and 50 of the Design of Experiments, Fisher discusses an experiment designed to compare the effects of several types of manure on yield. Each type of manure is applied at three dosage levels: zero, single, and double doses. Fisher points out that the usual contrasts constructed for a factorial experiment are unsatisfactory in this setting. In particular, since the response curves necessarily meet at the zero dose, the usual notion of interaction as a lack of parallelism cannot apply. Fisher then gives an appropriate definition for interaction in this setting. This paper is concerned with a class of orthogonal polynomials that can be used as an aid in the detection of this modified definition of interaction.     

Admissibility of a variance estimator in finite population sampling under Warner's randomized response plan with multiple responses

ABSTRACT

Let P be the proportion of individuals in a finite population possessing a sensitive attribute. We consider the problem of unbiased estimation of (i) the variance of a linear unbiased estimator of P and (ii) the population variance P (1—P) for a given probability sampling design under Warner's (1965 Warner, S.L. (1965). Randomized response - A survey technique for eliminating evasive answer bias. J. Amer. Statist. Assoc. 60:63–69.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) randomized response (RR) plan when independent responses are obtained from each sampled individual as many times as he/she is selected in the sample and prove the admissibility of a quadratic unbiased estimator for each.     

Evaluation of the economic statistical design of the multivariate T2 control chart with multiple variable sampling intervals scheme: NSGA-II approach

The economic and statistical merits of a multiple variable sampling intervals scheme are studied. The problem is formulated as a double-objective optimization problem with the adjusted average time to signal as the statistical objective and the expected cost per hour as the economic objective. Bai and Lee's [An economic design of variable sampling interval ¯X control charts. Int J Prod Econ. 1998;54:57–64] economic model is considered. Then we find the Pareto-optimal designs in which the two objectives are minimized simultaneously by using the non-dominated sorting genetic algorithm. Through an illustrative example, the advantages of the proposed approach are shown by providing a list of viable optimal solutions and graphical representations, which indicate the advantage of flexibility and adaptability of our approach.     

Design considerations in clinical trials with cure rate survival data: A case study in oncology

For clinical trials with time‐to‐event as the primary endpoint, the clinical cutoff is often event‐driven and the log‐rank test is the most commonly used statistical method for evaluating treatment effect. However, this method relies on the proportional hazards assumption in that it has the maximal power in this circumstance. In certain disease areas or populations, some patients can be curable and never experience the events despite a long follow‐up. The event accumulation may dry out after a certain period of follow‐up and the treatment effect could be reflected as the combination of improvement of cure rate and the delay of events for those uncurable patients. Study power depends on both cure rate improvement and hazard reduction. In this paper, we illustrate these practical issues using simulation studies and explore sample size recommendations, alternative ways for clinical cutoffs, and efficient testing methods with the highest study power possible.