Sample size recalculation for binary data in internal pilot study designs

For binary endpoints, the required sample size depends not only on the known values of significance level, power and clinically relevant difference but also on the overall event rate. However, the overall event rate may vary considerably between studies and, as a consequence, the assumptions made in the planning phase on this nuisance parameter are to a great extent uncertain. The internal pilot study design is an appealing strategy to deal with this problem. Here, the overall event probability is estimated during the ongoing trial based on the pooled data of both treatment groups and, if necessary, the sample size is adjusted accordingly. From a regulatory viewpoint, besides preserving blindness it is required that eventual consequences for the Type I error rate should be explained. We present analytical computations of the actual Type I error rate for the internal pilot study design with binary endpoints and compare them with the actual level of the chi‐square test for the fixed sample size design. A method is given that permits control of the specified significance level for the chi‐square test under blinded sample size recalculation. Furthermore, the properties of the procedure with respect to power and expected sample size are assessed. Throughout the paper, both the situation of equal sample size per group and unequal allocation ratio are considered. The method is illustrated with application to a clinical trial in depression. Copyright © 2004 John Wiley & Sons Ltd.     

EFFICIENCY EFFECTS OF EXCLUSIVE TERRITORIES: EVIDENCE FROM THE INDIANA BEER MARKET

The welfare effects of vertically imposed exclusive territories and the appropriate antitrust policy toward them have long been debated. This paper sheds light on the exclusive-territory controversy by examing the effects of Indiana's 1979 ban on the grant of exclusive territories to beer wholesalers. Using time-series data for 1948–1990 we find the ban reduced beer consumption in Indiana by 6 percent. Coupled with previous evidence that Indiana's ban reduced price, our results suggest that exclusive territories in the beer industry increase demand and enhance welfare by stimulating the provision of dealer services.     

A Model for Optimization of Biomarker Testing Frequency to Minimize Disease and Cost: Example of Beryllium Sensitization Testing

A common problem with medical surveillance programs using biomarkers is determining the optimal frequency of testing to minimize adverse health effects and cost. In the case of beryllium-exposed workers, frequency of testing for beryllium sensitization may be especially important. Recent studies indicate a lack of dose response for beryllium sensitization, but do support a dose response for the development of chronic beryllium disease (CBD). Though unproven, this implies that early identification of sensitization and immediate removal from exposure may reduce development of CBD. A model is proposed to project the optimal frequency of sensitization testing using the current beryllium lymphocyte proliferation test (BeLPT) to minimize disease-related costs, assuming that a positive BeLPT will precede CBD. Conversion rates for cumulative exposure to disease development were adapted from the literature and used with testing costs and cost of disease estimates in the model. The model was run assuming several test frequency regimes. Results support the use of periodic testing in line with the annual schedule proposed in the Final Chronic Beryllium Disease Prevention Program Rule (1999) following initial testing within three months of first beryllium exposure. The financial and health benefits of reducing the time from exposure to detection of early disease was also explored with the model and demonstrated as a highly desirable characteristic for an alternative test or improved BeLPT. Limitations of the approach are discussed as well as options for adapting this biomarker optimization methodology to consider biomarkers of other exposure-associated diseases.     

Blinded sample size re‐estimation in superiority and noninferiority trials: bias versus variance in variance estimation

The internal pilot study design allows for modifying the sample size during an ongoing study based on a blinded estimate of the variance thus maintaining the trial integrity. Various blinded sample size re‐estimation procedures have been proposed in the literature. We compare the blinded sample size re‐estimation procedures based on the one‐sample variance of the pooled data with a blinded procedure using the randomization block information with respect to bias and variance of the variance estimators, and the distribution of the resulting sample sizes, power, and actual type I error rate. For reference, sample size re‐estimation based on the unblinded variance is also included in the comparison. It is shown that using an unbiased variance estimator (such as the one using the randomization block information) for sample size re‐estimation does not guarantee that the desired power is achieved. Moreover, in situations that are common in clinical trials, the variance estimator that employs the randomization block length shows a higher variability than the simple one‐sample estimator and in turn the sample size resulting from the related re‐estimation procedure. This higher variability can lead to a lower power as was demonstrated in the setting of noninferiority trials. In summary, the one‐sample estimator obtained from the pooled data is extremely simple to apply, shows good performance, and is therefore recommended for application. Copyright © 2013 John Wiley & Sons, Ltd.     

The power of the circular cone test: A noncentral chi-bar-squared distribution

Pincus (1975) derived the null distribution of the likelihood-ratio test statistic for testing that the mean vector of a multivariate normal distribution is zero against the alternative that the mean vector lies in a circular cone. Under the null hypothesis, the likelihood-ratio test statistic has a chi-bar-squared distribution. We extend the results of Pincus by deriving the distribution of the likelihood-ratio test statistic under the alternative hypothesis. In a special case, the distribution is a “noncentral chi-bar-squared” distribution. To our knowledge, this is the first order-restricted testing problem for which the relationship between the null and alternative distributions of the test statistic is similar to the relationship in the linear-model setting. That is, the distribution of the likelihood-ratio test has a central form of a distribution under the null hypothesis and a noncentral form of the same distribution under the alternative.     

Goodness-of-fit test for uniform stochastic ordering among several distributions

The likelihood-ratio test (LRT) is considered as a goodness-of-fit test for the null hypothesis that several distribution functions are uniformly stochastically ordered. Under the null hypothesis, H₁ : F₁ ? F₂ ?···? F_N, the asymptotic distribution of the LRT statistic is a convolution of several chi-bar-square distributions each of which depends upon the location parameter. The least-favourable parameter configuration for the LRT is not unique. It can be two different types and depends on the number of distributions, the number of intervals and the significance level α. This testing method is illustrated with a data set of survival times of five groups of male fruit flies.     

Failure and maintenance data extraction from power plant maintenance management databases

Reliability analysis is plagued by a lack of accurate data, leading to suboptimal parameter estimates and inaccurate decisions about replacement intervals and preventive maintenance activities. This paper discusses some of the problems associated with failure and maintenance data extraction from coal-fired power plant maintenance databases. Data from four generating units were observed for over 5 years and a reasonable number of equipment classes reviewed. The coal mills are identified as significant equipment that affects the availability of the generating units. This paper describes the interplay of events which includes failure modes, failure, repair and operating time. We investigate a database showing operation of coal mills, and give an exploratory data analysis in which we investigate engineering hypotheses related to mill operation. A competing risk probability model is proposed which captures some of the observed features of the systems under study.     

Language and libertarianism: the politics of cyberculture and the culture of cyberpolitics

A significant number of theories concerning the nature of cyberspace or virtuality are being constructed with little regard for the empirical realities of online life. This article sets out certain simple empirical factors related to the nature first of politics in cyberspace and second culture in cyberspace. These questions are posed as ‘what is the politics of cyberculture?’ and ‘what is the culture of cyberpolitics?’. The politics of cyberculture revolves around issues of grossly uneven regional distribution of the Internet and a bias toward anglo‐american language and culture that is based on the competitive individual. The culture of cyberpolitics revolves around informational forms of libertarian and anarchist ideologies that posit cyberspace as the realm of individual freedom. These cultures and politics can be related to each other as the structure and action of cyberspace. The assumption that cyberspace is constituted by individuals is revealed as an assumption of both, and connection between, cyberpolitics and cybercultures.