Blinded continuous monitoring in clinical trials with recurrent event endpoints

In studies with recurrent event endpoints, misspecified assumptions of event rates or dispersion can lead to underpowered trials or overexposure of patients. Specification of overdispersion is often a particular problem as it is usually not reported in clinical trial publications. Changing event rates over the years have been described for some diseases, adding to the uncertainty in planning. To mitigate the risks of inadequate sample sizes, internal pilot study designs have been proposed with a preference for blinded sample size reestimation procedures, as they generally do not affect the type I error rate and maintain trial integrity. Blinded sample size reestimation procedures are available for trials with recurrent events as endpoints. However, the variance in the reestimated sample size can be considerable in particular with early sample size reviews. Motivated by a randomized controlled trial in paediatric multiple sclerosis, a rare neurological condition in children, we apply the concept of blinded continuous monitoring of information, which is known to reduce the variance in the resulting sample size. Assuming negative binomial distributions for the counts of recurrent relapses, we derive information criteria and propose blinded continuous monitoring procedures. The operating characteristics of these are assessed in Monte Carlo trial simulations demonstrating favourable properties with regard to type I error rate, power, and stopping time, ie, sample size.     

Matrix-trace Cauchy-Schwarz inequalities and applications in canonical correlation analysis

Various matrix-trace Cauchy-Schwarz and related inequalities involving positive semidefinite matrices are obtained. Applications of some of these results to canonical correlation analysis are presented.     

Multiple hypothesis tests based On conditional differences in means

Many hypothesis tests are univariate tests and cannot cope with multiple hypothesis without an auxiliary procedure as e. g. the Bonferroni-Holm-procedure. At the same time, there is an urgent need for testing multiple hypothesis due to the very simple existing methods as the Bonferroni-correction or the Bonferroni-Holm-procedure, which suffers from a very small local significance level to detect statistical inferences or the drawback that logical and statistical dependencies among the test statistics are not used, whereby its detection is NP-hard. In honour of this occasion, we present a multiple hypothesis test for i.i.d. random variables based on conditional differences in means, which is capable to cope with multiple hypothesis and does not suffer on such drawbacks as the Bonferroni-correction or the Bonferroni-Holm-procedure. Thereby, the computation time can be neglected.     

Complexity: Some Remarks about a Classical Aesthetic Concept

The connection between autonomous art and complexity has been extensively and deeply studied in literary theories in the 20th century. The rise of aesthetic autonomy implies the complexity of literary work as the concept of a sealed container arises from the relationship between the parts that make it up. In this model, the interpretation subject works to directly face literary texts. Instead of pursuing the author’s intention, it aims to reproduce the richness and subtlety of the aesthetic state, and consider the richness and subtlety revealed in the maximum amount of text details in literary works, even if procedurally deviating from the way of mainstream understanding. There is increasing skepticism about the consequences of the autonomous aesthetics, which has been coerced by the development of contemporary capitalism, and it is necessary to develop new forms of aesthetics to reflect the changing social situation.     

Sample size re‐estimation incorporating prior information on a nuisance parameter

Prior information is often incorporated informally when planning a clinical trial. Here, we present an approach on how to incorporate prior information, such as data from historical clinical trials, into the nuisance parameter–based sample size re‐estimation in a design with an internal pilot study. We focus on trials with continuous endpoints in which the outcome variance is the nuisance parameter. For planning and analyzing the trial, frequentist methods are considered. Moreover, the external information on the variance is summarized by the Bayesian meta‐analytic‐predictive approach. To incorporate external information into the sample size re‐estimation, we propose to update the meta‐analytic‐predictive prior based on the results of the internal pilot study and to re‐estimate the sample size using an estimator from the posterior. By means of a simulation study, we compare the operating characteristics such as power and sample size distribution of the proposed procedure with the traditional sample size re‐estimation approach that uses the pooled variance estimator. The simulation study shows that, if no prior‐data conflict is present, incorporating external information into the sample size re‐estimation improves the operating characteristics compared to the traditional approach. In the case of a prior‐data conflict, that is, when the variance of the ongoing clinical trial is unequal to the prior location, the performance of the traditional sample size re‐estimation procedure is in general superior, even when the prior information is robustified. When considering to include prior information in sample size re‐estimation, the potential gains should be balanced against the risks.     

The no-wait job shop with regular objective: a method based on optimal job insertion

The no-wait job shop problem (NWJS-R) considered here is a version of the job shop scheduling problem where, for any two operations of a job, a fixed time lag between their starting times is prescribed. Also, sequence-dependent set-up times between consecutive operations on a machine can be present. The problem consists in finding a schedule that minimizes a general regular objective function. We study the so-called optimal job insertion problem in the NWJS-R and prove that this problem is solvable in polynomial time by a very efficient algorithm, generalizing a result we obtained in the case of a makespan objective. We then propose a large neighborhood local search method for the NWJS-R based on the optimal job insertion algorithm and present extensive numerical results that compare favorably with current benchmarks when available.     

Model averaging for treatment effect estimation in subgroups

In many clinical trials, biological, pharmacological, or clinical information is used to define candidate subgroups of patients that might have a differential treatment effect. Once the trial results are available, interest will focus on subgroups with an increased treatment effect. Estimating a treatment effect for these groups, together with an adequate uncertainty statement is challenging, owing to the resulting “random high” / selection bias. In this paper, we will investigate Bayesian model averaging to address this problem. The general motivation for the use of model averaging is to realize that subgroup selection can be viewed as model selection, so that methods to deal with model selection uncertainty, such as model averaging, can be used also in this setting. Simulations are used to evaluate the performance of the proposed approach. We illustrate it on an example early‐phase clinical trial.