Comparison of Bayesian and frequentist group-sequential clinical trial designs

Background: There is a growing interest in the use of Bayesian adaptive designs in late-phase clinical trials. This includes the use of stopping rules based on Bayesian analyses in which the frequentist type I error rate is controlled as in frequentist group-sequential designs. Methods: This paper presents a practical comparison of Bayesian and frequentist group-sequential tests. Focussing on the setting in which data can be summarised by normally distributed test statistics, we evaluate and compare boundary values and operating characteristics. Results: Although Bayesian and frequentist group-sequential approaches are based on fundamentally different paradigms, in a single arm trial or two-arm comparative trial with a prior distribution specified for the treatment difference, Bayesian and frequentist group-sequential tests can have identical stopping rules if particular critical values with which the posterior probability is compared or particular spending function values are chosen. If the Bayesian critical values at different looks are restricted to be equal, O’Brien and Fleming’s design corresponds to a Bayesian design with an exceptionally informative negative prior, Pocock’s design to a Bayesian design with a non-informative prior and frequentist designs with a linear alpha spending function are very similar to Bayesian designs with slightly informative priors. This contrasts with the setting of a comparative trial with independent prior distributions specified for treatment effects in different groups. In this case Bayesian and frequentist group-sequential tests cannot have the same stopping rule as the Bayesian stopping rule depends on the observed means in the two groups and not just on their difference. In this setting the Bayesian test can only be guaranteed to control the type I error for a specified range of values of the control group treatment effect. Conclusions: Comparison of frequentist and Bayesian designs can encourage careful thought about design parameters and help to ensure appropriate design choices are made

On the number of partition weights with Kostka multiplicity one

Given a positive integer n, and partitions lambda and mu of n, let K-lambda mu denote the Kostka number, which is the number of semistandard Young tableaux of shape lambda and weight mu. Let J(lambda) denote the number of mu such that K lambda mu = 1. By applying a result of Berenshtein and Zelevinskii, we obtain a formula for J(lambda) in terms of restricted partition functions, which is recursive in the number of distinct part sizes of lambda. We use this to classify all partitions lambda such that J(lambda) = 1 and all lambda such that J(lambda) = 2. We then consider signed tableaux, where a semistandard signed tableau of shape lambda has entries from the ordered set {0 \u3c \u3c 1 \u3c (2) over bar \u3c 2 \u3c ...}, and such that i and (i) over bar contribute equally to the weight. For a weight (omega(0), mu) with mu a partition, the signed Kostka number K-lambda(omega 0, mu)(+/-) is defined as the number of semistandard signed tableaux of shape lambda and weight (omega(0), mu), and J(+/-)(lambda) is then defined to be the number of weights (omega(0), mu) such that K-lambda(omega 0,mu)(+/-) = 1. Using different methods than in the unsigned case, we find that the only nonzero value which J((lambda))(+/-) can take is 1, and we find all sequences of partitions with this property. We conclude with an application of these results on signed tableaux to the character theory of finite unitary groups

Training Evaluation for Introductory Ocean Lifeguard Instruction: A Practical Example from California

Ocean lifeguards have several responsibilities that require precise training. California State Parks is one of the largest providers of open water lifeguard services in the United States, and trains approximately 200 new lifeguards per year. As part of our lifeguard training section’s quality improvement efforts, we conducted a training needs assessment to help determine how well our introductory ocean lifeguard training curriculum prepared lifeguards to perform job related tasks upon successful completion of the training program. We surveyed both first year and seasoned lead lifeguards on operational needs, training gaps, and specific subject areas. We identified several areas where our training program required improvement. This assessment provided us with evidence from which to update our curriculum, helped identify gaps in the field, and provided a feedback mechanism from field staff not previously involved in prioritizing training needs

The Catholic Response to The Protestant Reformation

Within the 16th century leaves of the Theaturm Curdelitatum Haereticorum Nostri Temporis, one finds a myriad of emotionally charged, visceral images illustrating Catholic martyrdoms. At first glance, the Catholic book of martyrs appears to be a mere knee-jerk response to the Protestant martyrdoms springing up all over Europe. However, the specific way that this book is created is inherently Catholic; it is not just there to highlight to crimes of the Protestants, it is to teach and inspire persecuted Catholics about contemporary martyrs, using the age-old rhetoric of saintly worship. We aim to answer several questions: what about this source sets it apart from its Protestant counterpArts; what were the accused being tortured for and why was it significant doctrinally; and what is symbolic about the imagery? Preliminary research shows us that this document has specific Catholic characteristics. The language it was written in is Latin, for one, a language Protestants were crusading to discard from religious experience. There is no visible blood in the images—suggesting that the victims are sanctified even in their grotesque circumstances. This research matters for a number of reasons. Not only does exploring this issue give people a window into the religious turmoil of the Protestant Reformation, forcing them to imagine a time when people were drawn and quartered in the streets, but it also exposes the doctrinal differences between Catholics and Protestants that have, today, largely faded. Lastly, it leads us to ponder the natural human instinct toward hero-worship and the cultural elevation of martyrs

The Ocean Lifeguard Intervention Continuum: A Cognitive Aid for Surf Lifeguard Education

Ocean lifeguards are constantly engaged in beach risk analysis, required to efficiently evaluate a variety of environmental and other factors quickly in order to triage and prioritize who needs help. Teaching these skills is a challenge for introductory training programs. We sought to improve new lifeguards’ understanding of the interaction of various risk components in the beach environment and aid decision-making related to when a lifeguard should intervene in a situation. We developed a two-part cognitive aid for introductory ocean lifeguard education depicting individual and interacting elements of a beach goer’s risk of drowning or injury and the process by which that risk increases with associated lifeguard interventions on a continuum from low risk and no distress to drowning. This new cognitive aid represented an advancement in the presentation of complex material in introductory training programs for those involved in aquatic rescue

Bayesian adaptive designs for multi-arm trials: an orthopaedic case study

This is the final version. Available on open access from BMC via the DOI in this recordAvailability of data and materials: The data used in this study were generated as part of the CAST study. Requests to share individual, de-identified participant data, aggregated data, data dictionaries, and other study documents from this study should be sent to the CAST Chief Investigator (SEL). Data sharing requests will be assessed on their individual merits. The FACTS files used to simulate the Bayesian adaptive designs are publicly available at https://github.com/egryan90/Bayesian-adaptive-designs-for-CAST-study-Ryan-et-al.-2019Background: Bayesian adaptive designs can be more efficient than traditional methods for multi‐arm randomised controlled trials. The aim of this work was to demonstrate how Bayesian adaptive designs can be constructed for multi‐arm phase III clinical trials and assess potential benefits that these designs offer. Methods: We constructed several alternative Bayesian adaptive designs for the Collaborative Ankle Support Trial (CAST), which was a randomised controlled trial that compared four treatments for severe ankle sprain. These incorporated response adaptive randomisation, arm dropping, and early stopping for efficacy or futility. We studied the Bayesian designs’ operating characteristics via simulation. We then virtually re‐executed the trial by implementing the Bayesian adaptive designs using patient data sampled from the CAST study to demonstrate the practical applicability of the designs. Results: We constructed five Bayesian adaptive designs, each of which had high power and recruited fewer patients on average than the original design’s target sample size. The virtual executions 2 showed that most of the Bayesian designs would have led to trials that declared superiority of one of the interventions over the control. Bayesian adaptive designs with RAR or arm dropping were more likely to allocate patients to better performing arms at each interim analysis. Similar estimates and conclusions were obtained from the Bayesian adaptive designs as from the original trial. Conclusions: Using CAST as an example, this case study showed how Bayesian adaptive designs can be constructed for phase III multi‐arm trials using clinically relevant decision criteria. These designs demonstrated that they can potentially generate earlier results and allocate more patients to betterperforming arms. We recommend the wider use of Bayesian adaptive approaches in phase III clinical trials.Medical Research Council (MRC)National Co‐ordinating Centre for Health Technology AssessmentNational Institute of Health Researc

Bayesian adaptive designs for multi-arm trials: an orthopaedic case study

This is the final version. Available on open access from BMC via the DOI in this recordAvailability of data and materials: The data used in this study were generated as part of the CAST study. Requests to share individual, de-identified participant data, aggregated data, data dictionaries, and other study documents from this study should be sent to the CAST Chief Investigator (SEL). Data sharing requests will be assessed on their individual merits. The FACTS files used to simulate the Bayesian adaptive designs are publicly available at https://github.com/egryan90/Bayesian-adaptive-designs-for-CAST-study-Ryan-et-al.-2019Background: Bayesian adaptive designs can be more efficient than traditional methods for multi‐arm randomised controlled trials. The aim of this work was to demonstrate how Bayesian adaptive designs can be constructed for multi‐arm phase III clinical trials and assess potential benefits that these designs offer. Methods: We constructed several alternative Bayesian adaptive designs for the Collaborative Ankle Support Trial (CAST), which was a randomised controlled trial that compared four treatments for severe ankle sprain. These incorporated response adaptive randomisation, arm dropping, and early stopping for efficacy or futility. We studied the Bayesian designs’ operating characteristics via simulation. We then virtually re‐executed the trial by implementing the Bayesian adaptive designs using patient data sampled from the CAST study to demonstrate the practical applicability of the designs. Results: We constructed five Bayesian adaptive designs, each of which had high power and recruited fewer patients on average than the original design’s target sample size. The virtual executions 2 showed that most of the Bayesian designs would have led to trials that declared superiority of one of the interventions over the control. Bayesian adaptive designs with RAR or arm dropping were more likely to allocate patients to better performing arms at each interim analysis. Similar estimates and conclusions were obtained from the Bayesian adaptive designs as from the original trial. Conclusions: Using CAST as an example, this case study showed how Bayesian adaptive designs can be constructed for phase III multi‐arm trials using clinically relevant decision criteria. These designs demonstrated that they can potentially generate earlier results and allocate more patients to betterperforming arms. We recommend the wider use of Bayesian adaptive approaches in phase III clinical trials.Medical Research Council (MRC)National Co‐ordinating Centre for Health Technology AssessmentNational Institute of Health Researc

Effects of Short-Term Cattle Exclusion on Plant Community Composition: Prairie Dog and Ecological Site Influences

On the Ground Maintaining cattle and prairie dogs on rangelands is important ecologically, economically, and culturally. However, competition between these species, both actual and perceived, has led to conflict. We explored the effects of short-term (2-year) cattle exclusion on plant communities both on and off prairie dog towns and among three common ecological sites. Plant communities were different between on-town and off-town plots and among ecological sites but were similar between cattle-excluded and nonexcluded plots. Plant community composition did not differ between rangeland targeted for moderate forage utilization and that in which cattle had been excluded for 2 years