Volleyball coaches are frequently forced to address the question of athlete service errors as a part of their overall service strategy. This is usually done in an ad hoc fashion with an arbitrarily selected maximum allowable service error fraction or maximum allowable service error-to-ace ratio. In this article, an analysis of service outcomes leads to a mathematical expression for the point-scoring fraction in terms of service ace fraction, service error fraction, and opponent modified sideout fraction. These parameters are assumed to be monotonic functions of an athlete or team’s serving aggressiveness and a linear model for the service error-to-ace ratio is used to close the point-scoring optimization problem. The model provides estimates of the optimal service error fraction for individual athletes based on their service ace fraction and the opponent modified sideout fraction against the server overall and also when restricted to only serves that led to perfect passes. Case studies of the Bay to Bay 17 Black Boys’ USAV Juniors team and the Brigham Young University Men’s NCAA Division I team are used to demonstrate the application of the model and standard errors for the predicted optimal service error fractions are calculated with bootstrap resampling.
Decreased efficacy of antibiotics due to resistant pathogens has created a need for the development of more effective medical interventions. Despite the increasing prevalence of pathogens resistant to one or more drugs, identifying and enrolling participants into clinical trials that evaluate new interventions for the treatment of some diseases can be challenging given the low prevalence of disease in which there are no effective treatments. Thus researchers might be tempted to consider externally-controlled trials that may allow for a reduction of the necessary number of prospectively-identified trial participants, thus easing recruitment burden and resulting in more timely trial completion relative to randomized controlled trials. We discuss advantages and disadvantages in externally controlled trials and review requirements for a valid externally-controlled trial. As ECTs are subject to the bias of observational studies, the criteria for a valid ECT should be carefully evaluated before these designs are implemented. Given considerable variation in study results in the resistant pathogen setting, the lack of information on important patient characteristics that may confound estimates of treatment effects, as well as the improvements in medical practice and evolving antibiotic resistance, the use of ECTs in the resistant pathogen setting, is not recommended. ECTs should be should be limited to specific situations where superiority of the effect of the new intervention is dramatic, the usual course of the disease highly predictable, the endpoints are objective (e. g., all-cause mortality) and the impact of baseline and treatment variables on outcomes is well characterized. Given that the resistant pathogen setting does not satisfy these criteria, we conclude that that randomized clinical trials are needed to evaluate new treatments for resistant pathogens. Innovative approaches to trial design that may ease recruitment burden while evaluating the benefits and harms of new treatments are being developed and utilized.
Investigators can choose to analyze different patient populations in clinical trials. The different analysis populations answer different types of research questions, estimate different quantities, and evaluate the robustness of the trial results. Various analysis populations have different strengths and weaknesses depending on the type of question being addressed and the potential for bias from the selection of various groups of trial participants. We discuss analysis populations in the context of anti-infective clinical trials.