This is the author's version of a work that was accepted for publication in Journal of Statistical Planning and Inference. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Statistical Planning and Inference, [VOL 142, ISS 6, (2012
AbstractWe consider the problem of how to efficiently and safely design dose finding studies. Both current and novel utility functions are explored using Bayesian adaptive design methodology for the estimation of a maximum tolerated dose (MTD). In particular, we explore widely adopted approaches such as the continual reassessment method and minimizing the variance of the estimate of an MTD. New utility functions are constructed in the Bayesian framework and are evaluated against current approaches. To reduce computing time, importance sampling is implemented to re-weight posterior samples thus avoiding the need to draw samples using Markov chain Monte Carlo techniques.Further, as such studies are generally first-in-man, the safety of patients is paramount. We therefore explore methods for the incorporation of safety considerations into utility functions to ensure that only safe and well-predicted doses are administered. The amalgamation of Bayesian methodology, adaptive design and compound utility functions is termed adaptive Bayesian compound design (ABCD). The performance of this amalgamation of methodology is investigated via the simulation of dose finding studies. The paper concludes with a discussion of results and extensions that could be included into our approach.
ObjectiveThis research aimed to (i) assess the effects of time‐varying predictors (day of the week, month, year, holiday, temperature) on daily ED presentations and (ii) compare the accuracy of five methods for forecasting ED presentations, including four statistical methods and a machine learning approach.MethodsPredictors of ED presentations were assessed using generalised additive models (GAMs), generalised linear models, multiple linear regression models, seasonal autoregressive integrated moving average models and random forest. The accuracy of short‐term (14 days), mid‐term (30 days) and long‐term (365 days) forecasts were compared using two measures of forecasting error.ResultsThe data are the numbers of presentations to public hospital EDs in South‐East Queensland, Australia, from 2009 to 2015. ED presentations are largely affected by year of presentation, and to a lesser extent by month, day of the week and holidays. Maximum daily temperature is also a significant predictor of ED presentations. Of the four statistical models considered, the GAM had the greatest forecasting accuracy, and produced consistent and coherent forecasts, likely due to its flexibility in modelling complex time‐varying effects. The random forest machine learning approach had the lowest forecasting accuracy, likely due to overfitting the data.ConclusionsCalendar and temperature variables, not previously considered in the Australian literature, were found to significantly impact ED presentations. This study also demonstrates the potential of GAMs as a dual explanatory and forecasting method for the modelling, and more accurate prediction, of ED presentations.
A novel geostatistical modeling approach is developed to model nonlinear multivariate spatial dependence using nonlinear principal component analysis (NLPCA) and pair‐copulas. In spatial studies, multivariate measurements are frequently collected at each location. The dependence between such measurements can be complex. In this article, a multivariate geostatistical model is developed that can capture both nonlinear spatial dependence across locations and nonlinear dependence between measurements at a particular location. Nonlinear multivariate dependence between spatial variables is removed using NLPCA. Subsequently, a pair‐copula based model is fitted to each transformed variable to model the univariate nonlinear spatial dependencies. NLPCA and pair‐copulas, within the proposed model, are compared with stepwise conditional transformation (SCT) and conventional kriging. The results show that, for the two case studies presented, the proposed model that utilizes NLPCA and pair‐copulas reproduces nonlinear multivariate structures and univariate distributions better than existing methods based on SCT and kriging.
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