COVID-19 infected cases in Canada: Short-term forecasting models.

Governments have implemented different interventions and response models to combat the spread of COVID-19. The necessary intensity and frequency of control measures require us to project the number of infected cases. Three short-term forecasting models were proposed to predict the total number of infected cases in Canada for a number of days ahead. The proposed models were evaluated on how their performance degrades with increased forecast horizon, and improves with increased historical data by which to estimate them. For the data analyzed, our results show that 7 to 10 weeks of historical data points are enough to produce good fits for a two-weeks predictive model of infected case numbers with a NRMSE of 1% to 2%. The preferred model is an important quick-deployment tool to support data-informed short-term pandemic related decision-making at all levels of governance.

The use of non-uniform drowning terminology: a follow-up study.

BACKGROUND: In 2002, the World Congress on Drowning developed a uniform definition for drowning. The aim of this study is to determine the prevalence of "non-uniform drowning terminology" (NUDT) and "non-uniform drowning definitions" (NUDD) in peer-reviewed scientific literature from 2010 to 2016, and compare these findings with those from our unpublished study performing a similar analysis on literature from 2003 to 2010. METHODS: A systematic review was performed using drowning-specific search terms in Pubmed and Web of Science. Titles and abstracts published between July 2010 and January 2016 were screened for relevance to the study focus. Articles meeting screening criteria were reviewed for exclusion criteria to produce the final group of studies. These articles were reviewed by four reviewers for NUDT and NUDD. The Fisher exact test was used to determine any statistically significant changes. RESULTS: The final group of studies included 167 articles. A total of 53 articles (32%) utilized NUDT, with 100% of these including the term "near drowning". The proportion of articles utilizing NUDT was significantly less than reported by our previous study (p < 0.05). In addition, 32% of the articles included a definition for drowning (uniform or non-uniform), with 15% of these utilizing NUDD. DISCUSSION: Our study reveals a statistically significant improvement over the past thirteen years in the use of uniform drowning terminology in peer-reviewed scientific literature, although year-to-year variability over the current study period does not yield an obvious trend. CONCLUSIONS: Of the articles reviewed during the 2010-2016 study period, 32% included outdated and non-uniform drowning terminology and definitions. While this reveals an absolute decrease of 11% as compared with the previous study period (2003-2010), there is still significant room for improvement.

A novel dose-volume metric for optimizing therapeutic ratio through fractionation: retrospective analysis of lung cancer treatments.

PURPOSE: To explore the potential of a novel dose-volume based metric to assist in the selection of optimal fractionation schedules for lung cancer patients. METHODS: Selecting the dose per fraction that maximizes the therapeutic ratio via a linear-quadratic effect on normal tissue complication probability and tumor cell survival is an optimization problem. The mathematical solution reveals that the optimal fractionation schedule is determined by a generalized dose ratio between the normal tissue and the tumor, here termed the bifurcation number B, that can be derived from the dose-volume histogram of the normal tissue. The bifurcation number characterizes the volume effect of a normal tissue and its dependency on the fractionation schedule. The clinical relevance of the bifurcation number was evaluated in 46 patients previously treated for nonsmall cell lung cancer (NSCLC) according to various fractionation protocols. Bifurcation numbers were computed for both lung and esophagus as the normal tissues. RESULTS: The value of the bifurcation number determines whether the volume effect reverses the traditional radiobiological advantage of small dose per fraction for the normal tissue. If B is smaller than the ratio of alpha/beta ratios between normal tissue and tumor, then a single fraction is optimal; otherwise the optimal treatment is an infinite number of doses (hence the name "bifurcation" number). These fractionation schedules correspond clinically to hypo- and standard/hyperfractionation, respectively. Compared with traditional dose-volume metrics, the bifurcation number is a unitless ratio and independent of dose fractionation. The B-numbers derived from the clinical treatment plans are also strongly consistent with historically prescribed clinical fractionation protocols for NSCLC treatments. The B-numbers for esophagus and lung for all patients receiving a high dose per fraction protocol (>7.5 Gy/fraction) were all smaller than the B-numbers for the patients receiving standard 2 Gy/fraction, with the numbers for the 3 Gy/fraction group in between. CONCLUSIONS: The bifurcation numbers are strongly consistent with prescribed clinical fractionation protocols for NSCLC treatments. Due to their scale-free property the B-numbers may assist in the selection of an appropriate fractionation once the dose distribution has been optimized.

Measure of predictability.

Many techniques have been developed to measure the difficulty of forecasting data from an observed time series. This paper introduces a measure which we call the "forecast entropy" designed to measure the predictability of a time series. We use attractors reconstructed from the time series and the distributions in the regular and tangent spaces of the data which comprise the attractor. We then consider these distributions on different scales. We present a formula for calculating the forecast entropy. To provide a standard of predictability, we define an idealized random system whose forecast entropy will be maximal; we then use this measure to rescale the forecast entropy to lie in the range [0,1]. The time series obtained from several chaotic systems as well as from a pseudorandom system are studied using this measure. We present evidence that the forecast entropy can be used as a tool for determining optimal delays and embedding dimensions used for reconstructing better attractors. We also show that the forecast entropy of a random system has completely different characteristics from that of a deterministic one.