Environmental pathogen surveillance is a promising disease surveillance modality that has been widely adopted for SARS-CoV-2 monitoring. The highly variable nature of environmental pathogen data is a challenge for integrating these data into public health response. One source of this variability is heterogeneous infection both within an individual over the course of infection as well as between individuals in their pathogen shedding over time. We present a mechanistic modeling and estimation framework for connecting environmental pathogen data to the number of infected individuals. Infected individuals are modeled as shedding pathogen into the environment via a Poisson process whose rate parameter λt varies over the course of their infection. These shedding curves λt are themselves random, allowing for variation between individuals. We show that this results in a Poisson process for environmental pathogen levels with rate parameter a function of the number of infected individuals, total shedding over the course of infection, and pathogen removal from the environment. Theoretical results include determination of identifiable parameters for the model from environmental pathogen data and simple, explicit formulas for the likelihood for particular choices of individual shedding curves. We give a two step Bayesian inference framework, where the first step corresponds to calibration from data where the number of infected individuals is known, followed by an estimation step from environmental surveillance data when the number of infected individuals is unknown. We apply this modeling and estimation framework to synthetic data, as well as to an empirical case study of SARS-CoV-2 in environmental dust collected from isolation rooms housing university students. Both the synthetic data and empirical case study indicate high inter-individual variation in shedding, leading to wide credible intervals for the number of infected individuals. We examine how uncertainty in estimates of the number of infected individuals from environmental pathogen levels scales with the true number of infected individuals and model misspecification. While credible intervals for the number of infected individuals are wide, our results suggest that distinguishing between no infection and small-to-moderate levels of infection (≈10 infected individuals) may be possible, and that it is broadly possible to differentiate between moderate (≈40) and high (≈200) numbers of infected individuals.

West Nile virus (WNV) outbreaks raise the concern of WNV infection in donated blood and blood products destined for transfusion. We describe methods we developed to estimate time-dependent risk of WNV infection in donated blood, including improvements not previously detailed. The methods are then extended for use in estimation of the risk of WNV infection in donated cadaveric tissues by introducing stratification and stratum-specific weighting to address novel aspects of this application. Data from the WNV outbreak in Colorado in 2003 are used to estimate risk for donated cardiac tissue.

Given progressive developments and demands on clinical trials, accurate enrollment timeline forecasting is increasingly crucial for both strategic decision-making and trial execution excellence. Naïve approach assumes flat rates on enrollment using average of historical data, while traditional statistical approach applies simple Poisson-Gamma model using time-invariant rates for site activation and subject recruitment. Both of them are lack of non-trivial factors such as time and location. We propose a novel two-segment statistical approach based on Quasi-Poisson regression for subject accrual rate and Poisson process for subject enrollment and site activation. The input study-level data are publicly accessible and it can be integrated with historical study data from user\'s organization to prospectively predict enrollment timeline. The new framework is neat and accurate compared to preceding works. We validate the performance of our proposed enrollment model and compare the results with other frameworks on 7 curated studies.

The study of events distributed over time which can be quantified as point processes has attracted much interest over the years due to its wide range of applications. It has recently gained new relevance due to the COVID-19 case and death processes associated with SARS-CoV-2 that characterize the COVID-19 pandemic and are observed across different countries. It is of interest to study the behavior of these point processes and how they may be related to covariates such as mobility restrictions, gross domestic product per capita, and fraction of population of older age. As infections and deaths in a region are intrinsically events that arrive at random times, a point process approach is natural for this setting. We adopt techniques for conditional functional point processes that target point processes as responses with vector covariates as predictors, to study the interaction and optimal transport between case and death processes and doubling times conditional on covariates.

At the start of a journey home or to a foraging site, ants often stop, interrupting their forward movement, turn on the spot a number of times, and fixate in different directions. These scanning bouts are thought to provide visual information for choosing a path to travel. The temporal organization of such scanning bouts has implications about the neural organisation of navigational behaviour. We examined (1) the temporal distribution of the start of such scanning bouts and (2) the dynamics of saccadic body turns and fixations that compose a scanning bout in Australian desert ants, Melophorus bagoti, as they came out of a walled channel onto open field at the start of their homeward journey. Ants were caught when they neared their nest and displaced to different locations to start their journey home again. The observed parameters were mostly similar across familiar and unfamiliar locations. The turning angles of saccadic body turning to the right or left showed some stereotypy, with a peak just under 45°. The direction of such saccades appears to be determined by a slow oscillatory process as described in other insect species. In timing, however, both the distribution of inter-scanning-bout intervals and individual fixation durations showed exponential characteristics, the signature for a random-rate or Poisson process. Neurobiologically, therefore, there must be some process that switches behaviour (starting a scanning bout or ending a fixation) with equal probability at every moment in time. We discuss how chance events in the ant brain that occasionally reach a threshold for triggering such behaviours can generate the results.

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide new methods for inferring, predicting, and estimating them. The methods rely on an extension of Bayesian structural inference that takes advantage of neural network\'s universal approximation power. Based on experiments with complex synthetic data, the methods are competitive with the state-of-the-art for prediction and entropy-rate estimation.

Joint analysis of recurrent and nonrecurrent terminal events has attracted substantial attention in literature. However, there lacks formal methodology for such analysis when the event time data are on discrete scales, even though some modeling and inference strategies have been developed for discrete-time survival analysis. We propose a discrete-time joint modeling approach for the analysis of recurrent and terminal events where the two types of events may be correlated with each other. The proposed joint modeling assumes a shared frailty to account for the dependence among recurrent events and between the recurrent and the terminal terminal events. Also, the joint modeling allows for time-dependent covariates and rich families of transformation models for the recurrent and terminal events. A major advantage of our approach is that it does not assume a distribution for the frailty, nor does it assume a Poisson process for the analysis of the recurrent event. The utility of the proposed analysis is illustrated by simulation studies and two real applications, where the application to the biochemists\' rank promotion data jointly analyzes the biochemists\' citation numbers and times to rank promotion, and the application to the scleroderma lung study data jointly analyzes the adverse events and off-drug time among patients with the symptomatic scleroderma-related interstitial lung disease.

In recent times, several strategies to minimize the spread of 2019 novel coronavirus disease (COVID-19) have been adopted. Some recent technological breakthroughs like the drone-based tracking systems have focused on devising specific dynamical approaches for administering public mobility and providing early detection of symptomatic patients. In this paper, a smart real-time image processing framework converged with a non-contact thermal temperature screening module was implemented. The proposed framework comprised of three modules v i z . , smart temperature screening system, tracking infection footprint, and monitoring social distancing policies. This was accomplished by employing Histogram of Oriented Gradients (HOG) transformation to identify infection hotspots. Further, Haar Cascade and local binary pattern histogram (LBPH) algorithms were used for real-time facial recognition and enforcing social distancing policies. In order to manage the redundant video frames generated at the local computing device, two holistic models, namely, event-triggered video framing (ETVF) and real-time video framing (RTVF) have been deduced, and their respective processing costs were studied for different arrival rates of the video frame. It was observed that the proposed ETVF approach outperforms the performance of RTVF by providing optimal processing costs resulting from the elimination of redundant data frames. Results corresponding to autocorrelation analysis have been presented for the case study of India pertaining to the number of confirmed COVID-19 cases, recovered cases, and deaths to obtain an understanding of epidemiological spread of the virus. Further, choropleth analysis was performed for indicating the magnitude of COVID-19 spread corresponding to different regions in India.

The paper summarizes the design and implementation of a passenger traffic prediction model, based on Gaussian Process Regression (GPR). Passenger traffic analysis is the present day requirement for proper bus scheduling and traffic management to improve the efficiency and passenger comfort. Bayesian analysis uses statistical modelling to recursively estimate new data from existing data. GPR is a fully Bayesian process model, which is developed using PyMC3 with Theano as backend. The passenger data is modelled as a Poisson process so that the prior for designing the GP regression model is a Gamma distributed function. It is observed that the proposed GP based regression method outperforms the existing methods like Student-t process model and Kernel Ridge Regression (KRR) process.

In clinical trials, almost all key milestone dates can be defined in terms of time to endpoint maturation (TTEM). The real time monitoring and accurate prediction of TTEM have a significant impact on clinical trial planning and execution and can bring significant value to clinical trial practitioners. TTEM is defined as the time to achieve or observe a certain number or percentage of some endpoint of interest. It is a combination of time to site initiation, time to subject enrollment after site initiation and time to event of interest after subject enrollment. To better predict TTEM during the trial, the future site initiation and subject enrollment have to be taken into account while predicting the number of events. In this article, we propose a novel simulation-based framework combining time to site initiation, time to subject enrollment and time to event in order to predict TTEM. A nonhomogeneous Poisson process with a quadratic time-varying rate function is used to model site initiation and subject enrollment and more advanced time to event models had been explored and integrated on top of them, such as Weibull, piecewise exponential, and model averaging which is equivalent to a Bayesian model selection strategy. To evaluate the predictive performance of the proposed methodology, we conducted extensive simulations and applied the methodology to 14 randomly selected real oncology phase 2 and phase 3 studies in both solid tumor and hematology with a total 31 study-endpoint combinations. The predictive performance of the proposed methodology was then compared with popular and commonly available commercial software, for example, East (Cytel, Cambridge, MA, USA). From both simulation and real data, the proposed methodology can significantly improve the prediction accuracy by up to 54% compared to the commonly available method.