3,455 research outputs found

    Hybrid statistical and mechanistic mathematical model guides mobile health intervention for chronic pain

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    Nearly a quarter of visits to the Emergency Department are for conditions that could have been managed via outpatient treatment; improvements that allow patients to quickly recognize and receive appropriate treatment are crucial. The growing popularity of mobile technology creates new opportunities for real-time adaptive medical intervention, and the simultaneous growth of big data sources allows for preparation of personalized recommendations. Here we focus on the reduction of chronic suffering in the sickle cell disease community. Sickle cell disease is a chronic blood disorder in which pain is the most frequent complication. There currently is no standard algorithm or analytical method for real-time adaptive treatment recommendations for pain. Furthermore, current state-of-the-art methods have difficulty in handling continuous-time decision optimization using big data. Facing these challenges, in this study we aim to develop new mathematical tools for incorporating mobile technology into personalized treatment plans for pain. We present a new hybrid model for the dynamics of subjective pain that consists of a dynamical systems approach using differential equations to predict future pain levels, as well as a statistical approach tying system parameters to patient data (both personal characteristics and medication response history). Pilot testing of our approach suggests that it has significant potential to predict pain dynamics given patients' reported pain levels and medication usages. With more abundant data, our hybrid approach should allow physicians to make personalized, data driven recommendations for treating chronic pain.Comment: 13 pages, 15 figures, 5 table

    Personalized Treatment-Response Trajectories: Errors-in-variables, Interpretability, and Causality

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    One fundamental problem in many applications is to estimate treatment-response trajectories given multidimensional treatment variables. However, in reality, the estimation suffers severely from measurement error both in treatment timing and covariates, for example when the treatment data are self-reported by users. We introduce a novel data-driven method to tackle this challenging problem, which models personalized treatment-response trajectories as a sum of a parametric response function, based on restored true treatment timing and covariates and sharing information across individuals under a hierarchical structure, and a counterfactual trend fitted by a sparse Gaussian Process. In a real-life dataset where the impact of diet on continuous blood glucose is estimated, our model achieves a superior performance in estimation accuracy and prediction

    Continuous-time modelling of behavioural responses in animal movement

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    Funding: TM, RG, CH, and LT were funded by the US office of Naval Research, Grant N000141812807. This work was supported by the US Fleet Forces Command through the Naval Facilities Engineering Command Atlantic under Contract No. N62470-15-D-8006, Task Order 50, Issued to HDR, Inc.There is great interest in ecology to understand how wild animals are affected by anthropogenic disturbances, such as sounds. For example, behavioural response studies are an important approach to quantify the impact of naval activity on marine mammals. Controlled exposure experiments are undertaken where the behaviour of animals is quantified before, during, and after exposure to a controlled sound source, often using telemetry tags (e.g., accelerometers, or satellite trackers). Statistical modelling is required to formally compare patterns before and after exposure, to quantify deviations from baseline behaviour. We propose varying-coefficient stochastic differential equations (SDEs) as a flexible framework to model such data, with two components: (1) time-varying baseline dynamics, modelled with non-parametric or random effects of time-varying covariates, and (2) a nonparametric response model, which captures deviations from baseline. SDEs are specified in continuous time, which makes it straightforward to analyse data collected at irregular time intervals, a common situation for animal tracking studies. We describe how the model can be embedded into a state-space modelling framework to account for measurement error. We present inferential methods for model fitting, model checking, and uncertainty quantification (including on the response model). We apply this approach to two behavioural response study data sets on beaked whales: a satellite track, and high-resolution depth data. Our results suggest that the whalesā€™ horizontal movement and vertical diving behaviour changed after exposure to the sound source, and future work should evaluate the severity and possible consequences of these responses. These two very different examples showcase the versatility of varying-coefficient SDEs to measure changes in behaviour, and we discuss implications of disturbances for the whalesā€™ energetic balance.PostprintPeer reviewe

    Likelihood-Based Inference for Discretely Observed Birth-Death-Shift Processes, with Applications to Evolution of Mobile Genetic Elements

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    Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements - important genetic markers in molecular epidemiology. Estimation of the effects of individual covariates on the birth, death, and shift rates of the process can be accomplished by analyzing patient data, but inferring these rates in a discretely and unevenly observed setting presents computational challenges. We propose a mutli-type branching process approximation to BDS processes and develop a corresponding expectation maximization (EM) algorithm, where we use spectral techniques to reduce calculation of expected sufficient statistics to low dimensional integration. These techniques yield an efficient and robust optimization routine for inferring the rates of the BDS process, and apply more broadly to multi-type branching processes where rates can depend on many covariates. After rigorously testing our methodology in simulation studies, we apply our method to study intrapatient time evolution of IS6110 transposable element, a frequently used element during estimation of epidemiological clusters of Mycobacterium tuberculosis infections.Comment: 31 pages, 7 figures, 1 tabl

    Flexible semiparametric mixed models

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    In linear mixed models the influence of covariates is restricted to a strictly parametric form. With the rise of semi- and nonparametric regression also the mixed model has been expanded to allow for additive predictors. The common approach uses the representation of additive models as mixed models. An alternative approach that is proposed in the present paper is likelihood based boosting. Boosting originates in the machine learning community where it has been proposed as a technique to improve classification procedures by combining estimates with reweighted observations. Likelihood based boosting is a general method which may be seen as an extension of L2 boost. In additive mixed models the advantage of boosting techniques in the form of componentwise boosting is that it is suitable for high dimensional settings where many influence variables are present. It allows to fit additive models for many covariates with implicit selection of relevant variables and automatic selection of smoothing parameters. Moreover, boosting techniques may be used to incorporate the subject-specific variation of smooth influence functions by specifying random slopes on smooth e ects. This results in flexible semiparametric mixed models which are appropriate in cases where a simple random intercept is unable to capture the variation of e ects across subjects

    Principals as Agents: Subjective Performance Measurement in Education

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    In this paper, we compare subjective principal assessments of teachers to the traditional determinants of teacher compensation Ā”V education and experience Ā”V and another potential compensation mechanism -- value-added measures of teacher effectiveness based on student achievement gains. We find that subjective principal assessments of teachers predict future student achievement significantly better than teacher experience, education or actual compensation, though not as well as value-added teacher quality measures. In particular, principals appear quite good at identifying those teachers who produce the largest and smallest standardized achievement gains in their schools, but have far less ability to distinguish between teachers in the middle of this distribution and systematically discriminate against male and untenured faculty. Moreover, we find that a principalĀ”Ā¦s overall rating of a teacher is a substantially better predictor of future parent requests for that teacher than either the teacherĀ”Ā¦s experience, education and current compensation or the teacherĀ”Ā¦s value-added achievement measure. These findings not only inform education policy, but also shed light on subjective performance assessment more generally.

    Latent Gaussian Count Time Series Modeling

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    This paper develops theory and methods for the copula modeling of stationary count time series. The techniques use a latent Gaussian process and a distributional transformation to construct stationary series with very flexible correlation features that can have any pre-specified marginal distribution, including the classical Poisson, generalized Poisson, negative binomial, and binomial count structures. A Gaussian pseudo-likelihood estimation paradigm, based only on the mean and autocovariance function of the count series, is developed via some new Hermite expansions. Particle filtering methods are studied to approximate the true likelihood of the count series. Here, connections to hidden Markov models and other copula likelihood approximations are made. The efficacy of the approach is demonstrated and the methods are used to analyze a count series containing the annual number of no-hitter baseball games pitched in major league baseball since 1893
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