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In this paper, we aim to both borrow information from existing units and incorporate the target unit's history data in time series forecasting. We consider a situation when we have time series data from multiple units that share similar patterns when aligned in terms of an internal time. The internal time is defined as an index according to evolving features of interest. When mapped back to the calendar time, these time series can span different time intervals that can include the future calendar time of the targeted unit, over which we can borrow the information from other units in forecasting the targeted unit. We first build a hierarchical state space model for the multiple time series data in terms of the internal time, where the shared components capture the similarities among different units while allowing for unit‐specific deviations. A conditional state space model is then constructed to incorporate the information of existing units as the prior information in forecasting the targeted unit. By running the Kalman filtering based on the conditional state space model on the targeted unit, we incorporate both the information from the other units and the history of the targeted unit. The forecasts are then transformed from internal time back into calendar time for ease of interpretation. A simulation study is conducted to evaluate the finite sample performance. Forecasting state‐level new COVID‐19 cases in United States is used for illustration. [ABSTRACT FROM AUTHOR]

This preclinical study examines light fluence, photodynamic therapy ( PDT) dose and 'apparent reacted singlet oxygen,' [1O2]rx, to predict local control rate ( LCR) for Photofrin-mediated PDT of radiation-induced fibrosarcoma ( RIF) tumors. Mice bearing RIF tumors were treated with in-air fluences (50-250 J cm−2) and in-air fluence rates (50-150 mW cm−2) at Photofrin dosages of 5 and 15 mg kg−1 and a drug-light interval of 24 h using a 630-nm, 1-cm-diameter collimated laser. A macroscopic model was used to calculate [1O2]rx and PDT dose based on in vivo explicit dosimetry of the drug concentration, light fluence and tissue optical properties. PDT dose and [1O2]rx were defined as a temporal integral of drug concentration and fluence rate, and singlet oxygen concentration consumed divided by the singlet oxygen lifetime, respectively. LCR was stratified for different dose metrics for 74 mice (66 + 8 control). Complete tumor control at 14 days was observed for [1O2]rx ≥ 1.1 m m or PDT dose ≥1200 μ m J cm−2 but cannot be predicted with fluence alone. LCR increases with increasing [1O2]rx and PDT dose but is not well correlated with fluence. Comparing dosimetric quantities, [1O2]rx outperformed both PDT dose and fluence in predicting tumor response and correlating with LCR. [ABSTRACT FROM AUTHOR]

Adrenocorticotropic hormone (ACTH) diurnal patterns contain both smooth circadian rhythms and pulsatile activities. How to evaluate and compare them between different groups is a challenging statistical task. In particular, we are interested in testing (1) whether the smooth ACTH circadian rhythms in chronic fatigue syndrome and fibromyalgia patients differ from those in healthy controls and (2) whether the patterns of pulsatile activities are different. In this paper, a hierarchical state space model is proposed to extract these signals from noisy observations. The smooth circadian rhythms shared by a group of subjects are modeled by periodic smoothing splines. The subject level pulsatile activities are modeled by autoregressive processes. A functional random effect is adopted at the pair level to account for the matched pair design. Parameters are estimated by maximizing the marginal likelihood. Signals are extracted as posterior means. Computationally efficient Kalman filter algorithms are adopted for implementation. Application of the proposed model reveals that the smooth circadian rhythms are similar in the two groups but the pulsatile activities in patients are weaker than those in the healthy controls. [ABSTRACT FROM AUTHOR]

We extend a random pattern mixture joint model for longitudinal ordinal outcomes and informative dropouts. The patients are generalized to 'pattern' groups based on known covariates that are potentially surrogated for the severity of the underlying condition. The random pattern effects are defined as the latent effects linking the dropout process and the ordinal longitudinal outcome. Conditional on the random pattern effects, the longitudinal outcome and the dropout times are assumed independent. Estimates are obtained via the Expectation-maximization algorithm. We applied the model to the end-stage renal disease data. Anemia was found to be significantly affected by the baseline iron treatment when the dropout information was adjusted via the study model; as opposed to an independent or shared parameter model. Simulations were performed to evaluate the performance of the random pattern mixture model under various assumptions. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Branching curves are a technique for modeling curves that change trajectory at a change (branching) point. Currently, the estimation framework is limited to independent data, and smoothing splines are used for estimation. This article aims to extend the branching curve framework to the longitudinal data setting where the branching point varies by subject. If the branching point is modeled as a random effect, then the longitudinal branching curve framework is a semiparametric nonlinear mixed effects model. Given existing issues with using random effects within a smoothing spline, we express the model as a B-spline based semiparametric nonlinear mixed effects model. Simple, clever smoothness constraints are enforced on the B-splines at the change point. The method is applied to Women's Health data where we model the shape of the labor curve (cervical dilation measured longitudinally) before and after treatment with oxytocin (a labor stimulant). Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]