Extrapolation Model Research Articles

Bioconcentration Assessment in Fish Based on In Vitro Intrinsic Clearance: Predictivity of an Empirical Model Compared to In Vitro-In Vivo Extrapolation Models.

To estimate the bioconcentration factor (BCF), the in vitro intrinsic clearance (CLINVITRO,INT) from rainbow trout liver S9 fractions (RT-S9) can be applied to in vitro-in vivo extrapolation (IVIVE) models, yet uncertainties remain in model parameterization. An alternative model approach is evaluated: a regression model was built in the form log BCF = a × log Kow + b × log CLINVITRO,INT. The coefficients a and b were fitted based on a training set of 40 chemicals. A high robustness of the coefficients and good accuracy of BCF prediction were found on independent datasets of neutral organic chemicals (measured log Kow 3.3-6.2). BCF predictions were similar to or in better agreement with in vivo BCFs compared to IVIVE models (2.4- to 2.9- vs 2.8- to 3.6-fold misprediction) for training and test sets. Species-matched models (trout, carp) did not result in improvements. This study presents the largest dataset on CLINVITRO,INT and BCFs to assess predictivity of the RT-S9 assay. The robustness of the regression statistics on different datasets and the high statistical weight of the CLINVITRO,INT term illustrate the predictive power of the RT-S9 assay as an important step toward regulatory acceptance to replace animal experiments.

Machine-Learning Assisted Identification of Battery Life Models

Predictive battery life models are commonly utilized to extrapolate degradation trends observed during accelerated aging tests for simulation of degradation in real-world applications. Thus, fitting accelerated aging data as accurately as possible and with low uncertainty is crucial for making believable projections of battery lifetime, but it is challenging to identify algebraic expressions that accurately fit multivariate degradation trends. A review of models published in literature reveal some common expressions for fitting calendar aging data, which is only dependent on temperature and state-of-charge, but no consistency across many models for fitting cycle aging data, indicating the need for a statistically rigorous data driven approach for developing empirical models.This talk will describe a machine-learning assisted method for identification of predictive battery life models utilizing bilevel optimization and symbolic regression. Bilevel optimization with cross-validation is used to statistically determine cell- and stress-dependent model parameters, while symbolic regression identifies both linear and multiplicative candidate expressions to predict stress-dependent degradation rates by selecting low-order subsets of features from a generated feature library. Because model expressions are identified empirically, it is crucial to ensure resulting models behave according to physical expectations, so the stability of models for interpolation or extrapolation is interrogated qualitatively through simulation and quantitatively through cross-validation and uncertainty quantification via bootstrap resampling. This model identification approach substantially improves upon models identified purely using expert judgement in terms of both accuracy and uncertainty.Model simulation and validation is then conducted by deriving a state-equation form of the predictive model, enabling simulation of battery aging under dynamic stresses. This enables validation of the predictive battery model on lab-based tests with varying conditions or on drive-cycle or application-cycle testing protocols. Parameter uncertainty can be carried forward into model simulation, giving lifetime estimates and confidence windows for cell- or system-level lifetime. The financial impact of battery model uncertainty can be estimated by incorporating uncertainty into a technoeconomic model.

Taxation of Charitable Giving in Terms of Martial Law in Ukraine: Legislative Novelties and Future Models

The purpose of the article was to reveal the conditions and consequences of key developments in the Ukrainian tax legislation, with respect to charitable donations by residents and non-residents in the context of the martial law regime, but de facto, large-scale war; as well as to determine models of development forecasting tax incentives for the post-war period of the restoration of Ukraine. Interdisciplinary descriptive, analytical and prognostic methods were used in the development of the research; in particular, comparative, situational and matrix analysis, interpolation and extrapolation of trends, conceptual and cognitive modelling. It is concluded that, Ukrainian tax policy is being significantly modernized by implementing a wide range of novelties related to key national taxes, namely: corporate income tax and individual income tax, to create the most favourable treatment for charitable donations by individuals, legal entities, charitable organizations and business entities. It is expected that the post-war legislative strategy for taxation of charitable giving will be different from the peacetime and wartime models.

Comparative Thrombin Generation in Animal Plasma: Sensitivity to Human Factor XIa and Tissue Factor.

Preclinical evaluation of drugs in animals helps researchers to select potentially informative clinical laboratory markers for human trials. To assess the utility of animal thrombin generation (TG) assay, we studied the sensitivity of animal plasmas to triggers of TG, human Tissue Factor (TF), and Activated Factor XI (FXIa). Pooled human, mouse, rat, guinea pig, rabbit, bovine, sheep, and goat plasmas were used in this study. TF- or FXIa-triggered TG and clotting were measured via fluorescence and optical density, respectively. Thrombin peak height (TPH) and time (TPT), clot time (CT), and fibrin clot density (FCD) were all analyzed. The trigger low and high sensitivity borders (LSB and HSB) for each assay parameter were defined as TF and FXIa concentrations, providing 20 and 80% of the maximal parameter value, unless the baseline (no trigger) value exceeded 20% of the maximal, in which case, LSB was derived from 120% of baseline value. Normal human samples demonstrated lower TPH HSB than most of the animal samples for both TF and FXIa. Animal samples, except mice, demonstrated lower TPT LSB for FXIa versus humans. Most rodent and rabbit samples produced baseline TG in the absence of TG triggers that were consistent with the pre-activation of blood coagulation. FCD was not sensitive to both TF and FXIa in either of the plasmas. Animal plasmas have widely variable sensitivities to human TF and FXIa, which suggests that optimization of trigger concentration is required prior to test use, and this complicates the extrapolation of animal model results to humans.

A machine learning-based model for predicting distant metastasis in patients with rectal cancer.

Distant metastasis from rectal cancer usually results in poorer survival and quality of life, so early identification of patients at high risk of distant metastasis from rectal cancer is essential. The study used eight machine-learning algorithms to construct a machine-learning model for the risk of distant metastasis from rectal cancer. We developed the models using 23867 patients with rectal cancer from the Surveillance, Epidemiology, and End Results (SEER) database between 2010 and 2017. Meanwhile, 1178 rectal cancer patients from Chinese hospitals were selected to validate the model performance and extrapolation. We tuned the hyperparameters by random search and tenfold cross-validation to construct the machine-learning models. We evaluated the models using the area under the receiver operating characteristic curves (AUC), the area under the precision-recall curve (AUPRC), decision curve analysis, calibration curves, and the precision and accuracy of the internal test set and external validation cohorts. In addition, Shapley's Additive explanations (SHAP) were used to interpret the machine-learning models. Finally, the best model was applied to develop a web calculator for predicting the risk of distant metastasis in rectal cancer. The study included 23,867 rectal cancer patients and 2,840 patients with distant metastasis. Multiple logistic regression analysis showed that age, differentiation grade, T-stage, N-stage, preoperative carcinoembryonic antigen (CEA), tumor deposits, perineural invasion, tumor size, radiation, and chemotherapy were-independent risk factors for distant metastasis in rectal cancer. The mean AUC value of the extreme gradient boosting (XGB) model in ten-fold cross-validation in the training set was 0.859. The XGB model performed best in the internal test set and external validation set. The XGB model in the internal test set had an AUC was 0.855, AUPRC was 0.510, accuracy was 0.900, and precision was 0.880. The metric AUC for the external validation set of the XGB model was 0.814, AUPRC was 0.609, accuracy was 0.800, and precision was 0.810. Finally, we constructed a web calculator using the XGB model for distant metastasis of rectal cancer. The study developed and validated an XGB model based on clinicopathological information for predicting the risk of distant metastasis in patients with rectal cancer, which may help physicians make clinical decisions. rectal cancer, distant metastasis, web calculator, machine learning algorithm, external validation.

Identification of high-risk factors for recurrence of colon cancer following complete mesocolic excision: An 8-year retrospective study.

Colon cancer recurrence is a common adverse outcome for patients after complete mesocolic excision (CME) and greatly affects the near-term and long-term prognosis of patients. This study aimed to develop a machine learning model that can identify high-risk factors before, during, and after surgery, and predict the occurrence of postoperative colon cancer recurrence. The study included 1187 patients with colon cancer, including 110 patients who had recurrent colon cancer. The researchers collected 44 characteristic variables, including patient demographic characteristics, basic medical history, preoperative examination information, type of surgery, and intraoperative information. Four machine learning algorithms, namely extreme gradient boosting (XGBoost), random forest (RF), support vector machine (SVM), and k-nearest neighbor algorithm (KNN), were used to construct the model. The researchers evaluated the model using the k-fold cross-validation method, ROC curve, calibration curve, decision curve analysis (DCA), and external validation. Among the four prediction models, the XGBoost algorithm performed the best. The ROC curve results showed that the AUC value of XGBoost was 0.962 in the training set and 0.952 in the validation set, indicating high prediction accuracy. The XGBoost model was stable during internal validation using the k-fold cross-validation method. The calibration curve demonstrated high predictive ability of the XGBoost model. The DCA curve showed that patients who received interventional treatment had a higher benefit rate under the XGBoost model. The external validation set's AUC value was 0.91, indicating good extrapolation of the XGBoost prediction model. The XGBoost machine learning algorithm-based prediction model for colon cancer recurrence has high prediction accuracy and clinical utility.

The challenges of defining hormesis in epidemiological studies: The case of radiation hormesis

In the current radiation protection system, preventive measures and occupational exposure limits for controlling occupational exposure to ionizing radiation are based on the linear no-threshold extrapolation model. However, currently an increasing body of evidence indicates that this paradigm predicts very poorly biological responses in the low-dose exposure region. In addition, several in vitro and in vivo studies demonstrated the presence of hormetic dose response curves correlated to ionizing radiation low exposure. In this regard, it is noteworthy that also the findings of different epidemiological studies, conducted in different categories of occupationally exposed workers (e.g., healthcare, nuclear industrial and aircrew workers), observed lower rates of mortality and/or morbidity from cancer and/or other diseases in exposed workers than in unexposed ones or in the general population, then suggesting the possible occurrence of hormesis. Nevertheless, these results should be considered with caution since the identification of hormetic response in epidemiological studies is rather challenging because of a number of major limitations. In this regard, some of the most remarkable shortcomings found in epidemiological studies performed in workers exposed to ionizing radiation are represented by lack or inadequate definition of exposure doses, use of surrogates of exposure, narrow dose ranges, lack of proper control groups and poor evaluation of confounding factors. Therefore, considering the valuable role and contribution that epidemiological studies might provide to the complex risk assessment and management process, there is a clear and urgent need to overcome the aforementioned limits in order to achieve an adequate, useful and more real-life risk assessment that should also include the key concept of hormesis. Thus, in the present conceptual article we also discuss and provide possible approaches to improve the capacity of epidemiological studies to identify/define the hormetic response and consequently improve the complex process of risk assessment of ionizing radiation at low exposure doses.

CoPR: Toward Accurate Visual Localization With Continuous Place-Descriptor Regression

Visual Place Recognition (VPR) is an image-based localization method that estimates the camera location of a query image by retrieving the most similar reference image from a map of geo-tagged reference images. In this work, we look into two fundamental bottlenecks for its localization accuracy: reference map sparseness and viewpoint invariance. Firstly, the reference images for VPR are only available at sparse poses in a map, which enforces an upper bound on the maximum achievable localization accuracy through VPR. We therefore propose Continuous Place-descriptor Regression (CoPR) to densify the map and improve localization accuracy. We study various interpolation and extrapolation models to regress additional VPR feature descriptors from only the existing references. Secondly, we compare different feature encoders and show that CoPR presents value for all of them. We evaluate our models on three existing public datasets and report on average around 30% improvement in VPR-based localization accuracy using CoPR, on top of the 15% increase by using a viewpoint-variant loss for the feature encoder. The complementary relation between CoPR and Relative Pose Estimation is also discussed.

Impact ionization in silicon at low charge-carrier energies

Photons absorbed in silicon produce electron–hole pairs, which can cause impact ionization and quantum yield larger than one. Reliable determination of quantum yield at low charge-carrier energies (<4 eV) has been challenging because photon losses due to reflectance and charge-carrier losses due to recombination affect the resulting photocurrent. Here, we present how the measurement of this fundamental characteristic of silicon crystals can be improved in the charge-carrier energy range of 1.6–4 eV by using a predictable quantum efficient detector based on induced junction photodiodes optimized for photon-to-electron conversion efficiency. The measured quantum yield values are compared with the results of theoretical calculations, revealing increased impact-ionization probabilities at 2.25 and 3.23 eV on the top of a smooth background curve calculated by a model based on free charge carriers in the silicon lattice. For the results at the lowest energies, both data and an asymptotic extrapolation model suggest that quantum yield exceeds unity by ∼10−4 at 1.6 eV corresponding to a photon wavelength of 450 nm.

Using energy expenditure to estimate the minute ventilation and inhaled load of air pollutants: a pilot survey in young Chinese adults.

Existing equations to estimate ventilation (VE) may not represent the Chinese population. The objective is to develop regression equations to predict the basal metabolic rate (BMR) for ventilation estimation. 80 participants underwent the incremental tests on a bicycle ergometer, wearing a fitted facial mask with an airflow sensor connected to the cardiopulmonary gas analyzer, where the energy expenditure, metabolic factors and VE were monitored simultaneously. Linear regression models were established between BMR and body weight, which were used to estimate energy expenditure and VE. Extrapolation of the regression model was evaluated by the five-fold cross-validation. And we also assessed the inhaled load of air pollutants in subgroups at the same exposure levels. Regression models for males and females were BMR (kJ/d) = 107.58 × weight (kg)-172.61 and BMR (kJ/d) = 105.61 × weight (kg)-26.94, respectively. The model showed good fitness between the measured and predicted VE. Differences between the measured and predicted VE of this model are smaller than that of other models. There were significant differences in inhaled load participants in the same exposure concentrations. The regression model showed that weight and BMR are highly correlated and can be used to estimate individual VE.

INES: Interactive tool for construction and extrapolation of partitioned survival models

BackgroundINES (INteractive model for Extrapolation of Survival and cost) provides an open-access tool powered by R that implements three-state partitioned survival models (PSM). This article describes the properties of the tool, and the situations where INES may or may not be suitable.MethodsINES is designed to be used by investigators or healthcare professionals who have a good grasp of the principles of economic evaluation and understand the strengths and weaknesses of partitioned survival models, but are not sufficiently familiar with a statistical package such as Excel or R to be able to construct and test a de-novo PSM themselves.INES is delivered to the user via a batch file. Once downloaded to the user’s hard drive, it interacts with the user via a portable version of R with web interactivity built in Shiny. INES requires absolutely no knowledge of R and the user does not need to have R or any of its dependences installed. Hence the user will deal with a standalone Shiny app. Inputs (digitalized survival curves, unit costs, posology, hazard ratios, discount rate) can be uploaded from a template spreadsheet.ResultsThe INES application provides a seamlessly integrated package for estimating a set of parametric hazard functions for progression free and overall survival, selecting an appropriate function from this menu, and applying this as an input to a PSM to calculate mean costs and quality-adjusted life years. Examples are given that may serve as a tutorial.ConclusionINES offers a rapid, flexible, robust and transparent tool for parametric survival analysis and calculating a PSM that can be used in many different contexts.

An investigation into model extrapolation and stability in the system identification of a nonlinear structure

Estimating a nonlinear model from experimental measurements of a vibrating structure remains a challenge, despite huge progress in recent years. A major issue is that the dynamical behaviour of a nonlinear structure strongly depends on the magnitude of the displacement response. Thus, the validity of an identified model is generally limited to a certain range of motion. Also, outside this range, the stability of the solutions predicted by the model are not guaranteed. This raises the question as to how a nonlinear model derived using data from relatively low amplitude excitation can be used to predict the dynamical behaviour for higher amplitude excitation. This paper focuses on this problem, investigating the extrapolation capabilities of data-driven nonlinear state-space models based on a subspace approach. The experimental vibrating structure consists of a cantilever beam in which magnets are used to generate strong geometric nonlinearity. The beam is driven by an electrodynamic shaker using several levels of broadband random noise. Acceleration data from the beam tip are used to derive nonlinear state-space models for the structure. It is shown that model predictions errors generally tend to increase when extrapolating towards higher excitation levels. Furthermore, the validity of the estimated nonlinear models become poor for very strong nonlinear behaviour. Linearised models are also estimated to have a complete view of the performance of each candidate model for each level of excitation.

A creep life prediction model of P91 steel coupled with back-propagation artificial neural network (BP-ANN) and θ projection method

In order to predict the long-term creep life of P91 steel, this work proposed a coupled model, combining the error-trained back-propagation artificial neural network (BP-ANN) and an improved θ model. Both the short-term rupture life obtained by creep experiments and the related creep data of National Institute for Materials Science (NIMS) database were used to validate the above model. In this model, creep parameters (temperature, stress) were used as the input and relative error of 5 θ model extrapolations as the output. Then, the prediction errors of BP-ANN method were introduced to correct the 5 θ model extrapolation results to achieve a more accurate prediction. Consequently, the long-term creep life of P91 steel was predicted. It demonstrated that with the proposed model, the prediction capability for long-term creep life of P91 steel with 200,000 h is much better than those of other θ methods, which has a prediction uncertainty less than 5%.

Review and perspective on polyhedron model for estimating thermodynamic properties of oxides

AbstractKnowledge of thermodynamics and phase equilibria of oxidic materials is crucial for advancement in the field of ceramics and glass. With the development of computational thermodynamics, predicting phase diagrams and chemical reactions of multicomponent systems has become possible. However, there are still plenty of oxides, the thermodynamic properties of which have not been identified due to the challenges in conducting experiments. Therefore, a key to the advancement in thermodynamic modeling would be to develop a universal model that can be used to estimate the thermodynamic properties of oxides with reliable extrapolation capacity. Atomistic (or molecular) scale models are still insufficient in predicting the thermodynamic properties of oxides at any scale. Alternatively, among group contribution–based methods, the polyhedron model has presented its potential in the estimation of the thermodynamic properties of ionic crystals. However, this model still demands improvements that increase the model's accuracy and extrapolation capacity. In this paper, the background and the state‐of‐the‐art of polyhedron model will be presented together with its strengths and shortcomings. Subsequently, it will be briefly discussed how the field of artificial intelligence could be exploited to devise the next generation of the polyhedron model, the modified polyhedron model.

Machine-learning investigation on the creep-rupture time of heat-resistant steels

Currently, the reliable prediction of creep-rupture times of heat-resistant alloys is a major research area with regard to structural materials. Numerous efforts to predict creep rupture times have been made using phenomenological parameter methods; however, these approaches have only been able to achieve a limited prediction accuracy. Furthermore, the applicability of machine learning to improve the prediction accuracy of creep-rupture time has been investigated. In both studies, nevertheless, approaches have been used where explicit analytical formulas are not available. Because creep rupture is a safety issue, it is essential to use an analytical equation for predicting rupture time. Therefore, in this study, a machine learning method was applied to the analysis of creep-rupture time of heat-resistant steel to obtain an explainable prediction formula. An accurate regression model was obtained using the linear independent descriptor generation (LIDG) regression method of adding independent higher-order terms that were generated from operations between variables. By utilizing LIDG regression, we show that various creep-rupture times could be well-reproduced by different heats using explanatory variables such as creep conditions, chemical compositions, and Vickers hardness. The heat-to-heat variation in creep-rupture time could not be accounted for at all in the evaluation using the conventional parameter method. On the other hand, the LIDG regression could naturally explain the difference in the creep rupture time of various heats. Furthermore, the excellent extrapolation of the LIDG regression model was confirmed, showing its potential for long-time creep-rupture time prediction updating the conventional parametric method.

Examining the continuum of resistance model in two population-based screening studies in Sweden

In studies recruited on a voluntary basis, lack of representativity may impair the ability to generalize findings to the target population. Previous studies, primarily based on surveys, have suggested that generalizability may be improved by exploiting data on individuals who agreed to participate only after receiving one or several reminders, as such individuals may be more similar to non-participants than what early participants are. Assessing this idea in the context of screenings, we compared sociodemographic characteristics and health across early, late, and non-participants in two large population-based screening studies in Sweden: STROKESTOP II (screening for atrial fibrillation; 6,867 participants) and SCREESCO (screening for colorectal cancer; 39,363 participants). We also explored the opportunities to reproduce the distributions of characteristics in the full invited populations, either by assuming that the non-participants were similar to the late participants, or by applying a linear extrapolation model based on both early and late participants. Findings showed that early and late participants exhibited similar characteristics along most dimensions, including civil status, education, income, and health examination results. Both these types of participants in turn differed from the non-participants, with fewer married, lower educational attainments, and lower incomes. Compared to early participants, late participants were more likely to be born outside of Sweden and to have comorbidities, with non-participants similar or even more so. The two empirical models improved representativity in some cases, but not always. Overall, we found mixed support that data on late participation may be useful for improving representativeness of screening studies.

Nowcasting Multiparameter Phased-Array Weather Radar (MP-PAWR) Echoes of Localized Heavy Precipitation Using a 3D Recurrent Neural Network Trained with an Adversarial Technique

Abstract We present nowcasts of sudden heavy rains on meso-γ scales (2–20 km) using the high spatiotemporal resolution of a multiparameter phased-array weather radar (MP-PAWR) sensitive to rain droplets. The onset of typical storms is successfully predicted with 10-min lead time, i.e., the current predictability limit of rainfall caused by individual convective cores. A supervised recurrent neural network based on long short-term memory with 3D spatial convolutions (RN3D) is used to account for the horizontal and vertical changes of the convective cells with a time resolution of 30 s. The model uses radar reflectivity at horizontal polarization ZH and the differential reflectivity. The input parameters are defined in a volume of 64 × 64 × 8 km3 with the lowest level at 1.9 km and a resolution of 0.4 × 0.4 × 0.25 km3. The prediction is a 10-min sequence of ZH at the lowest grid level. The model is trained with a large number of observations of summer 2020 and an adversarial technique. RN3D is tested with different types of rapidly evolving localized heavy rainfalls of summers 2018 and 2019. The model performance is compared to that of an advection model for 3D extrapolation of PAWR echoes (A3DM). RN3D better predicts the formation and dissipation of precipitation. However, RN3D tends to underestimate heavy rainfall especially when the storm is well developed. In this phase of the storm, A3DM nowcast scores are found slightly higher. The high skill of RN3D to predict the onset of sudden localized rainfall is illustrated with an example for which RN3D outperforms the operational precipitation nowcasting system of Japan Meteorological Agency (JMA). Significance Statement Temporal extrapolation of radar observations is a means of nowcasting sudden heavy rains, i.e., forecasts with a few tens of minutes and a high spatial resolution better than 500 m. They are necessary to set up warning systems to anticipate damage to infrastructure and reduce the fatalities these storms cause. It is a difficult task due to the storm suddenness, restricted area, and nonlinear behavior that are not well captured by current operational observation and numerical systems. In this study, we use a new high-resolution weather radar with polarimetric information and a 3D recurrent neural network to improve 10-min nowcasts, the current limit of operational systems. This is a first and essential step before applying such a method for increasing the prediction lead time.

Pervasive impacts of climate change on the woodiness and ecological generalism of dry forest plant assemblages

Abstract Climate emergency is a significant threat to biodiversity in the 21st century, but species will not be equally affected. In summing up the responses of different species at the local scale, we can assess changes in the species quantity and composition of biotic assemblages. We used more than 420K curated occurrence records of 3060 plant species to model current and future patterns of plant species distribution in one of the world's largest tropical dry forests—the Caatinga. While allowing different model extrapolation scenarios, we estimated potential changes in the species richness and composition of dryland plant assemblages in response to projected climate change, and assessed how the ecological generalism and woodiness of plant assemblages can be impacted by the climate crisis. More than 99% of plant assemblages were projected to lose species by 2060, with biotic homogenisation—the decrease in spatial beta diversity—forecasted in 40% of the Caatinga. The replacement of narrow‐range woody species by wide‐range non‐woody ones should impact at least 90% of Caatinga plant assemblages. The exacerbated species loss in the dryland plant assemblages was connected to the heterogenisation and homogenisation of biotic assemblages. Still, the magnitude of climate change impacts on ecological generalism and woodiness patterns of dryland plant assemblages differ according to the direction of the biotic change process. Synthesis. The future increase in aridity will change the patterns of woodiness and ecological generalism of tropical dry forest plant assemblages by decreasing vegetation diversity and complexity. The projected biotic changes in dryland plant assemblages indicate the erosion of ecosystem services linked to biomass productivity and carbon storage. We highlight the importance of long‐term conservation planning for maintaining tropical dry forests.

Extending Beyond Bagust and Beale: Fully Parametric Piecewise Exponential Models for Extrapolation of Survival Outcomes in Health Technology Assessment

ObjectivesWhen extrapolating time-to-event data the Bagust and Beale (B&B) approach uses the Kaplan-Meier survival function until a manually chosen time point, after which a constant hazard is assumed. This study demonstrates an objective statistical approach to estimate this time point. MethodsWe estimate piecewise exponential models (PEMs), whereby the hazard function is partitioned into segments each with constant hazards. The boundaries of these segments are known as change points. Our approach determines the location and number of change points in PEMs from which the hazard in the final segment is used to model long-term survival. We reviewed previous applications of the B&B approach in National Institute for Health and Care Excellence Technology Appraisals (TAs) completed between July 2011 and June 2017. The time points after which constant hazards were assumed were compared between PEMs and the B&B approaches. When further survival data were published following the original TA, we compared these updated estimates to predicted survival from the PEM and other parametric models adjusted for general population mortality. ResultsSix of the 59 TAs in this review considered the B&B approach. There was general agreement between the location of time points identified through the PEM and the B&B approaches. In 2 of the identified TAs the best fitting model to the data was a no-change-point model. Of the 3 TAs for which further survival data became available, PEM provided the closest prediction for survival outcomes in 2 TAs. ConclusionsPEMs are useful for survival extrapolation when a long-term constant hazard trend for the disease is clinically plausible.

Long-term forcing of the Sun’s coronal field, open flux, and cosmic ray modulation potential during grand minima, maxima, and regular activity phases by the solar dynamo mechanism

ABSTRACT Magnetic fields generated in the Sun’s interior by the dynamo mechanism drive solar activity over a range of time-scales. Direct sunspot observations exist for a few centuries; reconstructed variations based on cosmogenic isotopes in the solar open flux and cosmic ray flux exist over thousands of years. While such reconstructions indicate the presence of extreme solar activity fluctuations in the past, causal links between millennia scale dynamo activity, consequent coronal field, solar wind, open flux and cosmic ray flux variations remain elusive; a lack of coronal field observations compounds this issue. By utilizing a stochastically forced solar dynamo model and potential field source surface extrapolation, we perform long-term simulations to illuminate how dynamo generated magnetic fields govern the structure of the solar corona and the state of the heliosphere – as indicated by variations in the open flux and cosmic ray modulation potential. We establish differences in the nature of the large-scale structuring of the solar corona during grand maximum, minimum, and regular solar activity phases and simulate how the open flux and cosmic ray modulation potential vary across these different phases of activity. We demonstrate that the power spectrum of simulated and observationally reconstructed solar open flux time series are consistent with each other. Our study provides the theoretical foundation for interpreting long-term solar cycle variations inferred from cosmogenic isotope based reconstructions and establishes causality between solar internal variations to the forcing of the state of the heliosphere.