A New Mixture Model With Cure Rate Applied to Breast Cancer Data.

We introduce a new modelling for long-term survival models, assuming that the number of competing causes follows a mixture of Poisson and the Birnbaum-Saunders distribution. In this context, we present some statistical properties of our model and demonstrate that the promotion time model emerges as a limiting case. We delve into detailed discussions of specific models within this class. Notably, we examine the expected number of competing causes, which depends on covariates. This allows for direct modeling of the cure rate as a function of covariates. We present an Expectation-Maximization (EM) algorithm for parameter estimation, to discuss the estimation via maximum likelihood (ML) and provide insights into parameter inference for this model. Additionally, we outline sufficient conditions for ensuring the consistency and asymptotic normal distribution of ML estimators. To evaluate the performance of our estimation method, we conduct a Monte Carlo simulation to provide asymptotic properties and a power study of LR test by contrasting our methodology against the promotion time model. To demonstrate the practical applicability of our model, we apply it to a real medical dataset from a population-based study of incidence of breast cancer in São Paulo, Brazil. Our results illustrate that the proposed model can outperform traditional approaches in terms of model fitting, highlighting its potential utility in real-world scenarios.

Achieving Equity in Transportation for Radiotherapy.

Transportation is a significant social determinant of health and a barrier to treatment for many patients. Cancer patients are disproportionately affected, and it can be especially salient for patients undergoing several weeks of daily radiation treatment. A prospective survey pilot study at our institution examining financial toxicity related to transportation for patients undergoing radiation treatment showed a correlation between high transportation costs and financial stress. Furthermore, those living >10 miles from the radiation center were associated with worse financial toxicity. Previous programs implemented to address the transportation issue in oncology have been mainly inadequate or ineffective. These programs have been set back due to a lack of awareness and low utilization. The Health Equity Achievement in Radiation Therapy (HEART) adjustment from the proposed Radiation Oncology Case Rate (ROCR) payment model for radiation oncology will greatly alleviate transportation barriers for patients undergoing radiation treatment. The $500 per patient can be utilized for those patients at the highest risk, like those living far away from the radiation center.

Firing rate models for gamma oscillations in I-I and E-I networks.

Firing rate models for describing the mean-field activities of neuronal ensembles can be used effectively to study network function and dynamics, including synchronization and rhythmicity of excitatory-inhibitory populations. However, traditional Wilson-Cowan-like models, even when extended to include an explicit dynamic synaptic activation variable, are found unable to capture some dynamics such as Interneuronal Network Gamma oscillations (ING). Use of an explicit delay is helpful in simulations at the expense of complicating mathematical analysis. We resolve this issue by introducing a dynamic variable, u, that acts as an effective delay in the negative feedback loop between firing rate (r) and synaptic gating of inhibition (s). In effect, u endows synaptic activation with second order dynamics. With linear stability analysis, numerical branch-tracking and simulations, we show that our r-u-s rate model captures some key qualitative features of spiking network models for ING. We also propose an alternative formulation, a v-u-s model, in which mean membrane potential v satisfies an averaged current-balance equation. Furthermore, we extend the framework to E-I networks. With our six-variable v-u-s model, we demonstrate in firing rate models the transition from Pyramidal-Interneuronal Network Gamma (PING) to ING by increasing the external drive to the inhibitory population without adjusting synaptic weights. Having PING and ING available in a single network, without invoking synaptic blockers, is plausible and natural for explaining the emergence and transition of two different types of gamma oscillations.

Modeling of Material Removal Rate for the Fixed-Abrasive Double-Sided Planetary Grinding of a Sapphire Substrate.

Double-sided planetary grinding (DSPG) with a fixed abrasive is widely used in sapphire substrate processing. Compared with conventional free abrasive grinding, it has the advantages of high precision, high efficiency, and environmental protection. In this study, we propose a material removal rate (MRR) model specific to the fixed-abrasive DSPG process for sapphire substrates, grounded in the trajectory length of abrasive particles. In this paper, the material removal rate model is obtained after focusing on the theoretical analysis of the effective number of abrasive grains, the indentation depth of a single abrasive grain, the length of the abrasive grain trajectory, and the groove repetition rate. To validate this model, experiments were conducted on sapphire substrates using a DSPG machine. Theoretical predictions of the material removal rate were then juxtaposed with experimental outcomes across varying grinding pressures and rotational speeds. The trends between theoretical and experimental values showed remarkable consistency, with deviations ranging between 0.2% and 39.2%, thereby substantiating the model's validity. Moreover, leveraging the insights from this model, we optimized the disparity in the material removal rate between two surfaces of the substrate, thereby enhancing the uniformity of the machining process across both surfaces.

Modelling passive sampling of hydrophilic compounds under time-variable aqueous concentrations.

Passive sampling is a crucial method for evaluating concentrations of hydrophilic organic compounds in the aquatic environment, but it is insufficiently understood to what extent passive samplers capture the intermittent emissions that frequently occur for this group of compounds. In the present study, silicone sheets and styrene-divinyl benzene-reversed phase sulfonated extraction disks with and without a polyethersulfone membrane were exposed under semi-field conditions in a 31 m3 flume at three different flow velocities. Natural processes and spiking/dilution measures caused aqueous concentrations to vary strongly with time. The data were analyzed using two analytical models that account for these time-variable concentrations: a sampling rate model and a diffusion model. The diffusion model generally gave a better fit of the data than the sampling rate model, but the difference in residual errors was quite small (median errors of 19 vs. 25% for silicone and 22 vs. 25% for SDB-RPS samplers). The sampling rate model was therefore adequate enough to evaluate the time-integrative capabilities of the samplers. Sampler performance was best for SDB-RPS samplers with a polyethersulfone membrane, despite the occurrence of lag times for some compounds (0.1 to 0.4 days). Sampling rates for this design also spanned a narrower range (80 to 110 mL/day) than SDB-RPS samplers without a membrane (100 to 660 mL/day). The effect of biofouling was similar for all compounds and was consistent with a biofouling layer thickness of 150 µm.

A New Approach to Modeling the Cure Rate in the Presence of Interval Censored Data.

We consider interval censored data with a cured subgroup that arises from longitudinal followup studies with a heterogeneous population where a certain proportion of subjects is not susceptible to the event of interest. We propose a two component mixture cure model, where the first component describing the probability of cure is modeled by a support vector machine-based approach and the second component describing the survival distribution of the uncured group is modeled by a proportional hazard structure. Our proposed model provides flexibility in capturing complex effects of covariates on the probability of cure unlike the traditional models that rely on modeling the cure probability using a generalized linear model with a known link function. For the estimation of model parameters, we develop an expectation maximization-based estimation algorithm. We conduct simulation studies and show that our proposed model performs better in capturing complex effects of covariates on the cure probability when compared to the traditional logit link-based two component mixture cure model. This results in more accurate (smaller bias) and precise (smaller mean square error) estimates of the cure probabilities, which in-turn improves the predictive accuracy of the latent cured status. We further show that our model's ability to capture complex covariate effects also improves the estimation results corresponding to the survival distribution of the uncured. Finally, we apply the proposed model and estimation procedure to an interval censored data on smoking cessation.

A flexible time-varying coefficient rate model for panel count data.

Panel count regression is often required in recurrent event studies, where the interest is to model the event rate. Existing rate models are unable to handle time-varying covariate effects due to theoretical and computational difficulties. Mean models provide a viable alternative but are subject to the constraints of the monotonicity assumption, which tends to be violated when covariates fluctuate over time. In this paper, we present a new semiparametric rate model for panel count data along with related theoretical results. For model fitting, we present an efficient EM algorithm with three different methods for variance estimation. The algorithm allows us to sidestep the challenges of numerical integration and difficulties with the iterative convex minorant algorithm. We showed that the estimators are consistent and asymptotically normally distributed. Simulation studies confirmed an excellent finite sample performance. To illustrate, we analyzed data from a real clinical study of behavioral risk factors for sexually transmitted infections.

Application of mechanistic modelling in membrane and fiber chromatography for purification of biotherapeutics - A review.

Mechanistic modelling is a simulation tool which has been effectively applied in downstream bioprocessing to model resin chromatography. Membrane and fiber chromatography are newer approaches that offer higher rates of mass transfer and consequently higher flow rates and reduced processing times. This review describes the key considerations in the development of mechanistic models for these unit operations. Mass transfer is less complex than in resin columns, but internal housing volumes can make modelling difficult, particularly for laboratory-scale devices. Flow paths are often non-linear and the dead volume is often a larger fraction of the overall volume, which may require more complex hydrodynamic models to capture residence time distributions accurately. In this respect, the combination of computational fluid dynamics with appropriate protein binding models is emerging as an ideal approach.

Modeling Instantaneous Firing Rate of Deep Brain Stimulation Target Neuronal Ensembles in the Basal Ganglia and Thalamus.

OBJECTIVE: Deep brain stimulation (DBS) is an effective treatment for movement disorders, including Parkinson disease and essential tremor. However, the underlying mechanisms of DBS remain elusive. Despite the capability of existing models in interpreting experimental data qualitatively, there are very few unified computational models that quantitatively capture the dynamics of the neuronal activity of varying stimulated nuclei-including subthalamic nucleus (STN), substantia nigra pars reticulata (SNr), and ventral intermediate nucleus (Vim)-across different DBS frequencies. MATERIALS AND METHODS: Both synthetic and experimental data were used in the model fitting; the synthetic data were generated by an established spiking neuron model that was reported in our previous work, and the experimental data were provided using single-unit microelectrode recordings (MERs) during DBS (microelectrode stimulation). Based on these data, we developed a novel mathematical model to represent the firing rate of neurons receiving DBS, including neurons in STN, SNr, and Vim-across different DBS frequencies. In our model, the DBS pulses were filtered through a synapse model and a nonlinear transfer function to formulate the firing rate variability. For each DBS-targeted nucleus, we fitted a single set of optimal model parameters consistent across varying DBS frequencies. RESULTS: Our model accurately reproduced the firing rates observed and calculated from both synthetic and experimental data. The optimal model parameters were consistent across different DBS frequencies. CONCLUSIONS: The result of our model fitting was in agreement with experimental single-unit MER data during DBS. Reproducing neuronal firing rates of different nuclei of the basal ganglia and thalamus during DBS can be helpful to further understand the mechanisms of DBS and to potentially optimize stimulation parameters based on their actual effects on neuronal activity.

A support vector machine-based cure rate model for interval censored data.

The mixture cure rate model is the most commonly used cure rate model in the literature. In the context of mixture cure rate model, the standard approach to model the effect of covariates on the cured or uncured probability is to use a logistic function. This readily implies that the boundary classifying the cured and uncured subjects is linear. In this article, we propose a new mixture cure rate model based on interval censored data that uses the support vector machine to model the effect of covariates on the uncured or the cured probability (i.e. on the incidence part of the model). Our proposed model inherits the features of the support vector machine and provides flexibility to capture classification boundaries that are nonlinear and more complex. The latency part is modeled by a proportional hazards structure with an unspecified baseline hazard function. We develop an estimation procedure based on the expectation maximization algorithm to estimate the cured/uncured probability and the latency model parameters. Our simulation study results show that the proposed model performs better in capturing complex classification boundaries when compared to both logistic regression-based and spline regression-based mixture cure rate models. We also show that our model's ability to capture complex classification boundaries improve the estimation results corresponding to the latency part of the model. For illustrative purpose, we present our analysis by applying the proposed methodology to the NASA's Hypobaric Decompression Sickness Database.

Existence of solutions for stress-rate type strain-limiting viscoelasticity in Gevrey spaces.

In this work, we deal with a one-dimensional stress-rate type model for the response of viscoelastic materials, in relation to the strain-limiting theory. The model is based on a constitutive relation of stress-rate type. Unlike classical models in elasticity, the unknown of the model under consideration is uniquely the stress, avoiding the use of the deformation. Here, we treat the case of periodic boundary conditions for a linearized model. We determine an optimal function space that ensures the local existence of solutions to the linearized model around certain steady states. This optimal space is known as the Gevrey-class [Formula: see text], which characterizes the regularity properties of the solutions. The exponent [Formula: see text] in the Gevrey-class reflects the specific dispersion properties of the equation itself. This article is part of the theme issue 'Foundational issues, analysis and geometry in continuum mechanics'.

Odor modality is transmitted to cortical brain regions from the olfactory bulb.

Odor perception is the impetus for important animal behaviors with two predominate modes of processing: odors pass through the front of the nose (orthonasal) while inhaling and sniffing, or through the rear (retronasal) during exhalation and while eating. Despite the importance of olfaction for an animal's well-being and that ortho and retro naturally occur, it is unknown how the modality (ortho vs. retro) is even transmitted to cortical brain regions, which could significantly affect how odors are processed and perceived. Using multielectrode array recordings in tracheotomized anesthetized rats, which decouples ortho-retro modality from breathing, we show that mitral cells in rat olfactory bulb can reliably and directly transmit orthonasal versus retronasal modality with ethyl butyrate, a common food odor. Drug manipulations affecting synaptic inhibition via GABAA lead to worse decoding of ortho versus retro, independent of whether overall inhibition increases or decreases, suggesting that the olfactory bulb circuit may naturally favor encoding this important aspect of odors. Detailed data analysis paired with a firing rate model that captures population trends in spiking statistics shows how this circuit can encode odor modality. We have not only demonstrated that ortho/retro information is encoded to downstream brain regions but also used modeling to demonstrate a plausible mechanism for this encoding; due to synaptic adaptation, it is the slower time course of the retronasal stimulation that causes retronasal responses to be stronger and less sensitive to inhibitory drug manipulations than orthonasal responses.NEW & NOTEWORTHY Whether ortho (sniffing odors) versus retro (exhalation and eating) is encoded from the olfactory bulb to other brain areas is not completely known. Using multielectrode array recordings in anesthetized rats, we show that the olfactory bulb transmits this information downstream via spikes. Altering inhibition degrades ortho/retro information on average. We use theory and computation to explain our results, which should have implications on cortical processing considering that only food odors occur retronasally.

Motor adaptation does not differ when a perturbation is introduced abruptly or gradually.

People continuously adapt their movements to ever-changing circumstances, and particularly in skills training and rehabilitation, it is crucial that we understand how to optimize implicit adaptation in order for these processes to require as little conscious effort as possible. Although it is generally assumed that the way to do this is by introducing perturbations gradually, the literature is ambivalent on the effectiveness of this approach. Here, we tested whether there are differences in motor performance when adapting to an abrupt compared to a ramped visuomotor rotation. Using a within-subjects design, we tested this question under 3 different rotation sizes: 30-degrees, 45-degrees, and 60-degrees, as well as in 3 different populations: younger adults, older adults, and patients with mild cerebellar ataxia. We find no significant differences in either the behavioural outcomes, or model fits, between abrupt and gradual learning across any of the different conditions. Neither age, nor cerebellar ataxia had any significant effect on error-sensitivity either. These findings together indicate that error-sensitivity is not modulated by introducing a perturbation abruptly compared to gradually, and is also unaffected by age or mild cerebellar ataxia.

A temperature-dependent phenology model for Bemisia tabaci MEAM1 (Hemiptera: Aleyrodidae).

The sweetpotato whitefly, Bemisia tabaci (Gennadius) Middle East-Asia Minor 1 (MEAM1), is widespread across tropical and subtropical regions, affecting hundreds of cultivated and wild plant species. Because the species transmits a variety of viruses, the whitefly has become one of the most economically significant insect pests in the world. Determining a pest's population growth potential as a function of temperature is critical for understanding a species population dynamics, predicting the potential range of the species and its associated diseases, and designing adaptive pest management strategies. The life history of B. tabaci MEAM1 was studied in life-table experiments at 7 constant temperatures ranging from 12 to 35 °C. Nonlinear equations were fitted to development, mortality, and reproduction data and compiled into an overall phenology rate-summation model using Insect Life Cycle Modeling (ILCYM) software, to simulate life-table parameters based on temperature. Life tables of B. tabaci MEAM1 observed at naturally variable temperature in La Molina, Lima, during different seasons, covering the entire temperature range of the species' predicted performance curve, were used to validate the model. Simulations predicted population growth within temperature between 13.9 and 33.4 °C, revealing a maximum finite rate of population increase (λ = 1.163), with a generation time of 33.3 days at 26.4 °C. Predicted species performance agreed well when compared against observed life tables and published data. The process-based physiological model presented here for B. tabaci MEAM1 should prove useful to predict the potential spatial distribution of the species based on temperature and to adjust pest control measures taking different population growth potentials due to prevailing temperature regimes into account.

A model description of beta oscillations in the external globus pallidus.

The external globus pallidus (GPe), a subcortical nucleus located in the indirect pathway of the basal ganglia, is widely considered to have tight associations with abnormal beta oscillations (13-30 Hz) observed in Parkinson's disease (PD). Despite that many mechanisms have been put forward to explain the emergence of these beta oscillations, however, it is still unclear the functional contributions of the GPe, especially, whether the GPe itself can generate beta oscillations. To investigate the role played by the GPe in producing beta oscillations, we employ a well described firing rate model of the GPe neural population. Through extensive simulations, we find that the transmission delay within the GPe-GPe pathway contributes significantly to inducing beta oscillations, and the impacts of the time constant and connection strength of the GPe-GPe pathway on generating beta oscillations are non-negligible. Moreover, the GPe firing patterns can be significantly modulated by the time constant and connection strength of the GPe-GPe pathway, as well as the transmission delay within the GPe-GPe pathway. Interestingly, both increasing and decreasing the transmission delay can push the GPe firing pattern from beta oscillations to other firing patterns, including oscillation and non-oscillation firing patterns. These findings suggest that if the transmission delays within the GPe are at least 9.8 ms, beta oscillations can be produced originally in the GPe neural population, which also may be the origin of PD-related beta oscillations and should be regarded as a promising target for treatments for PD.

Microclimate investigation of vehicular traffic on the urban heat island through IoT-Based device.

Anthropogenic is defined as one of the influencing factors of the climatic phenomenon, called Urban Heat Island (UHI), in which urban areas have higher air temperatures than their rural surroundings. Analyzing the impact of anthropogenic factors, such as vehicular traffic, has implications for the potential benefits of health monitoring systems; however, the spatiotemporal impact of anthropogenic factors, as well as vehicle mobility, has not been thoroughly investigated. This study incorporates vehicle mobility data by leveraging two different sensors; fixed station sensor instruments designed to integrate with the Internet of Things (IoT), and the camera of an area traffic control system (ATCS) that uses CCTV visualization with object detection. Using object detection and time-based traffic volume analysis, we obtain the level of the queue rate (λ) to present the level of the traffic flow based on the average velocity of the vehicle flow. Based on the results, it showed that the average temperature in urban areas is higher than in suburban areas, and the severe traffic jams caused a significant increase in temperature, that is until 7 Celsius when the weather is sunny. In addition, the theoretical UHI (UHI T ) model developed in this study can be used to estimate the UHI which is influenced by the queue rate.

A new cure rate regression framework for bivariate data based on the Chen distribution.

The present study introduces a new multivariate mixture cure rate model based on the Chen probability distribution to model recurrent event data in the presence of cure fraction. In this context, we provide an alternative for the use of some usual modeling approaches as the semiparametric Cox proportional hazards model commonly used in lifetime data analysis, considering a new bivariate parametric model to be used in the data analysis of bivariate lifetime data assuming a mixture structure for the bivariate data in presence of covariates, censored data and cure fraction. Under a Bayesian setting, the proposed methodology was considered to analyze two real medical datasets from a retrospective cohort study related to leukemia and diabetic retinopathy diseases. The model validation process was addressed by using the Cox-Snell residuals, which allowed us to identify the suitability of the new proposed mixture cure rate model.

The optimal industrial carbon tax for China under carbon intensity constraints: a dynamic input-output optimization model.

To reduce carbon emissions, the Chinese government is considering introducing a differentiated industrial carbon tax on enterprises outside the carbon trading market in the future. An efficient carbon tax must consider not only how carbon taxes impact the current economy but also how the size of the tax should be adjusted across time due to external changes. To calculate the optimal industrial carbon tax for China which is subject to certain constraints, this paper investigates the economic and environmental effects of four possible industrial carbon tax rate models under carbon intensity constraints from 2021 to 2030 by a dynamic input-output optimization model. The results show that the dynamic tax rate model leads to larger fluctuations in GDP growth than the other tax models, with a low initial tax rate in the beginning and a high tax rate exceeding ¥180/t in 2030. Second, a large quantity of capital stock is distributed across the energy-intensive industries, which leads the existing capital investment structure to be path-dependent. This offsets the performance of carbon taxes. Third, indirect energy-intensive industries such as construction and transport are insensitive to the industrial carbon tax. Finally, comparing the impacts of the four tax rate models, the optimal industrial carbon tax for China is found to be a fixed differentiated tax rate, in which energy-intensive sectors are taxed ¥75/t and low-carbon sectors are taxed ¥50/t.

Construction of a photosynthetic rate prediction model for greenhouse strawberries with distributed regulation of light environment.

In winter and spring, for greenhouses with larger areas and stereoscopic cultivation, distributed light environment regulation based on photosynthetic rate prediction model can better ensure good crop growth. In this paper, strawberries at flowering-fruit stage were used as the test crop, and the LI-6800 portable photosynthesis system was used to control the leaf chamber environment and obtain sample data by nested photosynthetic rate combination experiments under temperature, light and CO2 concentration conditions to study the photosynthetic rate prediction model construction method. For a small-sample, nonlinear real experimental data set validated by grey relational analysis, a photosynthetic rate prediction model was developed based on Support vector regression (SVR), and the particle swarm algorithm (PSO) was used to search the influence of the empirical values of parameters, such as the penalty parameter C, accuracy ε and kernel constant g, on the model prediction performance. The modeling and prediction results show that the PSO-SVR method outperforms the commonly used algorithms such as MLR, BP, SVR and RF in terms of prediction performance and generalization on a small sample data set. The research in this paper achieves accurate prediction of photosynthetic rate of strawberry and lays the foundation for subsequent distributed regulation of greenhouse strawberry light environment.

On a new piecewise regression model with cure rate: Diagnostics and application to medical data.

In this article, we discuss an extension of the classical negative binomial cure rate model with piecewise exponential distribution of the time to event for concurrent causes, which enables the modeling of monotonic and non-monotonic hazard functions (ie, the shape of the hazard function is not assumed as in traditional parametric models). This approach produces a flexible cure rate model, depending on the choice of time partition. We discuss local influence on this negative binomial power piecewise exponential model. We report on Monte Carlo simulation studies and application of the model to real melanoma and leukemia datasets.