Estimates Of Model Parameters Research Articles

Inference for dependent complementary competing risks model from an inverted Kumaraswamy distribution under ranked set sampling

AbstractRanked set sampling (RSS) has been proved to be an efficient sampling design for parametric and nonparametric inference. This paper explores inference for a maximum RSS procedure with unequal samples (MRSSU) with multiple dependent failure causes. When the lifetimes of units are characterized by a proposed complementary competing risks model, classical likelihood and Bayesian approaches are discussed for parameters and reliability estimation. Maximum likelihood estimators of model parameters and associated existence and uniqueness are established, and approximate confidence intervals are constructed using asymptotic theory and delta methods. With respect to general flexible priors, Bayesian estimates of interested quantities are also performed and a Monte Carlo sampling algorithm is proposed for complex posterior computation. Additionally, when extra historical information between the competing risks parameters is available, likelihood and Bayesian estimation are also studied under an order restriction case. Different methods are compared based on extensive simulation studies, and another real data example is demonstrated for application propose.

Parameter estimation for fractional mixed fractional Brownian motion based on discrete observations

The object of investigation is the mixed fractional Brownian motion of the form ${X_{t}}=\kappa {B_{t}^{{H_{1}}}}+\sigma {B_{t}^{{H_{2}}}}$, driven by two independent fractional Brownian motions ${B_{1}^{H}}$ and ${B_{2}^{H}}$ with Hurst parameters ${H_{1}}\lt {H_{2}}$. Strongly consistent estimators of unknown model parameters ${({H_{1}},{H_{2}},{\kappa ^{2}},{\sigma ^{2}})^{\top }}$ are constructed based on the equidistant observations of a trajectory. Joint asymptotic normality of these estimators is proved for $0\lt {H_{1}}\lt {H_{2}}\lt \frac{3}{4}$.

Targeting fidelity of pharmaceutical systems models by optimization of precision on parameter estimates

Quantitative models have gained momentum to drive the development of pharmaceutical processes. The assessment of the prediction fidelity of these models is key to provide interpretability of process phenomena and to enable decision-making. Evaluating parametric uncertainty is paramount when the focus is on systems models, which combine different sub-models together, and, thus, parameters related to previous units may strongly impact the prediction of one final output. A framework is proposed to assess reliability in model predictions, where the precision of parameter estimates is explicitly optimized to target pre-set tolerance requirements on process key performance indicators and product critical quality attributes. A direct compression systems model for the manufacturing of oral solid dosage products is used as a case study. Results show that the proposed methodology is effective at guaranteeing the target model fidelity and at quantifying the maximum acceptable uncertainty in the estimates of model parameters.

Integrated L1 adaptive cartesian PD control for robotic loco-manipulation

This paper presents an integrated framework of L1 adaptive control and Cartesian PD control that overcomes the inherent limitations of the latter controller in tracking end effector position for loco-manipulation tasks. In a simplified system, this work represented the loco-manipulation problem with the Cartesian space dynamics of the end effector object, capturing the dominating parts of the dynamics in linear terms. The unmodeled nonlinear dynamics, along with other model uncertainties and external disturbances, are accounted for by the L1 adaptive controller, taking the Cartesian PD input as a component of the control law to resemble its behavior for the desired system dynamics modeled in the state predictor of the L1 adaptive controller. Through simulation results of various combinations of model perturbations and external disturbances, we show that this integrated framework can achieve similar tracking performances of the end effector and object without the need to re-tune controller parameters. This work demonstrated the mitigation of effects from system uncertainties with model perturbation of up to 100% higher than expected mass and up to 15N of sinusoidal external disturbances, with higher disturbance rejection possible through designing for more conservative estimates of unknown model parameters. Combined with the low computational cost of this framework, the improvement in state command tracking gives rise to potential implementation on robotic systems controlled with linear optimization formulations.

A methodology of phenotyping ICU patients from EHR data: High-fidelity, personalized, and interpretable phenotypes estimation

Objective:Computing phenotypes that provide high-fidelity, time-dependent characterizations and yield personalized interpretations is challenging, especially given the complexity of physiological and healthcare systems and clinical data quality. This paper develops a methodological pipeline to estimate unmeasured physiological parameters and produce high-fidelity, personalized phenotypes anchored to physiological mechanics from electronic health record (EHR). Methods:A methodological phenotyping pipeline is developed that computes new phenotypes defined with unmeasurable computational biomarkers quantifying specific physiological properties in real time. Working within the inverse problem framework, this pipeline is applied to the glucose-insulin system for ICU patients using data assimilation to estimate an established mathematical physiological model with stochastic optimization. This produces physiological model parameter vectors of clinically unmeasured endocrine properties, here insulin secretion, clearance, and resistance, estimated for individual patient. These physiological parameter vectors are used as inputs to unsupervised machine learning methods to produce phenotypic labels and discrete physiological phenotypes. These phenotypes are inherently interpretable because they are based on parametric physiological descriptors. To establish potential clinical utility, the computed phenotypes are evaluated with external EHR data for consistency and reliability and with clinician face validation. Results:The phenotype computation was performed on a cohort of 109 ICU patients who received no or short-acting insulin therapy, rendering continuous and discrete physiological phenotypes as specific computational biomarkers of unmeasured insulin secretion, clearance, and resistance on time windows of three days. Six, six, and five discrete phenotypes were found in the first, middle, and last three-day periods of ICU stays, respectively. Computed phenotypic labels were predictive with an average accuracy of 89%. External validation of discrete phenotypes showed coherence and consistency in clinically observable differences based on laboratory measurements and ICD 9/10 codes and clinical concordance from face validity. A particularly clinically impactful parameter, insulin secretion, had a concordance accuracy of 83%±27%. Conclusion:The new physiological phenotypes computed with individual patient ICU data and defined by estimates of mechanistic model parameters have high physiological fidelity, are continuous, time-specific, personalized, interpretable, and predictive. This methodology is generalizable to other clinical and physiological settings and opens the door for discovering deeper physiological information to personalize medical care.

Pharmacodynamic Age Structured Population Model For Cell Trafficking

ObjectivesCell trafficking encompasses movement of the immune system cells (e.g., granulocytes, lymphocytes) between the blood and the extravascular tissues (e.g., lymph nodes). Corticosteroids are known to suppress cell trafficking. The age-structured cell population models introduce the transit time as a structure that allows one to quantify the distribution of times the immune cells spend in the blood and the extravascular tissues. The objective of this work is to develop an age-structured cell population model describing drug effects on cell trafficking and to implement the model in pharmacometric software to enable parameter estimation and simulations. MethodsWe adopted the well-known McKendrick age-structured population model to describe the age distributions in two cell populations: blood cells and cells in the extravascular space. The hazard of cell recirculation from the extravascular tissues was age dependent and described by the Weibull function with the shape ν and scale β parameters. The drug effect on cell trafficking was modeled as the product of the Emax function of the drug plasma concentration and the Weibull hazard. The model was implemented in NONMEM 7.5.1. The model was applied to the basophil data in 34 healthy subjects who received a single intramuscular or oral dose of 6 mg dexamethasone (DEX). A recently published pharmacokinetic model was applied to describe DEX plasma concentration. Typical values of parameter estimates were further used to simulate the DEX effect of the basophil mean transit time in the extravascular tissues. ResultsSimulations of basophil time courses for varying ν demonstrated that the rebound in the blood count data following drug administration is only possible for ν >1. The estimates of model parameters were ν = 3.02, β = 0.00863 1/h, and IC50 = 7.47 ng/mL. The calculated baseline mean transit times of basophils in the blood 7.2 h and extravascular tissues 104.9 h agree with the values reported in the literature. ConclusionsWe introduced an age-structured population model to describe cell trafficking between the blood and extravascular tissues. The model was adopted to account for the inhibitory drug effect on the cell recirculation. We showed that the age structure is essential to explain the rebound observed in the blood count response to a single dose drug administration. The model was validated using the basophil responses to DEX treatment in healthy subjects.

23 The Utility of Global versus Domain-specific Neuropsychological Test Score Dispersion as Markers of Cognitive Decline

Objective:Higher baseline dispersion (intra-individual variability) across neuropsychological test scores at a single time-point has been associated with more rapid cognitive decline, onset of Mild Cognitive Impairment (MCI) and Alzheimer’s disease (AD), faster rates of hippocampal and entorhinal atrophy, and increased AD neuropathology. Comparison between predictions made from test score dispersion within a cognitive domain versus global, cross-domain dispersion is understudied. Global dispersion may be influenced by ability-and test-specific characteristics. This study examined the performance of global versus domain-specific dispersion metrics to identify which is most predictive of cognitive decline over time.Participants and Methods:Data for baseline and five follow-up visits of 308 participants with normal cognition (Mage=73.90, SD=8.12) were selected from the National Alzheimer’s Coordinating Center (NACC) Dataset. Participants were required to have no focal neurological deficits, or history of depression, stroke, or heart attack. Diagnoses and progression to MCI and/or dementia were determined at each visit through consensus conferences. Raw neuropsychological scores were standardized using NACC norms. Global baseline dispersion was defined as the intraindividual standard deviation (ISD) across the 10 scores in the NACC battery. Domain-specific dispersions were calculated by constructing composites and ISD was computed across tests sampling their respective domains (executive functioning/attention/processing speed [EFAS], language, and memory; see Table 1 for details on these tests). Higher values on each of these metrics reflect greater dispersion. Multinomial logistic regression model fit statistics and parameter estimates were compared across four different models (global, EFAS, Language, and Memory dispersion) covarying for age, years of education, sex, race, ethnicity, and ApoE4 status. Models were compared using the Likelihood Ratio Test (LRT) and the Akaike Information Criteria (AIC) of Models statistics.Results:Of the 308 participants, 70 (22.7%) progressed to MCI, and 82 (26.6%) progressed to dementia. Tables 1 and 2 show the results of the logistic regressions for the four models. All models fit the data well, with statistically significant predictions of conversion. Model 1 (global dispersion) showed a better fit than domain-specific models of dispersion per LRT and AIC values. Consistent with the results from mean differences between groups, parameter estimates showed that only global dispersion and EFAS dispersion significantly predicted conversion to dementia (when included with other covariates in models), with higher dispersion reflecting a greater risk of conversion.Conclusions:In this sample, baseline global and EFAS dispersion measures significantly predicted conversion to dementia. Although global dispersion was a stronger predictor of dementia progression, findings suggest that executive functioning performance may be driving this relationship. A single index of global variability, from the calculation of standard deviation across test scores, may be supplementary for clinicians when distinguishing individuals at risk for dementia progression. None of the models were predictive of conversion to MCI. Further research is required to examine cognitive variability differences among patients who progress to MCI and patient-specific factors that may relate to test score dispersion and its utility in predicting the progression of symptoms.

Investigating Highway–Rail Grade Crossing Inventory Data Quality’s Role in Crash Model Estimation and Crash Prediction

The highway–rail grade crossings (HRGCs) crash frequency models used in the US are based on the Federal Railroad Administration’s (FRA) database for highway–rail crossing inventory. Inaccuracies or missing values within this database directly impact the estimated parameters of the crash models and subsequent crash predictions. Utilizing a set of 560 HRGCs in Nebraska, this research demonstrates variations in crash predictions estimated by the FRA’s 2020 Accident Prediction (AP) model under two scenarios: firstly, employing the unchanged, original FRA HRGCs inventory dataset as the input, and secondly, utilizing a field-validated inventory dataset for the same 560 HRGCs as input to the FRA’s 2020 Accident Prediction (AP) model. The findings indicated a significant statistical disparity in the predictions made with the two input datasets. Furthermore, two new Zero-inflated Negative Binomial (ZINB) models were estimated by employing 5-year reported HRGCs crashes and the two inventory datasets for the 560 HRGCs. These models facilitated the comparison of model parameter estimates and estimated marginal values. The results indicated that errors and missing values in the original FRA HRGCs inventory dataset resulted in crash predictions that statistically differed from those made using the more accurate and complete (validated in the field) HRGCs inventory dataset. Furthermore, the crash prediction model estimated upon the corrected inventory data demonstrated enhanced prediction performance, as measured by the statistical fitness criteria. The findings emphasize the importance of collecting complete and accurate inventory data when developing HRGCs crash frequency models. This will enhance models’ precision, improve their predictive capabilities to aid in better resource allocation, and ultimately reduce HRGCs crashes.

Bayesian Estimation and Prediction for Inverse Power Maxwell Distribution with Applications to Tax Revenue and Health Care Data

This article discusses the problem of estimating the unknown model parameters as well as prediction of future observations from inverse power Maxwell distribution. The maximum likelihood method is applied for estimating the model parameters using Newton-Rapson iterative procedures. The existence and uniqueness of maximum likelihood estimates are established using Cauchy-Schwartz inequality. Approximate confidence intervals are constructed using Fisher information matrix. Using independent gamma informative priors, the Bayes estimates of unknown model parameters are obtained under squared error and Linex loss functions. Two approximation techniques namely: Lindley’s approximation and Metropolis-Hastings within Gibbs sampler algorithm have been employed to derive the Bayes estimators and also to construct the associate highest posterior density credible intervals. Based on the informative (observed) sample, Bayesian prediction, predictive density, and predictive intervals are derived for future observation and decision. The performance of proposed methods are evaluated though a Monte Carlo simulation experiment. Two real-life datasets related to tax revenue and heath are incorporated to show the practical utility of proposed methodology in real phenomenon.

Inference and optimal design of accelerated life test using the geometric process for power rayleigh distribution under time-censored data

In this paper, a new extension of the standard Rayleigh distribution called the Power Rayleigh distribution (PRD) is investigated for the accelerated life test (ALT) using the geometric process (GP) under Type-I censored data. Point estimates of the formulated model parameters are obtained via the likelihood estimation approach. In addition, interval estimates are obtained based on the asymptotic normality of the derived estimators. To evaluate the performance of the obtained estimates, a simulation study of 4, 5 and 6 levels of stress is conducted for ALT in different combinations of sample sizes and censored times. Simulation results indicated that point estimates are very close to their initial true values, have small relative errors, are robust and are efficient for estimating the model parameters. Similarly, the interval estimates have small lengths and their coverage probabilities are almost converging to their 95% nominated significance level. The estimation procedure is also improved by the approach of finding optimum values of the acceleration factor to have optimum values for the reliability function at the specified design stress level. This work confirms that PRD has the superiority to model the lifetimes in ALT using GP under any censoring scheme and can be effectively used in reliability and survival analysis.

A critical re-evaluation of the slope factor of the operational model of agonism: When to exponentiate operational efficacy

Agonist efficacy denoting the “strength” of agonist action is a cornerstone in the proper assessment of agonist selectivity and signalling bias. The simulation models are very accurate but complex and hard to fit experimental data. The parsimonious operational model of agonism (OMA) has become successful in the determination of agonist efficacies and ranking them. In 1983, Black and Leff introduced the slope factor to the OMA to make it more flexible and allow for fitting steep as well as flat concentration–response curves. First, we performed a functional analysis to indicate the potential pitfalls of the OMA. Namely, exponentiation of operational efficacy may break relationships among the OMA parameters. The fitting of the Black & Leff equation to the theoretical curves of several models of functional responses and the experimental data confirmed the fickleness of the exponentiation of operational efficacy affecting estimates of operational efficacy as well as other OMA parameters. In contrast, fitting The OMA based on the Hill equation to the same data led to better estimates of model parameters. In conclusion, Hill equation-based OMA should be preferred over the Black & Leff equation when functional-response curves differ in the slope factor. Otherwise, the Black & Leff equation should be used with extreme caution acknowledging potential pitfalls.

Calibrating a remote sensing evapotranspiration model using the Budyko framework

Remote sensing (RS) evapotranspiration (ET) models are commonly used to estimate ET at a large scale. These models often include spatially varying parameters that need to be determined. Typically, these parameters are either held as constants or obtained from a pre-specified lookup table, potentially introducing bias into ET estimates. This study aimed to evaluate the feasibility of calibrating a RS ET model using Budyko-derived mean annual ET. We applied this approach to calibrate the single parameter of the Penman-Monteith-Leuning (PML) model. Instead of using the default Budyko-Fu parameter ω (ω=2.6), we developed a data-driven model that relates the basin-calibrated ω and its primary controls. Subsequently, we mapped the spatial pattern of ω across China. The calibrated PML model was evaluated using flux observations from 12 ChinaFlux sites and water balance-based ET estimates from 80 basins in China. Results indicate that the Budyko-based calibration significantly improved the performance of the PML model at both site and basin scales compared to the uncalibrated model. This study highlights the potential of leveraging the Budyko framework to constrain the parameter estimates of RS ET models, thereby enhancing the accuracy of large-scale ET estimates.

A cost comparison of benralizumab, mepolizumab, and dupilumab in patients with severe asthma: A US third-party payer perspective.

BACKGROUND: Clinical trials and real-world evidence (RWE) studies of biologics have demonstrated reduced exacerbations, decreased use of oral corticosteroids (OCS), and improvements in daily symptoms and health-related quality of life in patients with severe eosinophilic asthma (SEA). OBJECTIVE: To compare direct health care costs associated with biologic use for the treatment of SEA from a US third-party payer perspective. METHODS: We developed a cost-minimization model to compare costs and cost offsets associated with 3 biologics-benralizumab, mepolizumab, and dupilumab-for 2- and 4-year periods. The model relied on longitudinal data from clinical trials to inform the primary (base case) analysis cost comparison and RWE study data, in a separate scenario, to compare costs in nonclinical trial settings. Primary model outcomes included exacerbations (including hospitalizations), OCS-dependent years (including associated complications), and total direct health care biologic costs. Results were calculated at the per patient and population level (per 1,000 patients). Sensitivity analyses with key model parameters were performed. RESULTS: Benralizumab had the lowest total biologic costs per patient for both the 2- and 4-year periods. Over 4 years, the marginal cost difference in total biologic costs per patient was $23,061 lower for benralizumab vs mepolizumab and $17,242 lower for benralizumab vs dupilumab. The 4-year population level analysis of benralizumab vs mepolizumab revealed $4.8 million in marginal cost offsets due to 582 fewer exacerbations and 153 fewer OCS-dependent years and a marginal total cost savings of $27.9 million per 1,000 patients for benralizumab. The 4-year population level analysis of benralizumab vs dupilumab revealed $2.3 million in marginal cost offsets due to 291 fewer exacerbations and 64 fewer OCS-dependent years and marginal total cost savings of $19.5 million per 1,000 patients for benralizumab. RWE data were available for a 2-year cost comparison scenario of benralizumab vs mepolizumab, which showed similar results to the base case analysis. Sensitivity analyses varying assumptions on key model parameter estimates confirmed results, with benralizumab having lower total direct health care costs in all scenarios tested, and showed that model results were most sensitive to changes in biologic costs and exacerbation reduction rates. CONCLUSIONS: Patients receiving benralizumab had higher nonbiologic cost offsets because of reductions in exacerbations and OCS-dependent years, leading to greater cost savings for third-party payers compared with patients receiving mepolizumab or dupilumab. Taken together with biologic costs, benralizumab presents greater savings in health care costs for payers than patients with SEA who use mepolizumab or dupilumab. DISCLOSURES: This study was funded by AstraZeneca (Cambridge, UK). Drs Xu, Chung, Genofre, and Katial are or were AstraZeneca employees at the time this research was conducted and may be shareholders of AstraZeneca. Ms Schaefer and Dr Szende are employees of Labcorp Drug Development, which received funding from AstraZeneca to perform this research.

Sustainable development of Ukraine as a combination of social, economic and environmental components: structural econometric model of three-pillar approach

The combination of the economic, social and environmental issues of the country-level development in the case of Ukraine requires modernization of the national economic system and permanent deep institutional reforms. These measures should be aimed at forming a diverse, competitive and socially oriented post-industrial economy capable of ensuring sustainable development. To ensure the improvement of the management of Ukraine’s sustainable development strategy, structural (simultaneous) model is proposed, based on three endogenous (namely GDP as economic variable, income per household as social variable and the expenses for the environmental protection as environmental variable) and seven exogenous variables. Such an approach makes it possible to investigate the interdependence between variables. Model parameters estimates were calculated with the two-step least squares method. A forecast of the development of the main indicators characterizing the economic, social and environmental components of development at the country level was also estimated. For Ukraine in 2021, according to the forecast based on the structural model, the economic and environmental components will have positive dynamics and rapid growth, while the social component will develop, but more stably and without rapid growth.

An EM algorithm for estimating the parameters of the skew generalized t-normal distribution with application to robust finite mixture modeling

The present article describes an EM-type algorithm for estimation of the skew generalized t-normal (SGTN) distribution. The family of SGTN distributions can provide certain types of flexibility such as heavy tails and high kurtosis. The complexity of the SGTN distribution is traced to the ratio of the t density and distribution function of a normal distribution in the likelihood equations. To cope with this problem, we develop a feasible ECME algorithm for computing maximum likelihood estimates of model parameters via a selection mechanism. The proposed approach provides a robust parameter estimation method for the finite mixture model. Standard errors for the parameter estimates can be obtained via a general information-based method. Experimental results on simulated data and one real data example demonstrate the efficacy and usefulness of the proposed methodology.

Testing Data Cloning as the Basis of an Estimator for the Stochastic Volatility in Mean Model

Developed as a refinement of stochastic volatility (SV) models, the stochastic volatility in mean (SVM) model incorporates the latent volatility as an explanatory variable in both the mean and variance equations. It, therefore, provides a way of assessing the relationship between returns and volatility, albeit at the expense of complicating the estimation process. This study introduces a Bayesian methodology that leverages data-cloning algorithms to obtain maximum likelihood estimates for SV and SVM model parameters. Adopting this Bayesian framework allows approximate maximum likelihood estimates to be attained without the need to maximize pseudo likelihood functions. The key contribution this paper makes is that it proposes an estimator for the SVM model, one that uses Bayesian algorithms to approximate the maximum likelihood estimate with great effect. Notably, the estimates it provides yield superior outcomes than those derived from the Markov chain Monte Carlo (MCMC) method in terms of standard errors, all while being unaffected by the selection of prior distributions.

Test-retest reliability of reinforcement learning parameters.

It has recently been suggested that parameter estimates of computational models can be used to understand individual differences at the process level. One area of research in which this approach, called computational phenotyping, has taken hold is computational psychiatry. One requirement for successful computational phenotyping is that behavior and parameters are stable over time. Surprisingly, the test-retest reliability of behavior and model parameters remains unknown for most experimental tasks and models. The present study seeks to close this gap by investigating the test-retest reliability of canonical reinforcement learning models in the context of two often-used learning paradigms: a two-armed bandit and a reversal learning task. We tested independent cohorts for the two tasks (N = 69 and N = 47) via an online testing platform with a between-test interval of five weeks. Whereas reliability was high for personality and cognitive measures (with ICCs ranging from .67 to .93), it was generally poor for the parameter estimates of the reinforcement learning models (with ICCs ranging from .02 to .52 for the bandit task and from .01 to .71 for the reversal learning task). Given that simulations indicated that our procedures could detect high test-retest reliability, this suggests that a significant proportion of the variability must be ascribed to the participants themselves. In support of that hypothesis, we show that mood (stress and happiness) can partly explain within-participant variability. Taken together, these results are critical for current practices in computational phenotyping and suggest that individual variability should be taken into account in the future development of the field.

Analysing the financial landscape of European households: Insights from panel data

This article makes a significant contribution to the existing body of research concerning the subjective evaluations of household financial conditions and the objective analysis of economic circumstances and savings potential within households. The study elucidates the intricate relationships between subjective assessments of household financial situations, broader economic conditions, price trends, and savings potential. Drawing upon data pertaining to households' self-assessments of their current and future financial outlook, this paper undertakes a comprehensive examination of disparities across several European nations. The initial cross-sectional survey study encompassed all member countries of the European Union and Great Britain. The study spanned a timeframe of 32 months, from January 2018 to August 2020, divided into two distinct sub-periods: one preceding the onset of the pandemic and the other during its occurrence. Employing panel models, this research identifies factors significantly influencing subjective evaluations of household financial well-being. The estimations of model parameters during the pandemic period revealed noteworthy trends: assessments of household finances exhibited considerably greater consistency than those observed in the pre-pandemic era. Across both sub-periods, the findings consistently underscored a significant and positive correlation between the evaluation of the overall economic situation within the country and the potential for savings and the subjective assessment of household financial conditions. However, the findings from the pandemic period failed to corroborate a substantial link between assessments of past and future price trends and their impact on household financial evaluations. Furthermore, the regression coefficients within the models describing future financial evaluations demonstrated a pronounced increase when considering the dependent variable as the financial assessment of the preceding year. Given that household opinions hold paramount importance as target variables for economic policies, the investigation into the ramifications of subjective evaluations of household financial situations remains particularly pertinent. These evaluations can exert both direct influence, such as on household welfare, and indirect effects by guiding the formulation of pertinent financial instruments by institutions within the financial sector.

Low-Order Mechanistic Models for Volumetric and Temporal Capnography: Development, Validation, and Application.

The airflow model's single "alveolar" compartment has compliance and inertance, and feeds a resistive unperfused airway comprising a laminar-flow region followed by a turbulent-mixing region. The gas-mixing model tracks mixing-region CO 2 concentration, which is fitted breath-by-breath to the measured capnogram, yielding estimates of model parameters that characterize the capnogram. For the 17 examined records (310 breaths) of airflow, airway pressure and Tcap from ventilated adult patients, the models fit closely (mean rmse 1% of end-tidal cŞoncentration on Vcap; 1.7% on Tcap). The associated parameters (4 for Vcap, 5 for Tcap) for each exhalation, and airflow parameters for the corresponding forced inhalation, are robustly estimated, and consonant with each other and literature values. The models also allow, using Tcap alone, estimation of the entire exhaled airflow waveform to within a scaling. This suggests new Tcap-based tests, analogous to spirometry but with normal breathing, for discriminating chronic obstructive pulmonary disease (COPD) from congestive heart failure (CHF). A version trained on 15 exhalations from each of 24 COPD/24 CHF Tcap records from one hospital, then tested 100 times with 15 random exhalations from each of 27 COPD/31 CHF Tcap records at another, gave mean accuracy 80.6% (stdev 2.1%). Another version, tested on 29 COPD/32 CHF, yielded AUROC 0.84. Our mechanistic models closely fit Tcap and Vcap measurements, and yield subject-specific parameter estimates. This can inform cardiorespiratory care.

Asymptotic Normality of Parameter Estimators for~Mixed Fractional Brownian Motion with Trend

We investigate the mixed fractional Brownian motion of the form Xt = θt+σWt +κBtH , driven by a standard Brownian motion W and a fractional Brownian motion B H with Hurst parameter H. We consider strongly consistent estimators of unknown model parameters (θ, H, σ, κ) based on the equidistant observations of a trajectory. Joint asymptotic normality of these estimators is proved for H ∈ (0, 12 ).