Stochastic Sensitivity Analysis for Models with Parameter Correlation and Model Approximation Method

The International Commission on Radiological Protection (ICRP) has developed the reference Human Respiratory Tract Model (HRTM), detailed in ICRP Publications 66 and 130, to estimate the deposition and clearance of inhaled radionuclides. These models utilize reference anatomical and physiological parameters for particle deposition (PD). Biokinetic models further estimate retention and excretion of internalized particulates, aiding the derivation of inhalation dose coefficients (DC). This study aimed to assess variability in deterministic131I biokinetic and dosimetry models through stochastic analysis using the updated HRTM from ICRP Publication 130. The complexities of the ICRP PD model were reconstructed into a new, independent computational model. Comparison with reference data for total PD fractions for reference worker, solely a nose breather, covering activity median aerodynamic diameters from 0.3μm to 20μm, showed a 1.04% relative and 0.7% absolute difference, demonstrating good agreement with ICRP deposition fractions. The deterministic DC module was reconstructed in Python and expanded for stochastic analysis, systematically expanding deposition components from HRTM and assigning probability distribution functions to uncertain parameters. These were integrated into an in-house stochastic radiological exposure dose calculator, utilizing latin hypercube sampling. A case of an occupational radionuclide intake was explored, in which biodistribution and committed effective DC (CEDC) were computed for131I type F, considering a lognormal particle size distribution with a median of 5μm. Results showed the published ICRP reference CEDC marginally exceeds the 75th percentile of observed samples, with log-gamma distribution as the best-fit probability distribution. A Random Forest regression model with SHapley Additive exPlanations was employed for sensitivity analysis to predict feature importance. The analysis identified the HRTM particle transport rates scaling factor, followed by the aerodynamic deposition efficiency in the alveolar interstitial region as the most impactful parameters. This study offers a unique stochastic approach on inhaled particulate metabolism, enhancing radiation consequence management, medical countermeasures, and dose reconstruction for epidemiological studies.

This study focuses on fatigue reliability in steel bridges, a critical concern due to increasing traffic loads. Employing the S-N curve method, a Stochastic Sensitivity Analysis (SSA) is conducted to assess the impact of input parameters. Miner’s rule and fracture mechanics are compared for fatigue assessment, considering uncertainties through stochastic sensitivity analysis. Material-related factors and the equivalent stress range are identified as pivotal contributors to fatigue reliability. The study emphasizes the importance of understanding influential parameters for improved design and predictive insights in structural behavior.

Sensitivity analysis based approximation models for day-to-day link flow evolution process

The large number of input factors involved in a sophisticated geotechnical computational model is a challenge in the concept of probabilistic analysis. In the context of model calibration and validation, conducting a sensitivity analysis is substantial as a first step. Sensitivity analysis techniques can determine the key factors which govern the system responses. In this paper, three commonly used sensitivity analysis methods are implemented on a sophisticated geotechnical problem. The computational model of a compressed air energy storage, mined in a rock salt formation, includes many input parameters, each with large amount of uncertainties. Sensitivity measures of different variables involved in the mechanical response of the cavern are computed by different global sensitivity methods, namely, Sobol/Saltelli, Random Balance Design, and Elementary Effect method. Since performing sensitivity analysis requires a large number of model evaluations, the concept of surrogate modelling is utilised to decrease the computational burden. In the following, the accuracy levels of various surrogate techniques are compared. In addition, a comparative study on the applied sensitivity analysis methods shows that the applied sensitivity analysis techniques provide identical parameter importance rankings, although some may also give more information about the system behaviour.

There is uncertainty in the results of any mathematical model due to different reasons. It is important to estimate this uncertainty. Sensitivity analysis is commonly used to estimate how the changes in the input parameters affect the solutions of the model. In this paper, we discuss different ways of performing local and global sensitivity analyses and apply them to two models: an epidemic model and a new myocardial infarction model, both based on ordinary differential equations. The first model is a simple model used to explain the ideas, while the second one shows how to apply them to a model with more state variables and parameters. We find that if the parameters are not accurately known, local sensitivity analysis can be misleading and that global sensitivity methods that sample the whole parameter space, varying all the values of the parameters at the same time, are the most reliable. We also show how the sensitivity analysis results can be used to determine the uncertainty in the results of the model. We present numerical simulations.

Oseltamivir is effective in the treatment of influenza. Utilisation in The Netherlands is limited, but increasing. To estimate the cost effectiveness of oseltamivir treatment (vs symptom relief only) for patients with influenza-like illness (ILI) who are at increased risk for serious complications of influenza. A cost-effectiveness analysis was used, building on a previously developed model (decision tree) that was applied for evaluating influenza vaccination and pandemic preparedness plans. Three patient subgroups were assessed (elderly patients [aged > or = 65 years] without chronic disease, elderly patients with chronic disease, and chronically ill, non-elderly patients). Inputs for the model were taken from various sources including a meta-analysis. A societal perspective was adopted and costs were expressed in euro per life-year gained (year 2003 values). Life-years lost were discounted at 4% in accordance with Dutch guidelines. Deterministic and probabilistic sensitivity analyses were employed to assess the robustness of the results. For chronically ill patients with ILI, visits to the GP for oseltamivir treatment were cost saving. For non-chronically ill elderly patients, incremental cost-effectiveness was estimated at 1759 euros per life-year gained. Cost savings and favourable cost effectiveness were robust in a deterministic and stochastic sensitivity analysis. Our model-based analysis suggests that at-risk people presenting with ILI to a GP could be offered oseltamivir at favourable cost effectiveness or even cost savings in the Dutch setting compared with symptom relief with analgesics only.

SummaryIn this study, a post optimization technique for a correction of inaccurate optimum obtained using first‐order reliability method (FORM) is proposed for accurate reliability‐based design optimization (RBDO). In the proposed method, RBDO using FORM is first performed, and then the proposed second‐order reliability method (SORM) is performed at the optimum obtained using FORM for more accurate reliability assessment and its sensitivity analysis. In the proposed SORM, the Hessian of a performance function is approximated by reusing derivatives information accumulated during previous RBDO iterations using FORM, indicating that additional functional evaluations are not required in the proposed SORM. The proposed SORM calculates a probability of failure and its first‐order and second‐order stochastic sensitivity by applying the importance sampling to a complete second‐order Taylor series of the performance function. The proposed post optimization constructs a second‐order Taylor expansion of the probability of failure using results of the proposed SORM. Because the constructed Taylor expansion is based on the reliability method more accurate than FORM, the corrected optimum using this Taylor expansion can satisfy the target reliability more accurately. In this way, the proposed method simultaneously achieves both efficiency of FORM and accuracy of SORM. Copyright © 2015 John Wiley & Sons, Ltd.

BackgroundThe effectiveness of specific regimens of adjuvant therapy for gastric cancer has not been verified by large clinical trials. Recently, several large trials attempted to verify the effectiveness of adjuvant therapy. The Adjuvant Chemotherapy Trial of TS-1 for Gastric Cancer in Japan, a randomized controlled trial of adjuvant S-1 therapy for resected gastric cancer, demonstrated significant improvement in overall and relapse-free survival, compared to surgery alone. To evaluate value for money of S-1 therapy, cost-effective analysis was carried out.MethodsThe analysis was carried out from a payer’s perspective. As an economic measure, cost per quality-adjusted life-year (QALY) gained was estimated. Overall survival was estimated by the Kaplan-Meier method, up to 5-year observation. Beyond this period, it was simulated by the modified Boag model. Utility score is derived from interviews with sampled patients using a time trade-off method. Costs were estimated from trial data during observation, while in the period beyond observation they were estimated using simulation results. To explore uncertainty of the results, qualitative and stochastic sensitivity analyses were done.ResultsAdjuvant S-1 therapy gained 1.24 QALYs per patient and increased costs by $3,722 per patient for over lifetime (3% discount rate for both effect and costs). The incremental cost-effectiveness ratio (95% confidence intervals) for over lifetime was estimated to be $3,016 ($1,441, $8,840) per QALY. The sensitivity analyses showed the robustness of these results.ConclusionAdjuvant S-1 therapy for curatively resected gastric cancer is likely cost-effective. This therapy can be accepted for wide use in Japan.

Sensitivity analysis of parametric uncertainties and modeling errors in computational-mechanics models by using a generalized probabilistic modeling approach

This paper reviews five related types of analysis, namely (i) sensitivity or what-if analysis, (ii) uncertainty or risk analysis, (iii) screening, (iv) validation, and (v) optimization. The main questions are: when should which type of analysis be applied; which statistical techniques may then be used? This paper claims that the proper sequence to follow in the evaluation of simulation models is as follows. 1) Validation, in which the availability of data on the real system determines which type of statistical technique to use for validation. 2) Screening: in the simulation‘s pilot phase the really important inputs can be identified through a novel technique, called sequential bifurcation, which uses aggregation and sequential experimentation. 3) Sensitivity analysis: the really important inputs should be subjected to a more detailed analysis, which includes interactions between these inputs; relevant statistical techniques are design of experiments (DOE) and regression analysis. 4) Uncertainty analysis: the important environmental inputs may have values that are not precisely known, so the uncertainties of the model outputs that result from the uncertainties in these model inputs should be quantified; relevant techniques are the Monte Carlo method and Latin hypercube sampling. 5) Optimization: the policy variables should be controlled; a relevant technique is Response Surface Methodology (RSM), which combines DOE, regression analysis, and steepest-ascent hill-climbing. The recommended sequence implies that sensitivity analysis procede uncertainty analysis. Several case studies for each phase are briefly discussed in this paper.

Determination of sensitivity gradient is a major prerequisite for structural optimization, reliability assessment, and parameter identification. As the conventional deterministic sensitivity analysis cannot provide complete information, stochastic analysis is needed to tackle the uncertainties in structural parameters. This study focuses on the utility of the stochastic finite-element method for random response sensitivity analysis. The stochastic modeling of a random parameter is based on a commonly used 2D local averaging method generalized for a 3D case. The Choleski decomposition technique is then employed for digital simulation. The Neumann expansion based finite-element simulation method is extended for stochastic sensitivity analysis. This technique leads to a considerable saving of computational time. Example problems are used to compare the accuracy of this method to the direct Monte Carlo simulation and perturbation method in terms of varying stochasticity and efficiency in CPU time.

In this paper, a multi-objective optimization of a transonic axial fan to enhance aerodynamic stability has been conducted using three-dimensional Reynolds-Averaged Navier-Stokes equations, surrogate modeling and multi-objective genetic algorithm (MOGA). Hub radius and first rotor chord length of the axial fan were chosen as design variables for the optimization. Peak adiabatic efficiency of the axial fan and stall margin at 60% of the designed rotational speed, were used as objective functions. Latin Hypercube Sampling (LHS) method was used to select design points in the design space. The objective functions were formulated using the response surface approximation (RSA) model. Three LHS samples with different distributions of twelve design points were tested to study their effects on prediction accuracy of the RSA model and optimization results. MOGA with the RSA models based on the best LHS sample, was used to obtain the Pareto-optimal front. As a result of optimization, an improvement of 17.2% in the stall margin at 60% of the designed rotational speed and 2.96% in peak adiabatic efficiency were obtained compared to the reference design. It was also found that distribution of the design points generated by LHS affects the effectiveness of the surrogate-based optimization.

Collinearity-oriented sensitivity analysis for patterning energy factor significance in buildings

A comparison of uncertainty and sensitivity analysis results obtained with random and Latin hypercube sampling

The objective of this study was to evaluate the risk of feedlot finishing of steers (22.8 months) and young steers (15.2 months), using or not a correlation between the random input variables (data collected from 2004 to 2010) in the simulation of the Net Present Value (NPV) financial indicator. The animals were fed a diet containing roughage:concentrate ratio of 60:40 for 34 and 143 days, respectively, until they had reached a predetermined slaughter weight of 430 kg. For the NPV simulation, Latin Hypercube sampling was used, with 2000 interactions. The stochastic dominance analysis, test of differences between pairs of curves of cumulative distributions and sensitivity analysis were carried out. The NPV simulation using the correlation resulted in the best option for risk estimate. The confinement of young steers was the alternative of investment most viable than confinement of steers (NPV ≥ 0 of 80.4 vs. 62.3% in the simulation with correlation, respectively). Sensitivity analysis determined the following items had the greatest impact on the estimate of NPV: prices of fat and thin cattle, initial and final weights, diet costs, minimum rate of attractiveness and diet intake.