This study explores microgrids as small, independent electrical systems that reduce emissions, lower costs, and improve the efficiency and reliability of renewable energy sources (RES). It focuses on solving the optimal power flow (OPF) problem in isolated microgrids to minimize production costs, integrating variable RES like solar photovoltaic systems and wind turbines with a stable small hydropower plant. A novel physics-based Flow Direction Algorithm (FDA), inspired by the D8 hydrological model, is introduced, offering superior precision compared to bio-inspired metaheuristics. The FDA balances global and local search for accurate solutions. Monte Carlo simulation models uncertainties in wind speeds and solar irradiance. Validated on IEEE 33-bus, 69-bus, and 15-bus systems, the FDA outperforms algorithms like Whale Optimization, Ant Lion, Dung Beetle, and Walrus Optimization in efficiency and reliability, advancing microgrid performance.

Objectives Building upon prior systematic reviews and network meta-analyses, this study evaluated the cost-effectiveness of four commercial Chinese polyherbal preparations (CCPPs)—Tian Meng Oral Liquid/Capsules (TM), Shen-Qi-Wu-Wei-Zi Tablets (SQWWZ), Wu Ling Capsules (WL), and Bai-Le-Mian Capsules (BLM)—for treating primary insomnia. Comparative findings informed clinical decision-making and health policy formulation. Methods A cost-effectiveness analysis was conducted from a healthcare system perspective. A patient disease course model was developed using systematic literature search and network meta-analysis combined with drug pricing data. Intervention strategies (monotherapy or combination therapy) were simulated to assess per-capita costs and health outcomes. Incremental cost-effectiveness ratios were calculated and compared against the willingness-to-pay threshold. Deterministic sensitivity analysis (DSA), Monte Carlo simulations for probabilistic sensitivity analysis and cost-effectiveness acceptability curves were used to test the overall stability and acceptable probability of the evaluation results. Results At a WTP threshold of ¥89,358.00 per quality-adjusted life year (QALY), the combination of TM and benzodiazepines (BZDs) ranked highest in terms of cost-effectiveness, followed by WL, BLM, and SQWWZ. When the WTP threshold exceeded ¥5,897.63 per QALY, the probability that TM + BZDs was more cost-effective than WL increased. Likewise, when the WTP threshold was above ¥19,658.76 per QALY, the probability that BLM was more cost-effective than SQWWZ became greater. Conclusion Within the 60-day time horizon of this analysis, TM + BZDs demonstrated optimal cost-effectiveness for primary insomnia from a healthcare system perspective, followed by WL and BLM. Limitations in data sources constrain the generalizability of findings. Future studies adopt a societal perspective and incorporate individual-level data over longer time horizons to validate and extend current results through more comprehensive cost-utility evaluations. Furthermore, research should focus on Traditional Chinese medicine (TCM)-specific health utility scales and informing equity-focused reimbursement policies to fully capture the value of CCPPs, thereby ultimately optimizing healthcare access and resource allocation.

Abstract This study estimates the mean absorbed dose to the embryo of a pregnant caregiver assisting a child during an 18 F-FDG PET torso examination. Using the FLUKA Monte Carlo (MC) simulations, various clinical scenarios were modeled taking into account different ages of pediatric patients, caregiver’s positions and exposure scenarios. The accuracy and reliability of the simulation framework were validated by comparing its results with ICRP (Ann ICRP 38:7–96, 2008) and AAPM (Madsen et al. in Med Phys 33:4–15. 2006. https://doi.org/10.1118/1.2135911 ) data. Embryo dose estimates obtained using the FLUKA Monte Carlo code were also compared with those derived from ICRP Publication 116 (Ann ICRP 40(2–5):1–257, 2010). The embryo dose values obtained through the Monte Carlo simulations were consistently lower than the ICRP 116 values. Furthermore, these simulated doses were below the 1 mSv limit for the embryo/fetus over the entire pregnancy period (European Union in Off J Eur Union L 13:1–73, 2014) and the 3 mSv dose constraint for caregivers under 60 years old, as stipulated by Italian law (ITALIA in Gazz Uff Repub Ital Ser Gen, n. 201, 10 Aug. 2020, Suppl. ord. n. 29).

The goal of breast Intraoperative Electron Radiation Therapy (IOERT) is to deliver a uniform single fraction dose of 10-25 Gy to a surgically exposed volume of tissue at risk (tumor bed) while minimizing exposure to surrounding healthy tissue, with the patient under anesthesia. Currently, all the necessary information for the geometric and physical treatment arrangement is collected during the commissioning phase, when a preliminary dosimetric characterization of the accelerator is performed for clinical use in accordance with international protocols. During this process, output factors (OFs)-correction factors that account for dose differences relative to the reference condition-are measured. Therefore, since treatment plans rely exclusively on the OF and experimental measurements can be affected by large errors (on the order of 30%), a tuned Monte Carlo model provides a valuable tool for treatment validation. It is particularly valuable for evaluating quantities that are difficult to measure directly, such as dose variations resulting from shielding disk misalignment (to protect underlying healthy tissue) or out-of-field exposure to organs at risk in complex clinical scenarios (e.g., patients with implantable electronic devices or during pregnancy).

ABSTRACT Traditional control charts usually fail to perform well in the case of outliers, or when the mean and variability of a process vary at the same time in quality control. In this paper, a very powerful exponentially weighted moving average (EWMA) control chart using the robust coefficient of variation (CV) has been proposed to overcome these hurdles. Unlike approaches that require data transformation or adaptive tuning, the scale‐invariance of the robust CV‐statistic can be used to stabilize the proposed RCV‐EWMA chart, keeping it sensitive in a polluted data setting. Through extensive Monte Carlo simulations, the capabilities of the chart are analyzed in different conditions of contamination levels and shift level. The total key performance indicators, such as Average Run Length (ARL), Standard Deviation of Run Length (SDRL), and Median Run Length (MRL) are given. The findings show that the suggested chart has good in‐control characteristics (ARL = 370) and is a worthwhile chart to detect small‐to‐still shifts despite up to 25% contamination. Its applicability in practice is also confirmed by a real data application that demonstrates how the chart can determine the abnormalities in the processes and be resistant to outliers. The results place the RCV‐EWMA control chart as an effective and dependable modern tool of monitoring processes especially those in very noisy or highly variable conditions.

Influence Maximization(IM) is a fundamental problem in network science with applications in viral marketing, information dissemination, cybersecurity, and epidemiology. Classical IM solvers often trade off solution quality for runtime efficiency due to the NP-hardness of typical models such as Linear Threshold, Independent Cascade, and Triggering. Among these, the Linear Threshold model stands out by avoiding costly Monte Carlo simulations, enabling a more tractable Ising formulation. In this study, we propose a novel workflow for solving the Linear Threshold IM problem on directed acyclic graphs using a CMOS Ising solver through an Ising formulation. Our approach combines an integer linear programming-based Ising formulation with hardware-aware decomposition and preprocessing steps that adapt the model to the constraints of the hardware solver. We evaluate the efficiency of our approach under various coefficients and identify the optimized configuration. Experimental results show that our approach achieves superior solvability over some state-of-the-art IM solvers while maintaining competitive runtime and orders-of-magnitude lower energy consumption in both randomly generated and real-world benchmarks. These results demonstrate the potential of Ising solvers for energy-efficient IM applications.

Aminoglycoside pharmacokinetics is expected to change in premature infant. However, the PK profile of amikacin in Chinese premature infants has not been characterized. The aim of this study was to assess the safety and describe the pharmacokinetics properties of amikacin in Chinese premature infants. This was a two-center, retrospective, pharmacokinetic study. Phoenix NLME was used to construct a pharmacokinetics model. Monte Carlo simulations were performed to screen the optimal dosage regimen. A total of 54 amikacin concentrations from 23 patients were available for population pharmacokinetic analysis. The patients received an amikacin total daily dose (median(range)) of 14.32 (10.34-19.70) mg/kg. The distribution of Cmin (median(range)) was 4.07 (1.01-30.99)µg/mL, and Cmax (median(range)) was 17.45 (4.56-164.72) µg/mL. There were 14 patients achieved target Cmin, and 6 infants achieved Cmax. There were 3 cases occurred acute kidney injury, with Cmax and Cmin all exceeded the recommended range. A one-compartment model with first-order elimination best described the amikacin concentration-time data. The estimated typical values of clearance and volume of distribution for amikacin were 1.43L/h/70kg and 30.97L/70kg, respectively. Covariate analyses revealed that statistically significant relationships between amikacin clearance and weight, postmenstrual age and renal function, while there was a statistically significant relationship between volume of distribution and weight. Based on the model-based simulations, the initial recommend dosage regimens prior to therapeutic drug monitoring were suggested as 13mg/kg q24h, 12mg/kg q36h and q48h for serum creatinine between 15-22µmol/L; 23-36 and 37-60µmol/L, respectively. Weight, postmenstrual age and renal function have significant influence on the PK of amikacin in Chinese premature infants. The optimal dosage regimens might provide an alternative choice for premature infants in China in the therapy of amikacin.

We propose two novel logarithmic ratio-type estimators for the finite-population mean under simple random sampling without replacement (SRSWOR). The estimators integrate a logarithmic transformation of the auxiliary variable to stabilize variance, reduce the influence of outliers, and better capture nonlinear relationships between study and auxiliary variables. We derive closed-form expressions for first-order bias and mean squared error (MSE) and obtain analytic expressions for the optimal tuning constants by direct minimization of the approximate MSE. A comprehensive numerical study, comprising five real engineering datasets and extensive Monte-Carlo simulations from multivariate normal, log-normal and gamma populations, evaluates finite-sample behavior across a range of sample sizes and correlation structures. The proposed estimators consistently reduce MSE and deliver large percent-relative-efficiency (PRE) gains relative to the classical sample mean and common competitors (empirical PREs ≈ 283; simulation PREs up to ≈ 670), with especially large and stable improvements under skewed or heavy-tailed populations. Theoretical formulas and simulation evidence align closely, showing robustness to nonlinearity and skewness while retaining simple implementation for practitioners. Results are derived under SRSWOR using first-order approximations; extensions to higher-order corrections, stratified and two-phase designs, and uncertainty in auxiliary means are recommended for future work.

Paints consist of intricate combinations of solvents, additives, and pigments that provide the desired color, coverage, and durability, and pose a human health risk due to potentially toxic elements (PTEs), including lead (Pb), chromium (Cr), and cadmium (Cd), which accumulate in biological systems. This research innovatively assessed the non-carcinogenic and carcinogenic health risks posed by PTEs in Iranian decorative (ornamental) paints and emphasized the need for awareness raising and the development of control regulations. The PTEs concentrations were determined through wet acid digestion and analyzed through ICP-OES. The findings indicated that Pb concentrations ranged from 689.4 to 858.6mg/kg, Cr concentrations from 698 to 946.4mg/kg, and Cd concentrations between 0.24 and 0.37mg/kg, revealing that Pb and Cr values exceeded the permissible limits. The findings suggest that children exhibit a heightened susceptibility to these pollutants due to their unique behaviors and physiological traits. The ingestion route represented the primary contribution to the total hazard quotient, accounting for 96.8% in children and 58.4% in adults. The adults' hazard index (HI) for Pb and Cd was below the safe threshold of 1, whereas Cr surpassed this limit concerning non-carcinogenic risk. In children, the HI for both Pb and Cr surpassed the acceptable limit. Total Lifetime cancer risk (TLCR) values for both groups in Cr were higher than the acceptable range established by the USEPA, with relatively higher values observed in children. Among the three metals analyzed, Cr exhibited the most significant potential health risk, followed by Pb and Cd. Ingestion was identified as the primary route of exposure, while inhalation and dermal routes were less significant. To enhance the accuracy of exposure risk assessments for PTEs, a Monte Carlo simulation was utilized as a probabilistic algorithm to minimize uncertainties.

Long secondary periods (LSPs) occur in roughly one third of evolved stars, yet their origin remains uncertain. Two leading hypotheses are oscillatory convective modes and a binary companion enshrouded in dust. We investigate the LSP in the red giant RT Pav using multiwavelength interferometry to test these competing hypotheses. Observations of RT Pav were obtained with the VLTI instruments PIONIER, GRAVITY, and MATISSE spanning 1.5–5.0,μm, near the expected phase of maximum projected separation under a binary hypothesis. These data were complemented by photometric data and Gaia DR3 astrometry to constrain companion mass, orbital geometry, and photometric amplitude. Monte Carlo simulations evaluated expected interferometric signatures under both scenarios. Parametric models, including uniform-disk, limb-darkened, uniform-ellipse, binary, and oscillatory convective dipole representations, were fitted to squared-visibility and closure-phase data, informing image reconstructions. Gaia constrains any potential companion to a mass whose Roche-lobe volume is smaller than the minimum extent required by the observed photometric modulation, implying that any obscuring or scattering region capable of producing the observed variability would lie beyond the gravitationally bound zone of such a companion. Binary models often return the lowest ̧hi^2_ν, yet fitted positions are not consistent across wavelength, closure phases do not increase with wavelength as a dusty companion would predict, and we only find significant ($>3σ$) detections occurring in two of the four tested instrumental wavebands, which is inconsistent with a coherent companion signal. Furthermore simulations and theoretical estimates indicate that a companion with a ∼1,% flux ratio, at LSP-consistent separations should be consistently detectable (near or above our 3σ limits) for standard O-rich asymptotic giant branch (AGB) dust via scattering and/or thermal emission, which is not found. Conversely, an oscillatory convective dipole with a ∼200,K temperature contrast reproduces the H band morphology and the visible light-curve amplitude without violating Gaia or photometric constraints. Finally, significant short wavelength companion signals are completely removed when fitting the residuals of the best fit dipole model. Our interferometric snapshot of RT Pav, acquired near the phase of maximum projected separation under the binary hypothesis, supports oscillatory convective modes as the most physically consistent explanation for its LSP. A logical next step will be time-resolved spectro-interferometric monitoring across the LSP cycle.

Rural photovoltaic entrepreneurship in China faces critical challenges in aligning rapid technological advancements with lagging market responses, where 63% of technology adoption failures originate from mismatches between innovation maturity and regional policy adaptability. To address this, we propose a policy simulation-driven digital twins framework integrating three core innovations: (1) denoising diffusion models that reduce technology adoption prediction errors to <5% for mainstream photovoltaic technologies; (2) a dynamic policy sandbox identifying intervention thresholds through 10⁴ Monte Carlo simulations, revealing the ¥850 million subsidy ceiling that triggers 23% ROI decline; and (3) multi-agent coordination mechanisms optimizing resource allocation across 1,200 + entrepreneurial nodes. Empirical validation across 16 Anhui counties demonstrates the system’s effectiveness: 18% reduction in entrepreneurial failure rates through real-time policy adaptation, 12% annual growth in photovoltaic installed capacity, and ¥1.41 billion net policy-driven income. Crucially, our analysis establishes a 12% regional GDP threshold for subsidy intensity, beyond which land price inflation offsets entrepreneurial benefits. This framework provides actionable insights for synchronizing technological roadmaps with localized policy design in rural energy transitions.

Bacteriophage (phage) therapy holds great promise for treating antimicrobial-resistant infections. However, the pharmacokinetics (PK) of phage have been difficult to characterize due to a lack of standardized protocols for phage purification, labeling, and in vivo quantification. Here, we present robust methods for ultrapure phage preparation, as well as non-destructive, highly stable attachment of radio-iodide to phage using a well-described Sulfo-SHPP linker. We purified and radiolabeled the phage strains, PAML-31-1, OMKO1, and Luz24, lytic to drug-resistant Pseudomonas aeruginosa, for biodistribution assay in normal young adult CD-1 mice injected via intravenous injection. Groups of five mice were euthanized, and tissues/organs were removed for weighing and scintillation well counting of 125I activity. A physiologically based PK model was then constructed, focusing on compartments describing blood, lung, muscle, bone, liver, stomach, spleen, small intestines, large intestines, and kidney. Tissue partition coefficients (KP) were estimated for high-perfusion organs (lung and kidney) as 0.000138, GI organs (liver, spleen, and stomach) as 0.627, and all other organs as 0.220. Monte Carlo simulations predicted rapid elimination of phage in humans, with blood concentrations being <102 PFU/mL by 12 h, whereas simulated multi-dose regimens and continuous infusion regimens were predicted to have sustained concentrations. Our physiologically based PK model of phage represents the first rigorous preclinical assessment of phage PK utilizing contemporary pharmacometric approaches amenable to both preclinical and clinical study design.

This paper introduces the Topp–Leone Heavy-Tailed Odd Burr X-G (TL-HT-OBX-G) family of distributions (FOD), designed to model diverse data patterns. The new distribution is an infinite linear combination of the established exponentiated-G distributions. We used the established properties of the exponentiated-G distribution to infer the properties of the new FOD. The properties considered include the quantile function, moments and moment generating functions, probability-weighted moments, order statistics, stochastic orderings, and Rényi entropy. Parameter estimation is performed using multiple techniques, such as maximum likelihood, least squares, weighted least squares, Anderson–Darling, Cramér–von Mises, and Right-Tail Anderson–Darling. The maximum likelihood estimation method produced superior results in the Monte Carlo simulation studies. A special case of the developed model was applied to three real-world datasets. The model parameters were estimated using the maximum likelihood method. The selected special model was compared to other competing models, and goodness-of-fit was evaluated by the use of several goodness-of-fit statistics. The developed model fit the selected real-world datasets better than all the selected competing models. The new FOD provides a new framework for data modeling in health sciences and reliability datasets.

Multi-Function Radar(MFR) systems must concurrently perform search and tracking within strict time and energy limits, rendering resource allocation critical. This study applies Particle Swarm Optimization(PSO)-noted for its simplicity and global search capabilities-to optimize resource management in MFR operations. Three operational presets(SEARCH, BALANCED, and TRACK) were predefined to represent distinct operational modes. Monte Carlo simulations quantified each preset’s performance in search coverage, tracking retention, and time-budget compliance. Results demonstrated clear differentiation between presets, indicating that operators can seamlessly shift from search-oriented to tracking-oriented operations by merely adjusting preset parameters without redesigning system architecture. These findings provide a practical framework for enhancing flexibility in both design and operational phases. Future work will incorporate multi-objective optimization and adaptive parameter scheduling to further improve responsiveness to dynamic battlefield environments.

IntroductionSurvival time models are commonly employed in medicine and health sciences when analysing data. In these time-to-event analyses, it is often necessary to dichotomise variables that are metrically measured. One example could be to assign patients to different risk groups based on an occurring event. Besides univariable methods, multivariable approaches also exist for establishing cutpoints. Up to now, these multivariable approaches have hardly been investigated.MethodsUsing a Monte Carlo simulation study, we analysed eight multivariable methods from the literature to establish a cutpoint of a biomarker in the context of a semiparametric Cox regression model. The methods are the following: maximising the chi-square statistic, maximising the chi-square statistic with a split-sample approach, maximising the c-index using either the AddFor- or Genetic algorithm, maximising the concordance probability estimator (CPE) with the AddFor- or Genetic algorithm, and minimising the Akaike information criterion (AIC). We compared these methods with each other and in addition with the univariable log-rank minimum p-value approach. The simulation parameters analysed included the cutpoint’s distance from the biomarker’s median, sample size, total censoring, censoring before the end of the follow-up time (drop-outs), and the survival time distribution. Bias and empirical standard error were used as the primary performance measures. Furthermore, each method is illustrated using two practical data examples.ResultsAll analysed methods are biased towards the biomarker’s median. Multivariable methods that estimate the cutpoint by using the lowest AIC or the maximum of the chi-square statistic have the lowest bias and empirical standard error in most simulation scenarios. The difference in bias between the methods based on maximising the c-index or maximising the CPE is minimal. Regardless of the distribution used (Weibull, Gompertz, or exponential), the respective bias shows similar dependencies on the simulation parameters.ConclusionsMultivariable methods to estimate a biomarker’s cutpoint in survival time analyses using the Cox regression model may represent a good alternative to univariable methods. Our simulation has shown that methods maximising the chi-square statistic or minimising the AIC, respectively, perform better than the univariable method using the minimum p-value approach and outperform multivariable methods based on the c-index or CPE.

The safety criteria of a helicopter-launched missile is defined in MIL-STD-1289D as rotor disk clearance; 5-degree half angle cone between rotor blade and the outermost surface of the missile. Unlike an unguided rocket, missile's performance is not affected by the initial variation due the helicopter downwash. The safety condition, however, can be quite different according to the missile's initial dynamics. CFD(Computational Fluid Dynamics) is a conventional approach to analyze this kind of safety problem, but it may take several days or even months to solve a single case. For this safety problem, Monte-Carlo simulation method should be applied to consider various error conditions, which means CFD-based analysis is not applicable. In this paper we acquired CFD-based downwash database and applied the data on the missile's aerodynamic database. This method can check the safety conditions of 1,000 cases in a few hours and was validated by the launch test results.

For sustainable corrosion protection, this study introduces newly synthesized pyrazolyl-N-acetylthiocarbohydrazone (PTH) as a highly efficient and environmentally friendly inhibitor for carbon steel (CS) in an aggressive 1.0 M HCl solution. A comprehensive evaluation of PTH inhibition performance was conducted through chemical weight loss and electrochemical techniques, involving potentiodynamic polarization (PDP) and electrochemical impedance spectroscopy (EIS), which demonstrated a significant reduction in CS corrosion. PDP and EIS reinforced these findings, confirming the robust protective nature of PTH with an inhibition potency of 96%. The mitigation power of the PTH can be explained by its adsorption onto the CS surface, which followed the Langmuir adsorption model. The inhibitor exhibited exceptional stability and efficiency across varying temperature conditions and various immersion times using EIS, reinforcing its reliability in harsh acidic media, with a mitigation capacity of 97.16% at 50 °C and 97.3% after 24 h. The morphology of the CS surface was examined using SEM /EDX (Scanning Electron Microscopy), AFM (Atomic Force Microscopy), and XPS (X-ray Photoelectron Spectroscopy), exhibiting the PTH adsorption over CS, which was also proved and elucidated employing theoretical quantum investigations as density functional theory and Monte Carlo simulations.

Journal bearings play a critical role in many engineering systems, where their performance directly affects operational efficiency and reliability. This study investigates the effect of surface texturing on the thermo-hydrodynamic (THD) behavior of journal bearings with the goal of enhancing load-carrying capacity (LCC). Departing from conventional dimple-based textures, five continuous texture shapes are introduced and systematically analyzed using COMSOL Multiphysics. The thermo-hydrodynamic model is validated against the experimental data of Ferron, J., Frene, J. & Boncompain, R. A study of the thermohydrodynamic performance of a plain journal bearing comparison between theory and experiments. (1983). Optimization of texture parameters including height and distribution in both axial and circumferential directions is performed numerically using the Monte Carlo method. The study also evaluates the impact of texture placement in three distinct regions of the bearing surface. Results show that optimized continuous textures significantly outperform smooth bearings, achieving up to 144% increase in LCC. These findings offer new insights into texture design for high-performance journal bearings under thermal and hydrodynamic constraints.

Nature offers many intriguing examples of hierarchically self-assembled mesophases, such as lamellar, gyroid, hexagonal, and cholesteric phases. These structures are typically believed to emerge from complex, competing enthalpic interactions, as observed in block copolymers and amphiphilic surfactants. Here, using extensive Monte Carlo simulations, we demonstrate that even simple achiral hard particles with distorted tetrahedral shapes and purely excluded-volume interactions can spontaneously self-assemble into a diverse range of mesophases and liquid crystal phases, including the unexpected emergence of chiral structures. We attribute the formation of these phases to geometric frustration in the orientational ordering of neighboring particles, induced by their particle shape. The system resolves this frustration by coupling it with an energetically less favorable elastic deformation mode in the orientational ordering, such as twist or splay. We show that simple shape descriptors, such as anisotropy or biaxiality, predict the self-assembly behavior: rod-like particles stabilize cholesteric and twisted lamellar phases, plate-like particles form biaxial and splay nematic phases with randomly distributed splay domains as well as hexagonal cylindrical phases, while moderately anisotropic particles favor gyroid phases. This framework provides valuable insights for designing mesophases in supramolecular chemistry, liquid crystals, colloid science, and nanoparticle assembly.

BackgroundObservational studies have consistently reported large reductions in COVID-19 risk among vaccinated individuals. However, critics have raised concerns that unmeasured confounding may entirely explain these associations.MethodsWe combined the classical Cornfield inequality with a Monte Carlo sensitivity analysis to evaluate whether unmeasured confounding alone could plausibly account for the observed effectiveness of COVID-19 vaccines. The Cornfield inequality provides a lower bound on the strength of confounding required to explain a given association. The Monte Carlo analysis simulates uncertainty over possible confounder–exposure and confounder–outcome relationships by drawing from weakly informative prior distributions, allowing us to estimate the frequency with which such confounding would be sufficient.ResultsFor an observed risk ratio of 0.08—consistent with early estimates for the Pfizer-BioNTech vaccine—the confounder would need to be both highly imbalanced (e.g., 10 times more prevalent among vaccinated individuals) and strongly protective (e.g., reducing disease risk by 99%). Simulation results showed that, under the specified assumptions, fewer than 2% of draws satisfied this condition. Even in the more moderate case of a risk ratio of 0.25 (e.g., AstraZeneca), the proportion remained below 6%.ConclusionsOur findings suggest that while residual confounding may attenuate effect estimates, it is statistically and epidemiologically implausible that unmeasured confounding alone could fully account for the magnitude of observed vaccine effectiveness. This framework combines the falsificatory logic of Cornfield bounds with the flexibility of simulation-based sensitivity analysis, providing a transparent tool for evaluating confounding-based explanations in observational research.