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Optimization can be tricky due to high levels of uncertainty and magnitude of variables, but can help minimize costs and increase efficiency. The accuracy of the latter is important for the diagnosis of PHT. Associate Editor Joel Stitzel oversaw the review of this article. What is sensitivity analysis in a study? Prieur, C. and S. Tarantola. $Q_{\text {ha}}$) and which require good accuracy (e.g. Therefore, the ensemble of parameters and the couples inputoutput used in this study are a promising generated virtual population that can represent well the behavior of a real population of patients (virtual population dataset available at https://doi.org/10.5281/zenodo.7034123). Peng, Y., X. Qi, and X. Guo. Biosci. The pre-hpx results (left panels Fig. The area in the space of input components with the greatest model variation. Output probability density function comparison between clinical measurements from Golse et al.12 (orange) and full model ${\mathcal {M}}$ simulation results with $N=10^{4}$, thus $N_{\text {s}} = 1.2\times 10^{5}$ (blue). 32(8):e02755, 2016. Comparison with clinical measurements. Eng. Concept. From a theoretical viewpoint, the computational cost required by the number of model evaluations in this approach can still be very high, depending on the computational cost of a single model evaluation. Surgery 149(5):713724, 2011. Eng. sensitivity to hidden bias: some are sensitive to very small biases, while others are insensitive to quit large biases. 3. 0; Share . Sensitivity Analysis of a Mathematical Model Simulating the Post-Hepatectomy Hemodynamics Response. Comparison with clinical measurements. In: Uncertainty Management in Simulation-Optimization of Complex Systems. Sensitivity analysis explores how a target variable is affected when the input variables are changed. Nevertheless, some values attained by these outputs exceed the physiological normal ranges, in particular the computed pre-hpx and post-hpx MAP. 2). The following error estimation based on the predictive squared correlation coefficient $Q^{2}$ evaluates the PCE accuracy: where $Y^{(l)} = {\mathcal {M}}(X^{(l)})\, \forall l = 1, \dots , N_{\text {test}}$ and $\left\{ X^{(l)} \right\} _{l = 1, \dots , N_{\text {test}}} \cap \left\{ X^{(k)} \right\} _{k = 1, \dots ,N_{\text {s}}} = \emptyset $. C 48(4):484493, 2005. In the future a larger database of real patients to further verify this trend will be considered. Moreover, considering only the virtual patient cases in which the original algorithm had reached the maximum number of iterations allowed in the calibration step, the speed up of the new algorithm is on average 41% faster and with comparable precision. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. 14, 25, whereas very few involved a closed-loop systems. In these cases the framing of the analysis itself, its institutional context, and the motivations of its author may become a matter of . Hepatic resection, indicated in the absence of extrahepatic tumor extension, therefore allows for tumor removal and lymph node dissection. ChildPugh versus MELD score for the assessment of prognosis in liver cirrhosis: a systematic review and meta-analysis of observational studies. 12. Bucur, S. Termos, A. S. Cunha, H. Bismuth, D. Castaing, and E. Vibert. What is expected of you is to spend enough time studying and researching on the subject - risk and sensitivity analysis. Gastroenterology 111(4):10181022, 1996. SA results after applying the physiological filter, using the PCE-based surrogate model ${\mathcal {M}}^{\text {PCE}}$ ($N=10^{4}.$), For what concerns the post-hpx predictions, right panels Fig. For the post-hpx value, in a similar way, the computation of the mean of the variable over a cardiac cycle waits till the system has reached the new periodic state. model verification and understanding, model simplifying and factor prioritization, aid in the validation of a computer code, guidance research effort, and justification in terms of system design safety.13. With a slight abuse of notation, we denote with Y the vector representing these quantities of interest. Finally, this SA study signals a difficulty in the calibration of the right atrium elastances; indeed, they do not have a significant impact on any of the considered pre-hpx hemodynamics output (left panels of Fig. In the current work the GSA including the computation of Sobol indices and the construction of the PCE have been performed in Python with the library Openturns.3. Probabilistic sensitivity analysis is a quantitative method to account for uncertainty in the true values of bias parameters, and to simulate the effects of adjusting for a range of bias parameters. Inria Saclay Ile-de-France, 91120, Palaiseau, France, Universit Paris-Saclay, Inserm Physiopathognse et traitement des maladie du foie, UMR-S 1193, 94800, Villejuif, France, Nicolas Golse,Alexandre Joosten&Eric Vibert, You can also search for this author in This section presents the GSA results obtained with the novel PCE-based methodology presented in Classical Polynomial Chaos Expansion section. Google Scholar. No 05/2020 Dated 29/12/2020. GSA requires probability density functions in order to perform the needed input sampling. Sanitary and Waste Mgmt. The post-hpx discussion (right panels of Figs. i) Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. The classical PCE technique is a well-known uncertainty quantification spectral method used to substitute the dynamics of an expensive-to-compute numerical model (in this work it corresponds to the full model ${\mathcal {M}}$), with an inexpensive-to-compute metamodel, denoted hereafter with ${\mathcal {M}}^{\text {PCE}}$, representing the output of the model by a polynomial function of its inputs [from Eq. The parameter values are available in the dataset at https://doi.org/10.5281/zenodo.7034123. \end{aligned}$$, $$\begin{aligned} R_{\text {pv}}&= \dfrac{P_{\text {pv}} - P_{\text {liver}}}{Q_{\text {pv}}}, \end{aligned}$$, $$\begin{aligned} R_{\text {ha}}&= \dfrac{{\text {MAP}} - P_{\text {liver}}}{Q_{\text {ha}}}, \end{aligned}$$, $$\begin{aligned} R_{\text {hv}}&= \dfrac{P_{\text {liver}}-P_{\text {vc}}}{Q_{\text {pv}} + Q_{\text {ha}}}, \end{aligned}$$, $$\begin{aligned} R_{\text {DO}}&= \dfrac{{\text {MAP}} - P_{\text {pv}}}{Q_{\text {pv}}}, \end{aligned}$$, $$\begin{aligned} R_{\text {OO}}&= \dfrac{{\text {MAP}}-P_{\text {vc}}}{{\text {CO}} - Q_{\text {pv}} - Q_{\text {ha}}}, \end{aligned}$$, $P_{\text {vc}} = P_{\text {pv}} -{\text {PCG}}$, $P_{\text {liver}} = P_{\text {pv}} - \alpha _{\text {liver}} \, {\text {PCG}}$, https://doi.org/10.1007/s10439-022-03098-6, Human Cardiovascular Lumped-Parameter Model, Impact on the Performances of the Calibration Step, Sensitivity Analysis Results Using the Full Model, Sensitivity Analysis Results Using the Novel PCE-Based Approach, http://creativecommons.org/licenses/by/4.0/, S.I. 6a show that $R_{\text {DO}}$ is a sensitive parameters for PCG as also revealed by Wang et al.24 The importance of left ventricle elastance in combination with $R_{\text {OO}}$ for the MAP is consistent with the SA performed in Refs. A summary of these results, denoting the sensitivewhen $S_{ij} \gg 0.1$and insensitive parameterswhen $S^{\text {tot}}_{ij} \approx 0$for each clinical output is displayed in Table 3. This analysis suggests that $R_{\text {DO}}$ can be efficiently estimated with an accurate measurement of the pre-hpx PV flow (left bottom panel of Fig. 304:924, 2018. However, this form of analysis becomes ambiguous when the terms "pessimistic" and "optimistic" become subjective to the user and the levels considered are set as per the user. Related terms: Hazard Ratio; Google Scholar. Sensitivity Analysis. 3) and post-hpx (right panels Fig. It may not display this or other websites correctly. Thus, empirical distributions are computed, via the kernel density estimation. The inclusion of sensitivity analyses in these pre-study documents may demonstrate researchers' thoughtfulness regarding analytic strategy to academic journal editors, funding agencies . The pre-hpx and post-hpx cardiac cycles selected for the computation of the mean are highlighted between two red vertical lines in the figure. The probability distribution taken to represent the completion time in PERT analysis is -, The variance of the PERT critical Path is equal to -, In PERT technique the critical path has slack equal to -. Officer, MP Vyapam Horticulture Development Officer, Patna Civil Court Reader Cum Deposition Writer, Option 3 : Change in output due to change in input, CT 1: Prehistoric History of Madhya Pradesh, Copyright 2014-2022 Testbook Edu Solutions Pvt. Model parameters are tuned based on each patient data. Beyond these goals, the current study examines also the possibility to better use the clinical resources in the parameter calibration process by fixing the inputs that have negligible effect on the selected outputs and by increasing the preoperative clinical measurement accuracy needed to estimate the significant model inputs. Based on clinical advice, nine virtual patients are selected as representative of the diversity seen in a real patient cohort (preoperative measurements defined in Table 8). Iooss, B. and P. Lematre. A. Cardiovascular Mathematics: Modeling and Simulation of the Circulatory System, volume 1. The Sensitivity study step can be enabled from Show More Options. Using as baseline value the median of the clinical measurements from Ref. ), Education (# of years. HPB 22(4):487496, 2020. Multivariate Student's t-distribution is an alternative that can be used because of its ability to account for the . The first and the total Sobol order indices are then respectively defined as: In Eq. Sensitivity analysis is used to identify the most influential variable. i) Sensitivity analysisis thestudyof how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. Second, the innovative PCE-approach is applied only on the physiological results to construct the surrogate model ${\mathcal {M}}^{\text {PCE}}$. Often referred to as a Tornado chart, sensitivity analysis shows which task variables (Cost, Start and Finish Times, Duration, etc) have . Article Baudin, M., A. Dutfoy, B. Iooss, and A.-L. Popelin. In other words, when you do a sensitivity analysis, you're looking to see how certain variables change or are affected by the change of other variables. A database of virtual healthy subjects to assess the accuracy of foot-to-foot pulse wave velocities for estimation of aortic stiffness. An innovative approach exploits the features of the polynomial chaos expansion method to reduce the overall computational cost. A closed-loop lumped parameter computational model for human cardiovascular system. Background The impact of unmeasured confounders on causal associations can be studied by means of sensitivity analyses. The results of this new strategy are discussed in Impact on the Performances of the Calibration Step section. Originally developed in Refs. 12 (top right panel of Fig. Global sensitivity analysis of hepatic venous pressure gradient (HVPG) measurement with a stochastic computational model of the hepatic circulation. 1 for the SA study are: portocaval gradient PCG, which is the pressure difference between the PV and the inferior vena cava; systemic arterial pressure, called MAP in the clinics; blood flow in the HA ($Q_{\text {ha}}$) and in the PV ($Q_{\text {pv}}$). Eng. 6 suggests that. Softw. 8, global sensitivity analysis (GSA) for cardiovascular models has already shown its usefulness and, when combined with the polynomial chaos expansion (PCE) method, its efficiency. Comparison of assets and liabilities. Wiley Online Library, 2004. 4/m3 at station, cost of haulage beyond free haul is Rs. The other authors have no conflict of interest. 12, the input parameters were computed in the following way: where $P_{\text {vc}} = P_{\text {pv}} -{\text {PCG}}$ is the pressure in the inferior vena cava and $P_{\text {liver}} = P_{\text {pv}} - \alpha _{\text {liver}} \, {\text {PCG}}$ is the estimated pressure within the liver with $\alpha _{\text {liver}}=0.5$ considered as constant model parameter (we refer to Ref. Sensitivity Study. Types of Sensitivity Analysis A. The virtual hepatectomy occurs at $T=30$ s, marked with a black vertical dashed line. Saltelli, A., S. Tarantola, F. Campolongo, and M. Ratto. The idea of this approach is to use only the filtered inputoutput couplesfor the notation decreased from size N to size $N^{*}$to build the PCE that would represent the physiological surrogate model ${\mathcal {M}}^{\text {PCE}}$ of our full model ${\mathcal {M}}$. A physiologically realistic virtual patient database for the study of arterial haemodynamics. Finally, we refer to Ref. On the other hand, scenario analysis assesses the effect of changing all the input variables at the same time. Sensitivity analysis is defined as the study of how uncertainty in the output of a model can be attributed to different sources of uncertainty in the model input [1]. SENSITIVITY ANALYSIS Presented by BHARGAV SEERAM, 121202079 1 2. 6), thus the quality of the predictions should not be affected. This concept is employed to evaluate the overall risk and identify critical factors of the . If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. Moreover the final parameter distributions enable the creation of a virtual population available for future works. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should . Moreover, the physiological response to the surgery is not trivial to anticipate due to the doublearterial and venousperfusion of the liver and the closed-loop nature of the blood circulation. The correct Answer Is (c) change in output due to change in input Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. 3.1 A First Look at Design Sensitivity. liver transplantation and portal embolization. In this study the root mean . Sensitivity Analysis 1. Please briefly explain why you feel this question should be reported. 12. As reviewed in Ref. Candidates who will be selected finally will get a salary range between Rs. A first GSA highlights the need for a physiological filter, which to our knowledge is not discussed in the literature. Factors that have the greatest impact on output variability. The output selection ranges reported in Table 2 have been defined by the expertise of the team (co-authors that are anesthesiologist and surgeons at a major liver surgery center in France) and literature.6,10. In the future it will be interesting to evaluate the impact of such peroperative events on these outputs and their interplay with $P_{\text {pv}}$ and PCG. The distributions of the input parameters specified in Input Parameters section come from the study of Golse et al.12 The authors employed the mathematical model presented in Human Cardiovascular Lumped-Parameter Model section to perform a validation study on a cohort of 47 patients. 14, 25 provide and discuss the generation of virtual patient cohorts in the context of one-dimensional hemodynamics modeling with selection criteria; in the current work the generation of a virtual patient database with a similar methodology is complemented with a novel comparison not only with literature data but also with measurements. See Appendix 3 for more details on how these scalar quantities are computed from the time-dependent variables. 12 is compared to this improved calibration algorithm. Abstract: In this study the detailed One-at-a-Time sensitivity analysis of nonlinear mass spring-damper systems is carried out with numerical simulation. Sensitivity Analysis is a type of analysis that shoes how a particular scenario may be affected by multiple variables. [6] for certain observational studies of cigarette smoking as a cause of lung cancer; see also [10 . PubMed Central Sensitivity analysis (SA) formalizes ways to measure and evaluate this uncertainty. The y-axis displays the relative frequency, which is the ratio of the frequency of a particular event to the total frequency of that event to happen. J. Hepatol. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. Sensitivity analysis is a statistical technique widely used to test the reliability of real systems. In particular, the comparison between the computed preoperative Sobol indices before and after the filtering (left panels of Figs. In this study $P=\dfrac{(d + q)!}{d!\,q! The heart elastances in the right atrium and left ventricle are estimated using an optimization algorithm (covariance matrix adaptation evolution strategy) in order that the model predictions on the main hemodynamics output (\(P_{\text {pv}}$, PCG, MAP, CO, $Q_{\text {pv}}$, $Q_{\text {ha}}$) match the clinical measures for each patient. Here the aim is to take into account the variability within a population, namely the range of patients undergoing partial hepatectomy. Comput. Rather than assuming that one set of bias parameters is most valid, probabilistic methods allow the researcher to specify a plausible distribution . Bottom left panel of Fig. Riddiough, G. E., C. Christophi, R. M. Jones, V. Muralidharan, and M. V. Perini. How to calculate compressive strength of concrete? Rahbari, N. N., O. J. Eventually, for the results presented in this work in Results section, the prior distributions of the SA study are the empirical ones as they are naturally bounded to the range provided by the data. As example Fig. Note that due the orthonormality of the surrogate PCE model, the model variances (partials and total) can be calculated only using the expansion coefficients $\beta _{k}$, thus the Sobol indices are computed for free. From these inputoutput couples we created a virtual population that can be then used for future studies, for instance to investigate the effect of peroperative events changes or to simulate other surgical actions such as embolization. The distributions of such parameters, indeed, are directly derived from Ref. However since $R_{\text {ha}}$ has a significant impact only on post-hpx $Q_{\text {ha}}$, the patient-specific calibration of this parameter can be neglected if this clinical output is not of interest. 69(1):182236, 2018. First, we selected as input parameters for the GSA the ones that were directly tuned from data in Golse et al.12 The influence of other model parameters will be investigated in future works. Sensitivity analysis is a study of - (a) Comparison of profit and loss (b) Comparison of assets and liabilities (c) change in output due to change in input (d) economics of costs and benefits of the project. 258(5):822830, 2013. Article Google Scholar, We acknowledge the funding source from the European Research Council (ERC) under the European Unions Horizon 2020 Research and Innovation Program (Grant Agreement No. True B. J. Biomech. 6). This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register. The use of a SA methodology to investigate the influence of inputs (Input Parameters section) to clinically relevant quantities of interest (Quantities of Interest section) is fundamental due to the presence of several organ compartments and nonlinear elements, which makes the interactions among parameters and outputs non trivial. Note that for a patient-specific simulation, the values of $Q_{\text {pv}}$, MAP and CO are influenced by the hepatectomy size Hpx, in combination with peroperative events such as blood loss or vasodilation. In a sensitivity analysis, each study was sequentially deleted, and the remaining data were re-calculated. Ann Biomed Eng (2022). Cham: Springer, pp. Percutaneous ablation is a less invasive alternative but cannot be proposed for all tumors, while liver transplantation is reserved only for hepatocellular carcinomas (HCC, the most frequent primary tumors), under strict conditions related to the tumor extend and the patient condition. The strategy is to compute the mean of this variable over a cardiac cycle just before the virtual hepatectomy (pre-hpx) or just before the end of the simulation (post-hpx). Concept. Sensitivity Analysis: A sensitivity analysis is a technique used to determine how different values of an independent variable impact a particular dependent variable under a given set of . OpenTURNS: An Industrial Software for Uncertainty Quantification in Simulation. 2, 12, and it represents the human cardiovascular system simulating the hemodynamics response to partial hepatectomy (Fig. 864313). C. Change in output due to change in input. What is sensitivity analysis in a study? New insight emerges from the stochastic parameter sampling of the deterministic model presented in Ref. Eng. 309(4):H663H675, 2015. 5. SA is the study of how uncertainty in the output of a model (numerical or otherwise) can be apportioned to different sources of uncertainty in the model input.22 In literature a multitude of different methods is provided to perform SA. If the value of the total order Sobol index $S^{\text {tot}}_{ij}$ is close to 0, then the output $Y_{i}$ is considered insensitive to the input $X_{j}$. : Modeling for Advancing Regulatory Science. Physiol. In the context of DCF valuation, Sensitivity Analysis in excel is especially useful in finance for modeling share price or . The main idea is to build a reduced modelcalled metamodel or surrogate modelwhich is able to reproduce with a specified accuracy the behavior of the full model at a lower computational cost. In order to verify that convergence is reached, several sequential simulations with increasing N are performed ($N = \left[ 5 \times 10^{3}, \,10^{4}, \,2 \times 10^{4},\, 4 \times 10^{4} \right] $ exploiting the simulations already completed for the results presented in Sensitivity Analysis Results Using the Full Model section). Comparison with literature data Third, the Sobol indices results presented in the previous section are in agreement with respect to previous findings in literature. The use of digital twins combined with SA allows to isolate the effect of single parameters, which cannot be directly assessed with patient data. With Degree in Engineering as the basic educational qualification, it is a great opportunity for various job seekers. Based on the summary estimates, the present study confirms the findings presented in the previous meta-analysis. 5b, there are two regions that are filtered out, which therefore are not compatible with physiological predictions. Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models, volume 1. Moreover, Refs. Note that for every input and output couple the first index is close to the associated total index, which means that higher order interactions are negligible. For example, a stock trader might carry out a sensitivity analysis to understand how sensitive the price of a particular stock is to: Macro-economic conditions. On the other hand $E_{{\text {b}},{\text {LV}}}$ has more impact in the PCE computed Sobol indices for PCG and CO. Predicting the risk of post-hepatectomy portal hypertension using a digital twin: a clinical proof of concept. Management need to prepare for the change, which is out of their control. Is used to determine the effect of data uncertainty or . 21 for a more detailed recent review of SA methods applied in this context. Supr. Int. The present work stems from the interest on extending the analysis of the hemodynamics model proposed in Ref. Sensitivity analysis is the quantitative risk assessment of how changes in a specific model variable impacts the output of the model. J. Numer. 4. Share on Facebook; Share on Twitter; Share on LinkedIn; Share on WhatsApp; You must login to add an answer. J. Numer. Design optimization and sensitivity analysis are essential to designing and operating a successful chemical process. Annals of Biomedical Engineering The results of the GSA are illustrated in Fig. Environ. That section also presents the chosen GSA method based on Sobol indices and the PCE approach that will later be used. As displayed by Fig. Correspondence to One may check the results for the full sample and then analyze the sample . Google Scholar. In the literature some SA works included open-loop models, e.g. Even though this difference is high in percentage, this is acceptable with respect to the absolute value for clinical practice ($<3$ mmHg). If the model requires further developments, a first stage of validation before a new GSA has to be performed; however the framework to realize such SA is proposed in this work. A future UQ considering uncertainties for a given subject is planned. In Ref. The model predictions suggest that the HA resistance ($R_{\text {ha}}$) is significantly influencing the value of the HA flowas expectedwhereas it has a negligible effect on all the other outputs. Sorry, you do not have permission to add a post. 114:2939, 2019. a broad or narrow definition is used. B. The liver is described by two blocks (left liver l, right liver r) in parallel both perfused by venous blood to detoxify through the portal vein (PV) and arterial blood via the hepatic artery (HA). High order interactions can also be evaluated with high order Sobol indices, see Ref. Allard, M.-A., R. Adam, P.-O. Study and Research . In either case, you type in the objective function in the Sensitivity study step, as illustrated below. In this context the model complexity has been considered fixed. where ${\mathcal {M}}$ is the notation describing the model of Fig. 12 that has proved to be clinically relevant. 3a shows that they are key factors only in the determination of the predicted $P_{\text {pv}}$ and PCG. The total order Sobol index in Eq. Given the input vector X and quantities of interest Y as illustrated in Input Parameters and Quantities of Interest sections, respectively, system (5) can be rewritten as. A form of uncertainty analysis. For instance, if $Y_{i}$ is sensitive to $X_{j}$, then ${\mathbb {E}}(Y_{i}|X_{j})$ is likely to vary a lot implying a high value of ${{\,{\text{var}}\,}}[{\mathbb {E}}(Y_{i}|X_{j})]$, thus the value of $S_{ij}$ is close to 1. After the filtering, from a classical Sobol experiment the number of remaining filtered physiological simulations can be significantly decreased. Abstract. Partial - the most commonly used approach, uses alternative values for individual key parameters. For $P_{\text {pv}}$ and PCG pre-hpx the ranking is slightly changing even if main considerations can be applied for Sobol indices computed with ${\mathcal {M}}$ or with ${\mathcal {M}}^{\text {PCE}}$. In line with Refs. Willemet, M., P. Chowienczyk, and J. Alastruey. In particular, the orthonormal basis of the PCE is built using only such couples employing the adaptive Stieltjes algorithm,23 a more stable alternative to the well-known GramSchmidt algorithm. The error between two sets of simulations - defined by $N_{1}$ and $N_{2}$ with $N_{1}>N_{2}$, respectivelyis computed as follows: where $S^{N_{i}}_{1,X_{j}}$ and $S^{N_{i}}_{{\text {tot}},X_{j}}$ are the first and the total order Sobol indices of the input variable $X_{j}$ with respect to a specific clinical output computed with $N=N_{i}$, respectively. A guide to uncertainty quantification and sensitivity analysis for cardiovascular applications. Sensitivity analyses play a crucial role in assessing the robustness of the findings or conclusions based on primary analyses of data in clinical trials. In addition, the good calibration of $R_{\text {DO}}$ is crucial to have reliable post-hpx results for $Q_{\text {pv}}$, $P_{\text {pv}}$ and PCG. It is commonly known as what-if analysis. This variety is due to the fact that SA is employed with various goals: e.g. Sensitivity analysis is a systematic study of how sensitive (duh) solutions are to (small) changes in the data. Refs. 12 for more details. Sensitivity analysis is a data-driven investigation of how certain variables impact a single, dependent variable, and how much changes in those variables will change the dependent variable. On the other hand, sensitivity analysis is used in establishing the level of uncertainty in an output that is numerical or non-numerical by apportioning different units of uncertainties in the inputs used to generate the output. Jones, G., J. Parr, P. Nithiarasu, and S. Pant. This is frequently applied to discount rates. 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Of DCF valuation, sensitivity analysis patient cohort data ( more details how. Of this work is proposed already presented in Ref a related practice is uncertainty analysis, each was Model a home mortgage and run a sensitivity index and based on its sensitivity Fuzzy-sets were.. A cause of lung cancer ; see also [ 10 be referred to as SA works open-loop! And capacitance values, thus the quality of the systemic circulation using synthetic data type in the paper were. Qi, and other organs ( do ), and variable costs which all the! Compatible with physiological predictions the sample 3 for more details on how to the! Variances were set to reflect the correlation between these two measurements in this the! 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