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PubMed2006

Adjoint sensitivity analysis for a three-dimensional photochemical model: implementation and method comparison.

Photochemical air pollution forms when emissions of nitrogen oxides (NO(x)) and volatile organic compounds (VOC) react in the atmosphere in the presence of sunlight. The goal of applying three-dimensional photochemical air quality models is usually to conduct sensitivity analysis: for example, to predict changes in an ozone response due to changes in NO(x) and VOC emissions or other model data. Forward sensitivity analysis methods are best suited to investigating sensitivities of many model responses to changes in a few inputs or parameters. Here we develop a continuous adjoint model and demonstrate an adjoint sensitivity analysis procedure that is well-suited to the complementary case of determining sensitivity of a small number of model responses to many parameters. Sensitivities generated using the adjoint method agree with those generated using other methods. Compared to the forward method, the adjoint method had large disk storage requirements but was more efficient in terms of computer processor time for receptor-based investigations focused on a single response at a specified site and time. The adjoint method also generates sensitivity apportionment fields, which reveal when and where model data are important to the target response.

Air Pollutants↗
PubMed2003

Sensitivity analysis techniques applied to a revised model of molybdenum biokinetics.

A revised model of molybdenum biokinetics in humans was recently developed on the basis of experimental data gathered in specific investigations conducted with stable tracers. The model can be used for radiation protection purposes, and it is also a suitable working tool for designing new investigations aimed at further improvements to the model. For the latter goal, a sensitivity analysis was performed in order to determine the most significant model parameters in relation to output measurements performed in studies of molybdenum metabolism. A typical sensitivity analysis approach was adopted, considering the effects in variation of model parameters on the time courses of model outputs such as urinary excretion and blood clearance. A recent new sensitivity technique was considered too, based on the calculation of the so-called generalised sensitivity functions. This combines the sensitivities of the model output with respect to model parameters (as in the typical sensitivity analysis method), with the sensitivities of parameter estimates with respect to changes in model outputs. The results obtained in this analysis suggests that data collected in the first 7 h are critical for the definition of the process of blood clearance and related parameters, whereas reliable information at later times is required for a proper characterisation of urinary excretion.

Body Burden↗
PubMed1994

The carbon budget of Canadian forests: a sensitivity analysis of changes in disturbance regimes, growth rates, and decomposition rates.

Ecosystem responses to climate changes will affect the exchange of carbon (C) with the atmosphere, thus providing feedback for future climate response. We have developed a C budget model of Canadian forests and forest sector activities and used sensitivity analysis runs with changes in productivity, decomposition, and disturbance regimes to assess the sensitivity of the Canadian forest sector C budget over the next century. The model operates on data derived from Canada's National Forest Biomass Inventory, from the Oak Ridge National Laboratory global soil C data base, and from Canadian data bases that document areas annually disturbed by fire, insects, and harvesting. It simulates the dynamics of biomass and soil C pools (including detritus and coarse woody debris) as they are affected by growth, decomposition, and disturbances. For the reference run of the model, we assumed unchanging climate and disturbance regimes. Under these conditions, total ecosystem C increased by 2 Gt C (2.3%) over the 100-year simulation period. In the sensitivity analysis, we explored the effects of changes in the area annually disturbed by fire and insect-induced stand mortality (-60 to +300%), growth rates (-10 to +20%), decomposition rates (-10 to +25%), and combined changes in growth and decomposition rates. In every model run, the change of total ecosystem C relative to the reference run was less than 10%. Combined changes to growth and decomposition rates yielded very small deviations from the results of the reference run (-0.8 to +1.2%). Because disturbance regime changes affect forest age-class structure as well as forest dynamics, they are expected to affect C budgets strongly. Total ecosystem C, however, is slightly more sensitive to changes in growth and decomposition parameters than to changes in disturbance regimes. Although the sensitivity analysis results suggest that C budgets are little affected by the range of parameter changes implemented here, we must emphasize that our sensitivity analyses do not account for potentially important processes, such as regeneration failure or the shifts in forest distribution.

Journal Article↗
PubMed2003

Sensitivity analysis of stoichiometric networks: an extension of metabolic control analysis to non-steady state trajectories.

A sensitivity analysis of general stoichiometric networks is considered. The results are presented as a generalization of Metabolic Control Analysis, which has been concerned primarily with system sensitivities at steady state. An expression for time-varying sensitivity coefficients is given and the Summation and Connectivity Theorems are generalized. The results are compared to previous treatments. The analysis is accompanied by a discussion of the computation of the sensitivity coefficients and an application to a model of phototransduction.

Animals↗
PubMed2005

Adaptive approach for nonlinear sensitivity analysis of reaction kinetics.

We present a unified approach for linear and nonlinear sensitivity analysis for models of reaction kinetics that are stated in terms of systems of ordinary differential equations (ODEs). The approach is based on the reformulation of the ODE problem as a density transport problem described by a Fokker-Planck equation. The resulting multidimensional partial differential equation is herein solved by extending the TRAIL algorithm originally introduced by Horenko and Weiser in the context of molecular dynamics (J. Comp. Chem. 2003, 24, 1921) and discussed it in comparison with Monte Carlo techniques. The extended TRAIL approach is fully adaptive and easily allows to study the influence of nonlinear dynamical effects. We illustrate the scheme in application to an enzyme-substrate model problem for sensitivity analysis w.r.t. to initial concentrations and parameter values.

Algorithms↗
PubMed2002

Sensitivity analysis for importance assessment.

We review briefly some examples that would support an extended role for quantitative sensitivity analysis in the context of model-based analysis (Section 1). We then review what features a quantitative sensitivity analysis needs to have to play such a role (Section 2). The methods that meet these requirements are described in Section 3; an example is provided in Section 4. Some pointers to further research are set out in Section 5.

Journal Article↗
PubMed2005

Probabilistic sensitivity analysis for NICE technology assessment: not an optional extra.

Recently the National Institute for Clinical Excellence (NICE) updated its methods guidance for technology assessment. One aspect of the new guidance is to require the use of probabilistic sensitivity analysis with all cost-effectiveness models submitted to the Institute. The purpose of this paper is to place the NICE guidance on dealing with uncertainty into a broader context of the requirements for decision making; to explain the general approach that was taken in its development; and to address each of the issues which have been raised in the debate about the role of probabilistic sensitivity analysis in general. The most appropriate starting point for developing guidance is to establish what is required for decision making. On the basis of these requirements, the methods and framework of analysis which can best meet these needs can then be identified. It will be argued that the guidance on dealing with uncertainty and, in particular, the requirement for probabilistic sensitivity analysis, is justified by the requirements of the type of decisions that NICE is asked to make. Given this foundation, the main issues and criticisms raised during and after the consultation process are reviewed. Finally, some of the methodological challenges posed by the need fully to characterise decision uncertainty and to inform the research agenda will be identified and discussed.

Cost-Benefit Analysis↗
PubMed1989

Sensitivity analysis for GMDH correction modeling of MKG signals.

The purpose of this paper is to propose application of sensitivity analysis to the GMDH modeling for the correction of distorted kinesiographic signals recorded for inter-lattice points in space, and to evaluate its correction accuracy to estimate coordinates of an inter-lattice point, i.e., an observation, distorted coordinates of a nominal lattice point which is most adjacent to a given inter-lattice point is searched. Variations, i. e., differences, between distorted coordinates of the observations and their concomitant nominals are calculated. Instead of substituting kinesiographic measurements of the nominal and its neighbouring eight lattice points, the sum of the observation and its corresponding variation is substituted into the GMDH model which has been employed for the correction of distorted measurements of the aforementioned lattice point. A stereotaxic device is developed to stimulate mandibular jaw movement and determine position of a magnet transducer of a mandibular kinesiograph (MKG). Nominals of 3-D coordinates of the inter-lattice points are determined by the stimulator together with simultaneous recording of distorted output signals from the MKG which correspond to the nominals. Distorted signals are corrected on the basis of the sensitivity-oriented correction modeling. A mean estimation error of 0.16 mm (s. d., 0.19 mm) is determined for 24 inter-lattice coordinates. Thus, the application of sensitivity analysis to the GMDH modeling is confirmed to be effective.

Humans↗
PubMed2000

Sensitivity analysis in quantitative microbial risk assessment.

The occurrence of foodborne disease remains a widespread problem in both the developing and the developed world. A systematic and quantitative evaluation of food safety is important to control the risk of foodborne diseases. World-wide, many initiatives are being taken to develop quantitative risk analysis. However, the quantitative evaluation of food safety in all its aspects is very complex, especially since in many cases specific parameter values are not available. Often many variables have large statistical variability while the quantitative effect of various phenomena is unknown. Therefore, sensitivity analysis can be a useful tool to determine the main risk-determining phenomena, as well as the aspects that mainly determine the inaccuracy in the risk estimate. This paper presents three stages of sensitivity analysis. First, deterministic analysis selects the most relevant determinants for risk. Overlooking of exceptional, but relevant cases is prevented by a second, worst-case analysis. This analysis finds relevant process steps in worst-case situations, and shows the relevance of variations of factors for risk. The third, stochastic analysis, studies the effects of variations of factors for the variability of risk estimates. Care must be taken that the assumptions made as well as the results are clearly communicated. Stochastic risk estimates are, like deterministic ones, just as good (or bad) as the available data, and the stochastic analysis must not be used to mask lack of information. Sensitivity analysis is a valuable tool in quantitative risk assessment by determining critical aspects and effects of variations.

Animals↗
PubMed2006

Sensitivity analysis and optimization of a standing wave ultrasonic linear motor.

This paper presents the sensitivity analysis of an ultrasonic linear motor using design of experiments (DOE) and the finite element (FE) optimization of its deformation amplitude. A first ultrasonic linear motor prototype has been built at the laboratory. A deformation amplitude of about 6.6 microm can be obtained by applying a 100 V voltage. The goal is to obtain a bigger deformation amplitude by varying the motor parameters, in particular the vibratory piece dimensions. First of all, a parametrization of the motor structure is carried out. Then, with the aim of reducing the variation ranges of the input parameters--but also to avoid performing a large number of simulations--a preoptimization stage is necessary. Thus, sensitivity analysis is carried out using design of experiments, which is a good way to obtain the influence of the input parameters on the objective function. Factorial designs have been chosen to find out the effects of each input factor but also the effect of their interactions. This method then is compared with Doehlert design technique, which is generally used for optimization approaches. The results show that it is absolutely necessary to take into account the quadratic terms in the model because they represent an important effect. The use of design of experiments revealed to be an interesting way to analyze numerically the ultrasonic motor as a preoptimization stage and already allows one to improve the deformation amplitude but also to reduce the input parameter variation ranges. Different FE optimization methods are then applied, and results show that the deformation amplitude can be increased by a factor higher than 10 compared to the initial design.

Journal Article↗
PubMed1987

Spreadsheets simplify sensitivity analysis for capital decisions.

The availability and ease of use of electronic spreadsheets removes the previously cumbersome number crunching burden of sensitivity analysis. In this article, the advantages of sensitivity analysis will be reintroduced and a model will be presented using a pro forma statement for a freestanding magnetic resonance imaging center.

Capital Expenditures↗
PubMed2004

Sensitivity analysis of longitudinal normal data with drop-outs.

We propose to perform a sensitivity analysis to evaluate the extent to which results from a longitudinal study can be affected by informative drop-outs. The method is based on a selection model, where the parameter relating the dropout probability to the current observation is not estimated, but fixed to a set of values. This allows to evaluate several hypotheses for the degree of informativeness of the drop-out process. Expectation and variance of missing data, conditional on the drop-out time are computed, and a stochastic EM algorithm is used to obtain maximum likelihood estimates. Simulations show that when the drop-out parameter is correctly specified, unbiased estimates of the other parameters are obtained, and coverage percentages of their confidence intervals are close to their theoretical value. More interestingly, misspecification of the drop-out parameter does not considerably alter these results. This method was applied to a randomized clinical trial, designed to demonstrate non-inferiority of an inhaled corticosteroid in terms of bone density, compared with a reference treatment. Sensitivity analysis showed that the conclusion of non-inferiority was robust against different hypotheses for the drop-out process.

Adolescent↗
PubMed1998

Malononitrile as a new derivatizing reagent for high-sensitivity analysis of oligosaccharides by electrospray ionization mass spectrometry.

A new method for the high-sensitivity analysis of oligosaccharides by negative ion electrospray ionization mass spectrometry was developed through a chemical derivatization of oligosaccharides. Oligosaccharides were derivatized to dinitrile compounds from the reaction with malononitrile under mildly basic conditions. The derivative of maltoheptaose was detected mainly as the [M-2H]2- ion in negative ion mode with 20 fmol sensitivity, even in unpurified samples. In this malononitrile derivatization method, no inorganic reagent, other than sodium hydroxide as a base catalyst, is used. Also, because excess ligand (malononitrile) is volatile, high sensitivity detection is realized without any solvent extraction or chromatographic purification. The detection limit can also be decreased by simple on-line cartridge filtration to 200 attomol which is 10(5) times better than that of free maltoheptaose. Structural information for oligosaccharide derivatives was obtained by collision induced dissociation. This malononitrile derivatization method is convenient and efficient for the sensitive analysis of oligosaccharides.

Carbohydrate Sequence↗
PubMed1984

Design sensitivity analysis: a new method for implant design and a comparison with parametric finite element analysis.

A unified theory of structural design sensitivity is proposed to be used in conjunction with the parametric design variation method traditionally used in finite element analyses applied to biomechanics problems. Bone cement strain energy density dependence on cement and stem modulii of elasticity as analyzed with the theory of structural design sensitivity analysis is compared parametrically varied finite element results. Two-dimensional, eight-noded isoparametric and interface finite elements with optimal stresses at Gauss points are employed. Design sensitivity for strain energy density compares well with perturbation of design and reanalysis by finite element techniques.

Hip Prosthesis↗
PubMed1999

Estimating uncertainty ranges for costs by the bootstrap procedure combined with probabilistic sensitivity analysis.

When an economic evaluation incorporates patient-level data, there are two types of uncertainty over the results: uncertainty due to variation in the sampled data, and uncertainty over the choice of modelling parameters and assumptions. Previously statistical methods have been used to estimate the extent of the former, and sensitivity analysis to estimate the extent of the latter. Ideally interval estimates for economic variables should reflect both types of uncertainty. This paper describes a method for combining bootstrapping with probabilistic sensitivity analysis to estimate a total 'uncertainty range' for incremental costs. The approach is illustrated using cost data from a randomized controlled trial of endoscopy for Helicobactor pylori negative young dyspeptic patients. The trial failed to demonstrate any clinical benefit from endoscopy, which was on average pound 395 more costly. The combined 95% uncertainty range for incremental costs (-pound 236 to pound 931) was wider than 95% intervals estimated by either probabilistic sensitivity analysis (pound 43 to pound 592) or the non-parametric bootstrap method (-pound 95 to pound 667) alone. The method can easily be extended to the calculation of uncertainty ranges for incremental cost-effectiveness ratios.

Confidence Intervals↗
PubMed2006

Sensitivity analysis of an accident prediction model by the fractional factorial method.

Sensitivity analysis of a model can help us determine relative effects of model parameters on model results. In this study, the sensitivity of the accident prediction model proposed by Zegeer et al. [Zegeer, C.V., Reinfurt, D., Hummer, J., Herf, L., Hunter, W., 1987. Safety Effect of Cross-section Design for Two-lane Roads, vols. 1-2. Report FHWA-RD-87/008 and 009 Federal Highway Administration, Department of Transportation, USA] to its parameters was investigated by the fractional factorial analysis method. The reason for selecting this particular model is that it incorporates both traffic and road geometry parameters besides terrain characteristics. The evaluation of sensitivity analysis indicated that average daily traffic (ADT), lane width (W), width of paved shoulder (PA), median (H) and their interactions (i.e., ADT-W, ADT-PA and ADT-H) have significant effects on number of accidents. Based on the absolute value of parameter effects at the three- and two-standard deviation thresholds ADT was found to be of primary importance, while the remaining identified parameters seemed to be of secondary importance. This agrees with the fact that ADT is among the most effective parameters to determine road geometry and therefore, it is directly related to number of accidents. Overall, the fractional factorial method was found to be an efficient tool to examine the relative importance of the selected accident prediction model parameters.

Accidents, Traffic↗
PubMed1995

A comparison of sensitivity analysis techniques.

Modeling the movement and consequence of radioactive pollutants is critical for environmental protection and control of nuclear facilities. Sensitivity analysis is an integral part of model development and involves analytical examination of input parameters to aid in model validation and provide guidance for future research. Sensitivities of 21 input parameters have been analyzed for a specific-activity tritium dose model using fourteen methods of parameter sensitivity analysis. This report demonstrates, for each sensitivity method, the required calculational effort, the sensitivity ranking of parameters, and the relative method performance. The sensitivity measures include the following: partial derivatives, variation of inputs by 1 standard deviation (SD) and by 20%, a sensitivity index, an importance index, a relative deviation of the output distribution, a relative deviation ratio, partial rank correlation coefficients, standardized regression coefficients, rank regression coefficients, the Smirnov test, the Cramer-von Mises test, the Mann-Whitney test, and the squared-ranks test.

Diet↗
PubMed2000

A sensitivity analysis to separate bias due to confounding from bias due to predicting misclassification by a variable that does both.

Variables that predict misclassification of exposure, outcome, or a confounder cannot be controlled by techniques that adjust for predictors of risk. They must be controlled by external adjustments. We confronted an analysis in which a variable predicted misclassification of the exposure and of a confounder. The same variable confounded the exposure-outcome relation. The analysis focused on the relation between less-than-definitive therapy and breast cancer mortality in the 5 years after diagnosis. Receipt of less-than-definitive prognostic evaluation predicted misclassification of definitive therapy (the exposure) and stage (a confounder). Prognostic evaluation also confounded the therapy-breast cancer mortality relation. We used a sensitivity analysis to separate the misclassification biases from the confounding bias. The relative hazard associated with less-than-definitive therapy in the original multivariable model equaled 1.75 (95% confidence interval = 1.02-3.00). The median estimate in 2,500 repetitions of the sensitivity analysis was a relative hazard of 1.64, and 90% of the estimates fell between 1.47 and 1.83. The sensitivity analysis suggests that less-than-definitive therapy confers an excess relative hazard of breast cancer mortality in the 5 years after diagnosis. The original analysis, which adjusted for confounding by prognostic evaluation but not its misclassification biases, overestimated the relative hazard.

Age Factors↗