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Sensitivity analysis for estimating urea kinetics parameters during hemodialysis.

In this paper a time-varying volume, double-pool urea kinetics model is considered and a sensitivity analysis is carried out to determine those patient parameters that have greater influence on the time course of blood urea nitrogen concentration (BUN) during and between dialysis treatment. The model parameters include the urea generation rate, the initial distribution volume of the urea, the ratio between intracellular and extracellular volumes, and the mass transfer coefficient between the two pools. The analysis demonstrates that BUN is highly sensitive to the urea generation rate and total distribution volume whereas it is influenced by the remaining parameters to a much lesser extent. In addition, the location of the absolute maxima of BUN sensitivity functions suggests the rational placement of a reduced number of blood samples that may still allow sufficiently accurate estimates for the parameters of clinical interest, such as the urea generation rate, total distribution volume, and the ratio between intracellular and extracellular volumes. This conclusion has been confirmed by simulation studies where parameter estimation has been performed with a varying number of observation points.

Blood Urea Nitrogen↗

Monte Carlo probabilistic sensitivity analysis for patient level simulation models: efficient estimation of mean and variance using ANOVA.

Probabilistic sensitivity analysis (PSA) is required to account for uncertainty in cost-effectiveness calculations arising from health economic models. The simplest way to perform PSA in practice is by Monte Carlo methods, which involves running the model many times using randomly sampled values of the model inputs. However, this can be impractical when the economic model takes appreciable amounts of time to run. This situation arises, in particular, for patient-level simulation models (also known as micro-simulation or individual-level simulation models), where a single run of the model simulates the health care of many thousands of individual patients. The large number of patients required in each run to achieve accurate estimation of cost-effectiveness means that only a relatively small number of runs is possible. For this reason, it is often said that PSA is not practical for patient-level models. We develop a way to reduce the computational burden of Monte Carlo PSA for patient-level models, based on the algebra of analysis of variance. Methods are presented to estimate the mean and variance of the model output, with formulae for determining optimal sample sizes. The methods are simple to apply and will typically reduce the computational demand very substantially.

Analysis of Variance↗

Sensitivity analysis of the systemic circulation with a view to computer simulation and parameter estimation.

A sensitivity analysis study has been performed on a seven-parameter model of the systemic vascular bed in order to obtain structure reductions appropriate for simulation and estimation. This analysis considers separately the systolic and diastolic transfer functions between arterial and venous pressures in order to divide a non-linear problem in two distinct linear problems. The results obtained refer to nominal parameter values corresponding to normal circulatory conditions in man and supply guide-lines for an application-oriented selection of reduced models. Simple resistance-compliance models are preferred because the inertial effects appear to have only slight influence. In particular, the choice of a five-parameter model seems to be convenient for simulation purposes. An additional structure reduction is suggested to reach reliable results in parameter estimation problems. The resulting model is characterized by three elements: peripheral resistance, arterial compliance and venous compliance.

Blood Circulation↗

A Monte Carlo/response surface strategy for sensitivity analysis: application to a dynamic model of vegetative plant growth.

We describe the application of a strategy for conducting a sensitivity analysis for a complex dynamic model. The procedure involves preliminary screening of parameter sensitivities by numerical estimation of linear sensitivity coefficients, followed by generation of a response surface based on Monte Carlo simulation. Application is to a physiological model of the vegetative growth of soybean plants. The analysis provides insights as to the relative importance of certain physiological processes in controlling plant growth. Advantages and disadvantages of the strategy are discussed.

Carbon Dioxide↗

Sensitivity analysis of longitudinal binary data with non-monotone missing values.

This paper highlights the consequences of incomplete observations in the analysis of longitudinal binary data, in particular non-monotone missing data patterns. Sensitivity analysis is advocated and a method is proposed based on a log-linear model. A sensitivity parameter that represents the relationship between the response mechanism and the missing data mechanism is introduced. It is shown that although this parameter is identifiable, its estimation is highly questionable. A far better approach is to consider a range of plausible values and to estimate the parameters of interest conditionally upon each value of the sensitivity parameter. This allows us to assess the sensitivity of study's conclusion to assumptions regarding the missing data mechanism. The method is applied to a randomized clinical trial comparing the efficacy of two treatment regimens in patients with persistent asthma.

Adrenal Cortex Hormones↗

Sensitivity analysis of ECOSYS-87: an emphasis on the ingestion pathway as a function of radionuclide and type of deposition.

A sensitivity analysis of parameters associated with the ingestion pathway was conducted for the computer model ECOSYS-87. The model is currently being used extensively throughout Europe for accident consequence analysis following a nuclear release. Individual parameter perturbation was used to develop sensitivity indices. The sensitivity indices identified parameters whose uncertainties had a large impact on model results. The relative ranking of the sensitive parameters depended on the radionuclide (137Cs, 90Sr, 131I, or 239Pu), whether dose 1 y or 50 y postaccident was being considered, and whether the deposition event was dry or mixed. The most influential parameter for 239Pu was resuspension. Parameters to which human dose was sensitive following exposure to 137Cs, 90Sr, and 131I, were as follows: yield (biomass) of vegetation, transfer of radionuclides from plants to animals, deposition velocity, changes in radionuclide concentrations due to food processing, livestock feeding rates, and weathering of radionuclides from plant surfaces. The ranking of 131I's parameters was governed by its 8-d physical half-life. Parameters that affected the initial deposition, parameters that could rapidly affect the transfer of 131I from the biota to humans, or parameters that allowed 131I to decay prior to consumption were important. Important parameters specific to 90Sr and 137Cs included transfer of radionuclides from soil to plant, leaching from the plant rooting zone, and resuspension. Parameters associated with the movement of radionuclides within the soil were not as important for 137Cs as they were for 90Sr. With the exception of the deposition velocity, if a parameter proved to be sensitive for dry deposition, it was as sensitive, or even more so, for a mixed deposition event. Extending the model end point from 1 y to 50 y postaccident also caused a shift in the relative ranking of sensitive parameters for 137Cs and 90Sr. Parameters that were not important for any of the radionuclides considered under this scenario were those related to timing and length of crop harvest, transfer of radionuclides from leaf surfaces to edible portions of plants, rate at which radionuclide concentrations in plants decrease due to growth dilution, and time for animals to reach marketable size.

Accidents↗

A model for compound action potentials and currents in a nerve bundle. II: A sensitivity analysis of model parameters for the forward and inverse calculations.

We present a detailed analysis of the sensitivity of simulated Compound Action Current (CAC) and Compound Action Potential (CAP) recordings to specific model parameters, including the Single Fiber Action Currents (SFACs) and Single Fiber Action Potentials (SFAPs) that represent the contributions of each axon in the nerve bundle. In the preceding paper, we described a general method for simulating CACs and CAPs. This method uses a volume conduction model that incorporates the effects of the nerve bundle and other anisotropic properties of the region of the bundle that surrounds an individual nerve axon. In this paper, we present a complete analysis of the effects of incorrectly assigned model parameters on the simulated CAC and CAP. We also investigate the effects of incorrectly assigned parameters, recording noise, and data smoothing on the Conduction Velocity Distributions (CVDs) predicted from the CAC and CAP. We find that the simulated CAC is less sensitive to most of the parameters than is the CAP.

Action Potentials↗

A local influence sensitivity analysis for incomplete longitudinal depression data.

In the analyses of incomplete longitudinal clinical trial data, there has been a shift, away from simple ad hoc methods that are valid only if the data are missing completely at random (MCAR), to more principled (likelihood-based or Bayesian) ignorable analyses, which are valid under the less restrictive missing at random (MAR) assumption. The availability of the necessary standard statistical software allows for such analyses in practice. Although the possibility of data missing not at random (MNAR) cannot be ruled out, it is argued that analyses valid under MNAR are not well suited for the primary analysis in clinical trials. Therefore, rather than either forgetting about or blindly shifting to an MNAR framework, the optimal place for MNAR analyses is within a sensitivity analysis context. Such analyses can be used, for example, to assess how sensitive results from an ignorable analysis are to possible departures from MAR and how much results are affected by influential observations. In this article, we apply the local influence sensitivity tool (Verbeke et al., 2001) to a longitudinal depression trial, thereby applying it to continuous outcomes from clinical trials.

Antidepressive Agents↗

Illustration of sampling-based methods for uncertainty and sensitivity analysis.

A sequence of linear, monotonic, and nonmonotonic test problems is used to illustrate sampling-based uncertainty and sensitivity analysis procedures. Uncertainty results obtained with replicated random and Latin hypercube samples are compared, with the Latin hypercube samples tending to produce more stable results than the random samples. Sensitivity results obtained with the following procedures and/or measures are illustrated and compared: correlation coefficients (CCs), rank correlation coefficients (RCCs), common means (CMNs), common locations (CLs), common medians (CMDs), statistical independence (SI), standardized regression coefficients (SRCs), partial correlation coefficients (PCCs), standardized rank regression coefficients (SRRCs), partial rank correlation coefficients (PRCCs), stepwise regression analysis with raw and rank-transformed data, and examination of scatter plots. The effectiveness of a given procedure and/or measure depends on the characteristics of the individual test problems, with (1) linear measures (i.e., CCs, PCCs, SRCs) performing well on the linear test problems, (2) measures based on rank transforms (i.e., RCCs, PRCCs, SRRCs) performing well on the monotonic test problems, and (3) measures predicated on searches for nonrandom patterns (i.e., CMNs, CLs, CMDs, SI) performing well on the nonmonotonic test problems.

Journal Article↗

Sensitivity analysis and external adjustment for unmeasured confounders in epidemiologic database studies of therapeutics.

BACKGROUND: Large health care utilization databases are frequently used to analyze unintended effects of prescription drugs and biologics. Confounders that require detailed information on clinical parameters, lifestyle, or over-the-counter medications are often not measured in such datasets, causing residual confounding bias. OBJECTIVE: This paper provides a systematic approach to sensitivity analyses to investigate the impact of residual confounding in pharmacoepidemiologic studies that use health care utilization databases. METHODS: Four basic approaches to sensitivity analysis were identified: (1) sensitivity analyses based on an array of informed assumptions; (2) analyses to identify the strength of residual confounding that would be necessary to explain an observed drug-outcome association; (3) external adjustment of a drug-outcome association given additional information on single binary confounders from survey data using algebraic solutions; (4) external adjustment considering the joint distribution of multiple confounders of any distribution from external sources of information using propensity score calibration. CONCLUSION: Sensitivity analyses and external adjustments can improve our understanding of the effects of drugs and biologics in epidemiologic database studies. With the availability of easy-to-apply techniques, sensitivity analyses should be used more frequently, substituting qualitative discussions of residual confounding.

Anti-Inflammatory Agents, Non-Steroidal↗

Sensitivity analysis of pharmacodynamic parameters in pharmacodynamic models.

The quantitative properties of a pharmacodynamic model can be characterized by the pharmacodynamic parameters. The sensitivity analysis of pharmacodynamic parameters in eight kinds of pharmacodynamic models was conducted. The sensitivity functions with respect to different pharmacodynamic parameters for these pharmacodynamic models were deduced using the partial derivative. The pharmacodynamic parameters were ranked according to their sensitivity functions.

Algorithms↗

A sensitivity analysis of the Bongaarts-Feeney method for adjusting bias in observed period total fertility rates.

Our sensitivity analysis shows that the adjusted TFR'(t) using the formula of Bongaarts and Feeney (1998), which assumes an invariant shape for the fertility schedule, usually does not differ significantly from an adjusted TFR"(t) that allows the shape of the fertility schedule to change at a constant annual rate. Because annual changes in the shape of the fertility schedules often are approximately constant except in abnormal conditions, the Bongaarts-Feeney (B-F) method is generally robust for producing reasonable estimates of the adjusted TFR'(t). The adjusted TFR'(t) neither represents any real cohort experiences from the past nor forecasts any future trend. It merely provides an improved reading of the period fertility measure, which reduces the tempo distortion.

Analysis of Variance↗

Computer simulation of metabolism in palmitate-perfused rat heart. III. Sensitivity analysis.

The behavior of a computer model of metabolism in glucose- and palmitate-perfused rat hearts was interpreted by sensitivity analysis to explain why the heart preferentially utilizes fatty acids as fuel even in the presence of substantial exogenous glucose. The sensitivity functions identified those metabolites and enzymes which were most important in regulating the metabolic rate and determined which enzymes set the levels of the critical metabolites. Control of the mitochondrial redox potential and the distribution of coenzyme A thioesters regulated the rate of fatty acid utilization while strong inhibition of citrate synthetase resulted in accumulation of acetyl CoA and suppression of pyruvate oxidation. Glycolysis was limited by the cytosolic ATP/ADP ratio set largely by the creatine shuttle. Metabolic control appears to be widely distributed rather than localized at "key" enzymes. Metabolite levels are usually set by enzymes controlled by modifiers whereas metabolic flux is regulated by the enzymes that produce ligands for the modifier-controlled enzymes.

Animals↗

Application of global sensitivity analysis to determine goals for design of experiments: an example study on antibody-producing cell cultures.

Global sensitivity analysis (GSA) can be used to quantify the importance of model parameters and their interactions with respect to model output. In this study, the Sobol' method for GSA is applied to a dynamic model of monoclonal antibody-producing mammalian cell cultures in order to identify the parameters that need to be accurately determined experimentally. Our results show that most parameters have low sensitivity indices and exhibit strong interactions with one another. These parameters can be set at their nominal values and unnecessary experimentation can therefore be avoided. In contrast, certain parameters are identified as sensitive, necessitating their estimation given sufficiently rich experimental data. Moreover, parameter sensitivity varies during culture time in a biologically meaningful manner. In conclusion, GSA can serve as an excellent precursor to optimal experiment design.

Antibodies, Monoclonal↗

Reliable and sensitive analysis of occult bone marrow metastases using automated cellular imaging.

The presence of occult bone marrow metastases (OM) has been reported to represent an important prognostic indicator for patients with operable breast cancer and other malignancies. Assaying for OM most commonly involves labor-intensive manual microscopic analysis. The present report examines the performance of a recently developed automated cellular image analysis system (ACIS; ChromaVision Medical Systems, Inc.) for identifying and enumerating OM in human breast cancer specimens. OM analysis was performed after immunocytochemical staining. Specimens used in this study consisted of normal bone marrow (n = 10), bone marrow spiked with carcinoma cells (n = 20), and bone marrow obtained from breast cancer patients (n = 39). The reproducibility of ACIS-assisted analysis for tumor cell detection was examined by having a pathologist evaluate montage images generated from multiple ACIS runs of five specimens. Independent ACIS-assisted analysis resulted in the detection of an identical number of tumor cells for each specimen in all instrument runs. Additional studies were performed to analyze OM from 39 breast cancer patients with two pathologists performing parallel analysis using either manual microscopy or ACIS-assisted analysis. In 17 of the 39 cases (44%), specimens were classified by the pathologist as positive for tumor cells after ACIS-assisted analysis, whereas the same pathologist failed to identify tumor cells on the same slides after analysis by manual microscopy. These studies indicate that the ACIS-assisted analysis provides excellent sensitivity and reproducibility for OM detection, relative to manual microscopy. Such performance may enable an improved approach for disease staging and stratifying patients for therapeutic intervention.

Bone Marrow Neoplasms↗

A simple local sensitivity analysis tool for nonignorable coarsening: application to dependent censoring.

Right- and interval-censored data are common special cases of coarsened data (Heitjan and Rubin, 1991, Annals of Statistics19, 2244-2253). As with missing data, standard statistical methods that ignore the random nature of the coarsening mechanism may lead to incorrect inferences. We extend a simple sensitivity analysis tool, the index of local sensitivity to nonignorability (Troxel, Ma, and Heitjan, 2004, Statistica Sinica14, 1221-1237), to the evaluation of nonignorability of the coarsening process in the general coarse-data model. By converting this index into a simple graphical display one can easily assess the sensitivity of key inferences to nonignorable coarsening. We illustrate the validity of the method with a simulated example, and apply it to right-censored data from an observational study of cardiac transplantation and to interval-censored data on time to detectable viral load from a clinical trial in HIV disease.

Biometry↗

Sensitivity analysis for validating expert opinion as to ideal data set criteria for transport modeling.

Environmental fate modeling results are often used in risk assessment without adequately considering uncertainty in exposure predictions. Sensitivity analysis is fundamental to model validation and error prediction since sensitive model input parameters account for the largest variance in model prediction. Once identified, sensitive model input parameters can be used to propagate parametric uncertainty in numerical predictions. Output sensitivity to variation in input code sequences was investigated for the pesticide root zone model (PRZM 3) using Plackett-Burman analysis for six runoff and leaching data sets. The analysis utilized an incomplete block factorial design with even parameter weighting and uniform proportional input perturbation. Timing and duration of key period rainfall were assumed a priori to be dominant sensitive inputs. Thus, meteorological data were fixed, allowing identification of additional input components contributing to model sensitivity. Results validated expert modeler assumptions concerning parameters most critical for model validation. For leaching data sets, the application rate, soil bulk density (an indicator of available water-holding capacity), chemical partition coefficient, and pesticide degradation rates were commonly the most sensitive inputs. For runoff data sets, the in-crop runoff curve number was the most significant input governing pesticide loss in runoff and erosion flux. The chemical partition coefficient, soil and foliar decay rates, and soil bulk density were also common sensitive components for runoff predictions. These commonly observed sensitive components for runoff and leaching prediction need to be carefully considered in the design and conduct of relevant field studies, modeling assessment of such studies, and future improvements in algorithms for environmental transport modeling.

Meteorological Concepts↗

Bone remodelling using sensitivity analysis.

A boundary element formulation is presented for analysing the surface bone remodelling. The formulation is based on sensitivity analysis and utilises design parameters which are related to the shape of the bone. An application of the method to the modelling of bone ingrowth into a slot of an implant is presented.

Biomechanical Phenomena↗