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Projected number of diabetic renal disease patients among insulin-dependent diabetes mellitus children in Japan using a Markov model with probabilistic sensitivity analysis.

BACKGROUND: To plan prevention programmes for the diabetic renal disease among insulin-dependent diabetes mellitus (IDDM) children, projections of future trends for the disease is crucial. We projected future trends in the number of diabetic renal disease patients among IDDM children and assessed an impact of treatment dissemination in Japan. METHODS: We used a Markov model to describe the clinical courses of diabetic renal disease. Future trends in the number of patients with diabetic nephropathy (DN) and end-stage renal disease (ESRD) were projected from the year 1995 to 2015. We made three scenarios for assessing an impact of the dissemination of new treatment. We performed a probabilistic sensitivity analysis for the uncertainty of transition probabilities. RESULTS: The results showed that the number of patients with DN was 790.5 (5th to 95th percentile: 652.5-955.1), ESRD was 253.3 (5th to 95th percentile: 207.3-310.0) in year 2015 on basic scenario. Considering the dissemination of intensive insulin therapy, under the scenario of the gradual increase of the treatment, the result showed that the number of patients with DN was 713.1 (5th to 95th percentile: 546.2-930.6), ESRD was 231.0 (5th to 95th percentile: 176.6-296.2). Under the scenario of the immediate change of the treatment, the results showed that the number of patients with DN in 2015 was 418.9 (5th percentile; 345.4; 95th percentile; 506.1) and with ESRD was 133.4 (5th percentile; 109.0; 95th percentile; 163.8). CONCLUSIONS: The results of the projection showed a gradual increase in the number of patients with DMN and ESRD. Examination of three possible scenarios showed that the programme of dissemination of intensive insulin therapy prevented the progression of diabetic renal disease.

Adolescent↗

Sensitivity analysis of parameters controlling oscillatory signalling in the NF-kappaB pathway: the roles of IKK and IkappaBalpha.

Analysis of cellular signalling interactions is expected to create an enormous informatics challenge, perhaps even greater than that of analysing the genome. A key step in the evolution towards a more quantitative understanding of signalling is to specify explicitly the kinetics of all chemical reaction steps in a pathway. We have reconstructed a model of the nuclear factor, kappaB (NF-kappaB) signalling pathway, containing 64 parameters and 26 variables, including steps in which the activation of the NF-kappaB transcription factor is intimately associated with the phosphorylation and ubiquitination of its inhibitor kappaB by a membrane-associated kinase, and its translocation from the cytoplasm to the nucleus. We apply sensitivity analysis to the model. This identifies those parameters in this (IkappaB)/NF-kappaB signalling system (containing only induced IkappaBalpha isoform) that most affect the oscillatory concentration of nuclear NF-kappaB (in terms of both period and amplitude). The intention is to provide guidance on which proteins are likely to be most significant as drug targets or should be exploited for further, more detailed experiments. The sensitivity coefficients were found to be strongly dependent upon the magnitude of the parameter change studied, indicating the highly non-linear nature of the system. Of the 64 parameters in the model, only eight to nine exerted a major control on nuclear NF-kappaB oscillations, and each of these involved as reaction participants either the IkappaB kinase (IKK) or IkappaBalpha, directly. This means that the dominant dynamics of the pathway can be reflected, in addition to that of nuclear NF-kappaB itself, by just two of the other pathway variables. This is conveniently observed in a phase-plane plot.

Animals↗

Sensitivity analysis of ground-level ozone concentration to emission changes in two urban regions of southeast Texas.

Air pollutant emission is one of the predominant factors affecting urban air quality such as ground-level ozone formation. This paper assesses the impact of changing emission inventory scenarios, based on combinations of point, mobile, area/non-road and biogenic sources, on the tropospheric ozone concentration in two southeast Texas urban areas, i.e. Houston-Galveston and Beaumont-Port Arthur, during the rapid ozone formation event (ROFE) on August 25, 2000. The EPA's Community Multiscale Air Quality (CMAQ) modeling system with 1999 national emission inventory (NEI99) estimates and updated SAPRC99 chemical mechanism are used in the sensitivity analysis for twelve different emission scenarios. Based on model results, it is found that the point source emission of NOx and VOC contributes the greatest ozone peak in the ROFE. Removing Texas point sources of VOC and NOx emission from the inventory results in a reduction in peak O3 concentration by 128 and 70 ppbv in Houston urban area, respectively. Similar but less drastic impact from point source is also observed in the Beaumont-Port Arthur area. The effect on peak ozone concentration due to mobile, area and non-road sources emissions are less significant compared to that of point source emission. Reducing VOC emission appears to be more effective than reducing NOx emission in lowering peak O3 concentration in the studied region. Although biogenic emission can contribute up to 37 ppbv of peak ozone level over a large area, the affected area is away from the urban region of concern, and should not be the main cause for O3 non-attainment in the two urban areas. Removing CO emission from mobile sources does not lead to significant reduction (< 1 ppbv) in ozone concentrations. The modeled data also show that the transport of O3 precursors from adjacent states can cause a significant ozone plume near Beaumont due to its proximity to the state border based on the conditions during the August 25, 2000 O3 episode.

Air Pollutants↗

Sensitivity analysis for the assessment of causal vaccine effects on viral load in HIV vaccine trials.

Vaccines with limited ability to prevent HIV infection may positively impact the HIV/AIDS pandemic by preventing secondary transmission and disease in vaccine recipients who become infected. To evaluate the impact of vaccination on secondary transmission and disease, efficacy trials assess vaccine effects on HIV viral load and other surrogate endpoints measured after infection. A standard test that compares the distribution of viral load between the infected subgroups of vaccine and placebo recipients does not assess a causal effect of vaccine, because the comparison groups are selected after randomization. To address this problem, we formulate clinically relevant causal estimands using the principal stratification framework developed by Frangakis and Rubin (2002, Biometrics 58, 21-29), and propose a class of logistic selection bias models whose members identify the estimands. Given a selection model in the class, procedures are developed for testing and estimation of the causal effect of vaccination on viral load in the principal stratum of subjects who would be infected regardless of randomization assignment. We show how the procedures can be used for a sensitivity analysis that quantifies how the causal effect of vaccination varies with the presumed magnitude of selection bias.

AIDS Vaccines↗

Multicomponent dynamical nucleation theory and sensitivity analysis.

Vapor to liquid multicomponent nucleation is a dynamical process governed by a delicate interplay between condensation and evaporation. Since the population of the vapor phase is dominated by monomers at reasonable supersaturations, the formation of clusters is governed by monomer association and dissociation reactions. Although there is no intrinsic barrier in the interaction potential along the minimum energy path for the association process, the formation of a cluster is impeded by a free energy barrier. Dynamical nucleation theory provides a framework in which equilibrium evaporation rate constants can be calculated and the corresponding condensation rate constants determined from detailed balance. The nucleation rate can then be obtained by solving the kinetic equations. The rate constants governing the multistep kinetics of multicomponent nucleation including sensitivity analysis and the potential influence of contaminants will be presented and discussed.

Journal Article↗

A sensitivity analysis for nonrandomly missing categorical data arising from a national health disability survey.

Using data from 145,007 adults in the Disability Supplement to the National Health Interview Survey, we investigated the effect of balance difficulties on frequent depression after controlling for age, gender, race, and other baseline health status information. There were two major complications: (i) 80% of subjects were missing data on depression and the missing-data mechanism was likely related to depression, and (ii) the data arose from a complex sample survey. To adjust for (i) we investigated three classes of models: missingness in depression, missingness in depression and balance, and missingness in depression with an auxiliary variable. To adjust for (ii) we developed the first linearization variance formula for nonignorable missing-data models. Our sensitivity analysis was based on fitting a range of ignorable missing-data models along with nonignorable missing-data models that added one or two parameters. All nonignorable missing-data models that we considered fit the data substantially better than their ignorable missing-data counterparts. Under an ignorable missing-data mechanism, the odds ratio for the association between balance and depression was 2.0 with a 95% CI of (1.8, 2.2). Under 29 of the 30 selected nonignorable missing-data models, the odds ratios ranged from 2.7 with 95% CI of (2.3, 3.1) to 4.2 with 95% CI of (3.9, 4.6). Under one nonignorable missing-data model, the odds ratio was 7.4 with 95% CI of (6.3, 8.6). This is the first analysis to find a strong association between balance difficulties and frequent depression.

Adult↗

Probabilistic modelling of human exposure to intense sweeteners in Italian teenagers: validation and sensitivity analysis of a probabilistic model including indicators of market share and brand loyalty.

For the assessment of exposure to food-borne chemicals, the most commonly used methods in the European Union follow a deterministic approach based on conservative assumptions. Over the past few years, to get a more realistic view of exposure to food chemicals, risk managers are getting more interested in the probabilistic approach. Within the EU-funded 'Monte Carlo' project, a stochastic model of exposure to chemical substances from the diet and a computer software program were developed. The aim of this paper was to validate the model with respect to the intake of saccharin from table-top sweeteners and cyclamate from soft drinks by Italian teenagers with the use of the software and to evaluate the impact of the inclusion/exclusion of indicators on market share and brand loyalty through a sensitivity analysis. Data on food consumption and the concentration of sweeteners were collected. A food frequency questionnaire aimed at identifying females who were high consumers of sugar-free soft drinks and/or of table top sweeteners was filled in by 3982 teenagers living in the District of Rome. Moreover, 362 subjects participated in a detailed food survey by recording, at brand level, all foods and beverages ingested over 12 days. Producers were asked to provide the intense sweeteners' concentration of sugar-free products. Results showed that consumer behaviour with respect to brands has an impact on exposure assessments. Only probabilistic models that took into account indicators of market share and brand loyalty met the validation criteria.

Adolescent↗

Sensitivity analysis of a novel mathematical model identifies factors determining bone resorption rates.

The development of pharmaceutical treatments for bone disease can be enhanced by computational models that predict their effects on resorption and rates of remodeling. Therefore, a simple mathematical model was formulated to simulate erosion depth and duration of resorption, using Michaelis-Menten (M-M) equations to describe changing rates of cellular activity during the two phases of bone resorption. The model was based on histomorphometric data and cellular interactions that occur in the bone microenvironment cited from the literature. Availability of bone substrate for osteoclastic activity during Phase I was assumed to be limited by the ratio of RANKL (ligand for receptor activator for nuclear factor kappaB) to osteoprotegerin (OPG) ('effective RANKL'). The required presence of marrow stromal cell produced macrophage-colony stimulating factor (M-CSF) for osteoclast action was represented as a factor equal to 1 for healthy bone. Growth factors released from the matrix during Phase I were assumed to cause two negative feedback effects: (1) the inhibitory effect of transforming growth factor-beta1 (TGFbeta1)-induced production of OPG by marrow osteoblast stromal cells, reducing effective RANKL; (2) the apoptosis of osteoclast nuclei assumed to occur at high concentrations of TGFbeta. This signaled the end of Phase I. During Phase II, cellular activity to remove the collagen fibrils left behind by osteoclasts was also simulated by Michaelis-Menten kinetic equations. Results of sensitivity analysis revealed variation in resorption depth and duration to fluctuate within 6% and 7% of the baseline value for changes in most input parameters. However, resorption depth was reduced and the duration of resorption lengthened by both a decrease in matrix TGFbeta and an increase the apoptotic threshold. Furthermore, the duration of resorption, but not erosion depth, was sensitive to changes in the maximum rate of cellular activity during removal of collagen fibrils. This mathematical model, which simulates the changing rates of cellular activity, has identified factors that reduce the duration and depth of resorption. It also suggests new targets for modeling therapeutic intervention to slow the rate of bone remodeling.

Bone Resorption↗

Sensitivity analysis and other improvements to tailored combinatorial library design

"Tailoring" combinatorial libraries was developed several years ago as a very general and intuitive method to design diverse compound collections while controlling the profile of other pharmaceutically relevant properties. The candidate substituents were assigned to "categorical bins" according to their properties, and successive steps of D-optimal design were performed to generate diverse substituent sets consistent with required membership quotas from each bin. This serial algorithm was expedient to implement from existing D-optimal design codes, but was order-dependent and did not generally locate the very best possible design. A new "parallel" Fedorov search algorithm has now been implemented that can find the most diverse property-tailored design. An ambiguous mass penalty has been added, whereby most duplicate masses can be eliminated with little loss of library diversity. Sensitivity analysis has also been added to quantitatively explore the diversity trade-offs due to increasing or decreasing each specific kind of bias.

Journal Article↗

Biomechanical modeling and sensitivity analysis of bipedal running ability. II. Extinct taxa.

Using an inverse dynamics biomechanical analysis that was previously validated for extant bipeds, I calculated the minimum amount of actively contracting hindlimb extensor muscle that would have been needed for rapid bipedal running in several extinct dinosaur taxa. I analyzed models of nine theropod dinosaurs (including birds) covering over five orders of magnitude in size. My results uphold previous findings that large theropods such as Tyrannosaurus could not run very quickly, whereas smaller theropods (including some extinct birds) were adept runners. Furthermore, my results strengthen the contention that many nonavian theropods, especially larger individuals, used fairly upright limb orientations, which would have reduced required muscular force, and hence muscle mass. Additional sensitivity analysis of muscle fascicle lengths, moment arms, and limb orientation supports these conclusions and points out directions for future research on the musculoskeletal limits on running ability. Although ankle extensor muscle support is shown to have been important for all taxa, the ability of hip extensor muscles to support the body appears to be a crucial limit for running capacity in larger taxa. I discuss what speeds were possible for different theropod dinosaurs, and how running ability evolved in an inverse relationship to body size in archosaurs.

Animals↗

Sensitivity Analysis and Optimal Shape Design for Bone-Prosthesis Interfaces in a Femoral Head Surface Replacement.

A numerical optimization procedure has been applied for the shape optimal design of a femoral head surface replacement. The failure modes of the prosthesis that were considered in the formulation of the objective functions concerned the interface stress magnitude and the bone remodelling activity beneath the implant. In order to find a compromising solution between different requirements demanded by the two objective functions, a two step optimization procedure has been developed. Through step 1 the minimization of interface stress was achieved, through step 2 the minimization of bone remodelling was achieved with constraints on interface stresses. The results obtained provided an optimal design that generates limited bone remodelling activity with controlled interface stress distribution. The computational procedure was based on the application of the finite element method, linked to a mathematical programming package and a design sensitivity analysis package.

Journal Article↗

Sensitivity analysis for the estimation of rates of change with non-ignorable drop-out: an application to a randomized clinical trial of the vitamin D3.

The vitamin D(3) trial was a repeated measures randomized clinical trial for secondary hyperparathyroidism in haemodialysis patients where the efficacy of the vitamin D(3) infusions for suppressing the secretion of parathyroid hormone (PTH) was compared among four dose groups over 12 weeks. In this trial, patients terminated the study before the scheduled end of the study due to their elevated serum calcium (Ca) level, that is, the administration of the vitamin D(3) was expected to cause hypercalcaemia as an adverse event. In this setting of monotone missingness, there is a potential for bias in estimation of mean rates of decline in PTH for each treatment group using the standard methods such as the generalized estimating equations (GEE) which ignore the observed past Ca histories. We estimated the treatment-group-specific mean rates of decline in PTH by the inverse probability of censoring weighted (IPCW) methods which account for the observed past histories of time-dependent factors that are both a predictor of drop-out and are correlated with the outcomes. The IPCW estimator can be viewed as an extension of the GEE estimator that allows for the data to be MAR but not MCAR. With missing data, it is rarely appropriate to analyse the data solely under the assumption that the missing data process is ignorable, because the assumption of ignorable missingness cannot be guaranteed to hold and is untestable from the observed data. We proposed a sensitivity analysis that examines how inference about the IPCW estimates of the treatment-group-specific mean rates of decline in PTH changes as we vary the non-ignorable selection bias parameter over a range of plausible values.

Bias↗

Sensitivity analysis of Salmonella enteritidis levels in contaminated shell eggs using a biphasic growth model.

Salmonella enteritidis (SE) is a common foodbome pathogen, the transmission of which is primarily associated with the consumption of contaminated Grade A shell eggs. In order to estimate the level of SE present in raw shell eggs, it is necessary to consider the protective effects of the egg albumin, which effectively inhibits SE growth in a time- and temperature-dependent manner. In this study, a SE growth model was produced by combining two mathematical equations that described both the extended lag phase of SE growth (food component) and a SE growth model (pathogen component). This biphasic growth model was then applied to various egg handling scenarios based on the farm-to-table continuum, including in-line and off-line processing facilities with consideration of key events in production, processing, transportation, and storage. Seasonal effects were also studied. Monte Carlo simulation was used to characterize variability in temperature and time parameter values influencing the level of SE to which individuals are exposed. The total level of SE consumed was estimated under best, most likely, and time-temperature abusive handling scenarios. The model estimated that, in most cases, there was no SE growth in contaminated eggs handled under most likely practices, because 10-70% of the yolk membrane remained intact. Under abusive handling scenarios, complete loss of yolk membrane integrity frequently occurred by the time eggs reach the distribution phase, followed by subsequent SE growth, which was often quite rapid. In general, the effect of season and processing method (in-line vs. off-line) was minimal. Further sensitivity analysis demonstrated that the initial SE contamination level significantly influenced the final exposure levels only under no-abuse or mildly abusive conditions. The results of our study suggest that, for maximum reduction of SE exposure level, cooling strategies should not only focus on the on-farm or processing phases, but should emphasize the importance of cooling strategies at the distribution and consumer phases of the farm-to-fork continuum.

Animals↗

Enhanced cardiac thermal dilution analysis for cardiac output, volumes, stroke volumes, and regurgitation rates--sensitivity analysis using digital simulation.

Cardiac output is measured by placing a double lumen catheter with a thermistor on the tip through the right ventricle into the pulmonary artery, injecting cold saline into the right atrium, and integrating the resulting pulmonary artery temperature profile. If a similar procedure is performed with thermistors located in the right atrium, right ventricle, and pulmonary artery, the resulting temperature curves are determined by the known or easily measured quantities: injectate temperature, injectate volume, heart rate, systolic time interval, body temperature, and time in the cardiac cycle at which injection begins and the unknown quantities: right atrial, right ventricular, pulmonary artery mean and stroke volumes, inflow and outflow valve regurgitation rates, and cardiac output. A digital computer program using a lumped parameter model has been developed to use these quantities to produce thermal dilution curves and optimize the fit of the model curves to the temperature curves from the thermal dilution measurement to determine the unknown quantities. The program is used to investigate the effects of measuring system time constant, heat transfer, and noise on the accuracy of these measurements. The results indicate that the method is practical.

Cardiac Output↗

Modeling splanchnic hemodynamics after distal splenorenal shunt: a computer simulation and sensitivity analysis.

The distal splenorenal shunt operation was specifically designed to preserve portal flow and maintain elevated portal pressure. However, although this goal is met in the immediate postoperative period, flow decreases over time, and in as many as 75% of alcoholic patients, portal flow is lost in the first year. Various explanations have been offered for this observation, and modifications of the original operation have been proposed (splenopancreatic disconnection). Although other portacaval shunts have been successfully modeled as electrical circuits, this approach has never been described for the distal splenorenal shunt. In this study we developed a computer program that modeled the distal splenorenal shunt as an electrical circuit. We performed an analysis to determine the sensitivity of portal flow to changes in each resistance element and then performed a series of simulation experiments to critically examine the various explanations offered for the gradual changes in hepatic hemodynamics. We found that portal flow was most sensitive to resistance in the renal vein followed by resistance in the anastomosis. The simulation experiments suggested a new alternative to splenopancreatic disconnection--restricting the ability of the splenic vein, anastomosis, or renal vein to dilate. Additional clinical studies will be needed to test these predictions.

Collateral Circulation↗

Probabilistic cost-effectiveness analysis of HIV prevention. Comparing a Bayesian approach with traditional deterministic sensitivity analysis.

In cost-effectiveness analysis, the incremental cost-effectiveness ratio is used to measure economic efficiency of a new intervention, relative to an existing one. However, costs and effects are seldom known with certainty. Uncertainty arises from two main sources: uncertainty regarding correct values of intervention-related parameters and uncertainty associated with sampling variation. Recently, attention has focused on Bayesian techniques for quantifying uncertainty. We computed the Bayesian-based 95% credible interval estimates of the incremental cost-effectiveness ratio of several related HIV prevention interventions and compared these results with univariate sensitivity analyses. The conclusions were comparable, even though the probabilistic technique provided additional information.

Bayes Theorem↗

Uncertainty, variability and sensitivity analysis applied to the RAGENA model of radon generation, entry and accumulation indoors.

The application of a radon model is useful to understand the processes that drive the radon gas behaviour from its sources to its accumulation indoors. Since in a given inhabited house the detailed knowledge of the values of all the parameters that affect indoor radon levels is not available, the response of the model has to be explored in a reference site in which all the parameters are supposed to be known. We call this site the reference configuration. In this paper we report on the procedure followed to carry out uncertainty, sensitivity and variability analysis of the model response for a reference configuration that corresponds to a single family multi-zone house. We have obtained from the uncertainty analysis that, assuming a normal distribution of all the input parameters with a 10% relative standard deviation (R.S.D.), the model outputs present a R.S.D. in the range 17-22%. The sensitivity analysis reflects, in general, a good behaviour of the model, in the sense that its response describes a realistic behaviour of the system. The variability analysis has shown that the model is applicable to a wide range of situations, and that the most relevant parameters for the reference configuration are: the soil gas-permeability (obtained from the mean soil grain diameter); the ventilation rate of the rooms; the air-exchange rate between the basement and room 2; the soil-indoor pressure difference; the open area; and the concrete radium content.

Journal Article↗