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The case for stratified cost-effectiveness analysis by baseline health-related QOL: theory and sensitivity analysis.

The purpose of this paper is to argue that systematic data heterogeneity exists when the objective of pharmacotherapy is improved health-related quality of life (HR-QOL), and that the pharmacotherapy's cost effectiveness will vary inversely with the patient's baseline HR-QOL (BHR-QOL), the patient's HR-QOL just prior to treatment. It is argued that when improved HR-QOL is the primary objective of a pharmacotherapy, the magnitude of the HR-QOL response to treatment may be negatively correlated with BHR-QOL and that the net cost of the pharmacotherapy may be positively correlated with BHR-QOL. It is also argued that the value placed on a given increment in HR-QOL declines as BHR-QOL rises. The case for sample stratification by BHR-QOL, and for conducting cost-effectiveness analysis (CEA) at the stratum level, is illustrated with numerical examples using hypothetical data and the incremental net monetary benefit (INMB) criterion. Sensitivity analysis is used to explore the response of the INMB at the stratum level to different degrees of data heterogeneity across the BHR-QOL strata. This paper demonstrates that because of cumulative effects, even relatively minor data heterogeneity related to BHR-QOL results in substantial differences in the cost effectiveness of treatments across BHR-QOL strata. CEA stratified by BHR-QOL enables a more efficient and equitable allocation of public healthcare funding than standard cost-effectiveness screening of pharmaceutical drugs based on full-sample averages.

Cost-Benefit Analysis↗

A graphical sensitivity analysis for clinical trials with non-ignorable missing binary outcome.

Many clinical trials are analysed using an intention-to-treat (ITT) approach. A full application of the ITT approach is only possible when complete outcome data are available for all randomized subjects. In a recent survey of clinical trial reports including an ITT analysis, complete case analysis (excluding all patients with a missing response) was common. This does not comply with the basic principles of ITT since not all randomized subjects are included in the analysis. Analyses of data with missing values are based on untestable assumptions, and so sensitivity analysis presenting a range of estimates under alternative assumptions about the missing-data mechanism is recommended. For binary outcome, extreme case analysis has been suggested as a simple form of sensitivity analysis, but this is rarely conclusive. A graphical sensitivity analysis is proposed which displays the results of all possible allocations of cases with missing binary outcome. Extension to allow binomial variation in outcome is also considered. The display is based on easily interpretable parameters and allows informal examination of the effects of varying prior beliefs.

Angioplasty, Balloon, Coronary↗

Sensitivity analysis and calibration of the parameters of ESWAT: application to the River Dender.

The paper deals with the sensitivity analysis and parameter calibration of a complex river water quality model, implemented in ESWAT. The Extended SWAT includes a QUALIIE-based river quality simulator, in view of an integrated analysis of water quantity and quality management practises. The sensitivity analysis uses Latin Hypercube Sampling and criteria related to the duration of low concentrations of dissolved oxygen and the occurrence of high algae concentrations. The analysis on the river Dender shows that parameters related to the growth and die-off of the algae have the largest impact, while also the BOD decay constant and the benthic oxygen demand are important. A subsequent calibration of these most important parameters shows however that the optimal values of the parameters related to the activity of the algae are statistically not significant. This apparent contradiction is due to the poor information content of the measurements. It is concluded that the application illustrates the complementarity of the sensitivity analysis and the parameter calibration.

Belgium↗

Evidence synthesis, parameter correlation and probabilistic sensitivity analysis.

Over the last decade or so, there have been many developments in methods to handle uncertainty in cost-effectiveness studies. In decision modelling, it is widely accepted that there needs to be an assessment of how sensitive the decision is to uncertainty in parameter values. The rationale for probabilistic sensitivity analysis (PSA) is primarily based on a consideration of the needs of decision makers in assessing the consequences of decision uncertainty. In this paper, we highlight some further compelling reasons for adopting probabilistic methods for decision modelling and sensitivity analysis, and specifically for adopting simulation from a Bayesian posterior distribution. Our reasoning is as follows. Firstly, cost-effectiveness analyses need to be based on all the available evidence, not a selected subset, and the uncertainties in the data need to be propagated through the model in order to provide a correct analysis of the uncertainties in the decision. In many--perhaps most--cases the evidence structure requires a statistical analysis that inevitably induces correlations between parameters. Deterministic sensitivity analysis requires that models are run with parameters fixed at 'extreme' values, but where parameter correlation exists it is not possible to identify sets of parameter values that can be considered 'extreme' in a meaningful sense. However, a correct probabilistic analysis can be readily achieved by Monte Carlo sampling from the joint posterior distribution of parameters. In this paper, we review some evidence structures commonly occurring in decision models, where analyses that correctly reflect the uncertainty in the data induce correlations between parameters. Frequently, this is because the evidence base includes information on functions of several parameters. It follows that, if health technology assessments are to be based on a correct analysis of all available data, then probabilistic methods must be used both for sensitivity analysis and for estimation of expected costs and benefits.

Bayes Theorem↗

Addressing uncertainty in medical cost-effectiveness analysis implications of expected utility maximization for methods to perform sensitivity analysis and the use of cost-effectiveness analysis to set priorities for medical research.

This paper examines the objectives for performing sensitivity analysis in medical cost-effectiveness analysis and the implications of expected utility maximization for methods to perform such analyses. The analysis suggests specific approaches for optimal decision making under uncertainty and specifying such decisions for subgroups based on the ratio of expected costs to expected benefits, and for valuing research using value of information calculations. Though ideal value of information calculations may be difficult, certain approaches with less stringent data requirements may bound the value of information. These approaches suggest methods by which the vast cost-effectiveness literature may help inform priorities for medical research.

Cost-Benefit Analysis↗

Evaluation and recommendation of sensitivity analysis methods for application to Stochastic Human Exposure and Dose Simulation models.

Sensitivity analyses of exposure or risk models can help identify the most significant factors to aid in risk management or to prioritize additional research to reduce uncertainty in the estimates. However, sensitivity analysis is challenged by non-linearity, interactions between inputs, and multiple days or time scales. Selected sensitivity analysis methods are evaluated with respect to their applicability to human exposure models with such features using a testbed. The testbed is a simplified version of a US Environmental Protection Agency's Stochastic Human Exposure and Dose Simulation (SHEDS) model. The methods evaluated include the Pearson and Spearman correlation, sample and rank regression, analysis of variance, Fourier amplitude sensitivity test (FAST), and Sobol's method. The first five methods are known as "sampling-based" techniques, wheras the latter two methods are known as "variance-based" techniques. The main objective of the test cases was to identify the main and total contributions of individual inputs to the output variance. Sobol's method and FAST directly quantified these measures of sensitivity. Results show that sensitivity of an input typically changed when evaluated under different time scales (e.g., daily versus monthly). All methods provided similar insights regarding less important inputs; however, Sobol's method and FAST provided more robust insights with respect to sensitivity of important inputs compared to the sampling-based techniques. Thus, the sampling-based methods can be used in a screening step to identify unimportant inputs, followed by application of more computationally intensive refined methods to a smaller set of inputs. The implications of time variation in sensitivity results for risk management are briefly discussed.

Analysis of Variance↗

Sensitivity analysis of biological models.

An inhomogenous linear model of the lung mechanics system was selected for the demonstration of one of the methods of sensitivity analysis. Given the values of state variables, the sensitivity of the model makes possible a safe adjustment of coefficients, without leading to large errors of solution with even a small deviation in adjustment. Any mathematical model only represents a picture of basic and substantial dynamic properties and relations of a real object. By means of sensitivity analysis it is possible to obtain a faithful description of the real object's behavior by computing the simplest model solution, with knowing at the same time, by sensitivity analysis, the range of errors introduced by simplifications and approximations.

Computers↗

Technical needs assessment: UWMC's sensitivity analysis guides decision-making.

In today's healthcare market, it is critical for provider institutions to offer the latest and best technological services while remaining fiscally sound. In academic practices, like the University of Washington Medical Center (UWMC), there are the added responsibilities of teaching and research that require a high-tech environment to thrive. These conditions and needs require extensive analysis of not only what equipment to buy, but also when and how it should be acquired. In an organization like the UWMC, which has strategically positioned itself for growth, it is useful to build a sensitivity analysis based on the strategic plan. A common forecasting tool, the sensitivity analysis lays out existing and projected business operations with volume assumptions displayed in layers. Each layer of current and projected activity is plotted over time and placed against a background depicting the capacity of the key modality. Key elements of a sensitivity analysis include necessity, economic assessment, performance, compatibility, reliability, service and training. There are two major triggers that cause us to consider the purchase of new imaging equipment and that determine how to evaluate the equipment we buy. One trigger revolves around our ability to serve patients by seeing them on a timely basis. If we find a significant gap between demand and our capacity to meet it, or anticipate a greater increased demand based upon trends, we begin to consider enhancing that capacity. A second trigger is the release of a breakthrough or substantially improved technology that will clearly have a positive impact on clinical efficacy and efficiency, thereby benefiting the patient. Especially in radiology departments, where many technologies require large expenditures, it is no longer acceptable simply to spend on new and improved technologies. It is necessary to justify them as a strong investment in clinical management and efficacy. There is pressure to provide "proof" at the department level and beyond. By applying sensitivity analysis and other forecasting methods, we are able to spend our resources judiciously in order to get the equipment we need when we need it. This helps ensure that we have efficacious, efficient systems--and enough of them--so that our patients are examined on a timely basis and our clinics run smoothly. It also goes a long way toward making certain that the best equipment is available to our clinicians, researchers, students and patients alike.

Academic Medical Centers↗

Application of classification and regression trees for sensitivity analysis of the Escherichia coli O157:H7 food safety process risk model.

Microbial food safety process risk models are simplifications of the real world that help risk managers in their efforts to mitigate food safety risks. An important tool in these risk assessment endeavors is sensitivity analysis, a systematic method used to quantify the effect of changes in input variables on model outputs. In this study, a novel sensitivity analysis method called classification and regression trees was applied to safety risk assessment with the use of portions of the Slaughter Module and Preparation Module of the E. coli O157:H7 microbial food safety process risk as an example. Specifically, the classification and regression trees sensitivity analysis method was evaluated on the basis of its ability to address typical characteristics of microbial food safety process risk models such as nonlinearities, interaction, thresholds, and categorical inputs. Moreover, this method was evaluated with respect to identification of high exposure scenarios and corresponding key inputs and critical limits. The results from the classification and regression trees analysis applied to the Slaughter Module confirmed that the process of chilling carcasses is a critical control point. The method identified a cutoff value of a 2.2-log increase in the number of organisms during chilling as a critical value above which high levels of contamination would be expected. When classification and regression trees analysis was applied to the cooking effects part of the Preparation Module, cooking temperature was found to be the most sensitive input, with precooking treatment (i.e., raw product storage conditions) ranked second in importance. This case study demonstrates the capabilities of classification and regression trees analysis as an alternative to other statistically based sensitivity analysis methods, and one that can readily address specific characteristics that are common in microbial food safety process risk models.

Consumer Product Safety↗

Bayesian sensitivity analysis for unmeasured confounding in observational studies.

We consider Bayesian sensitivity analysis for unmeasured confounding in observational studies where the association between a binary exposure, binary response, measured confounders and a single binary unmeasured confounder can be formulated using logistic regression models. A model for unmeasured confounding is presented along with a family of prior distributions that model beliefs about a possible unknown unmeasured confounder. Simulation from the posterior distribution is accomplished using Markov chain Monte Carlo. Because the model for unmeasured confounding is not identifiable, standard large-sample theory for Bayesian analysis is not applicable. Consequently, the impact of different choices of prior distributions on the coverage probability of credible intervals is unknown. Using simulations, we investigate the coverage probability when averaged with respect to various distributions over the parameter space. The results indicate that credible intervals will have approximately nominal coverage probability, on average, when the prior distribution used for sensitivity analysis approximates the sampling distribution of model parameters in a hypothetical sequence of observational studies. We motivate the method in a study of the effectiveness of beta blocker therapy for treatment of heart failure.

Adrenergic beta-Antagonists↗

Early assessment of the likely cost-effectiveness of a new technology: A Markov model with probabilistic sensitivity analysis of computer-assisted total knee replacement.

OBJECTIVES: The objective of this study is to apply a Markov model to compare cost-effectiveness of total knee replacement (TKR) using computer-assisted surgery (CAS) with that of TKR using a conventional manual method in the absence of formal clinical trial evidence. METHODS: A structured search was carried out to identify evidence relating to the clinical outcome, cost, and effectiveness of TKR. Nine Markov states were identified based on the progress of the disease after TKR. Effectiveness was expressed by quality-adjusted life years (QALYs). The simulation was carried out initially for 120 cycles of a month each, starting with 1,000 TKRs. A discount rate of 3.5 percent was used for both cost and effectiveness in the incremental cost-effectiveness analysis. Then, a probabilistic sensitivity analysis was carried out using a Monte Carlo approach with 10,000 iterations. RESULTS: Computer-assisted TKR was a long-term cost-effective technology, but the QALYs gained were small. After the first 2 years, the incremental cost per QALY of computer-assisted TKR was dominant because of cheaper and more QALYs. The incremental cost-effectiveness ratio (ICER) was sensitive to the "effect of CAS," to the CAS extra cost, and to the utility of the state "Normal health after primary TKR," but it was not sensitive to utilities of other Markov states. Both probabilistic and deterministic analyses produced similar cumulative serious or minor complication rates and complex or simple revision rates. They also produced similar ICERs. CONCLUSIONS: Compared with conventional TKR, computer-assisted TKR is a cost-saving technology in the long-term and may offer small additional QALYs. The "effect of CAS" is to reduce revision rates and complications through more accurate and precise alignment, and although the conclusions from the model, even when allowing for a full probabilistic analysis of uncertainty, are clear, the "effect of CAS" on the rate of revisions awaits long-term clinical evidence.

Arthroplasty, Replacement, Knee↗

Time-dependent sensitivity analysis of biological networks: coupled MAPK and PI3K signal transduction pathways.

Sensitivity analysis has been widely used in the studies of complicated chemical reaction and biological networks, for example, in combustion studies and metabolic control analysis of pathways. In the latter cases, the responses of system properties at steady states with respect to changes of parameters, such as initial concentrations and rate constants, are often expressed as sensitivities. Besides steady-state sensitivities, time-dependent sensitivities should be useful; however, the explicit use of them in analyzing complicated biological systems has so far been limited. Using the coupled mitogen activated protein kinase (MAPK)-phophatidylinoisitol 3'-kinase (PI3K) system of the Ras pathways, known to be involved in about 30% of human cancers, as an example, we show that time-dependent sensitivities are useful for the studies of complex biological systems. They provide, for example, the following information: (a) multiple time scales existing in a complex system involving cross-talks and feedback loops; (b) the signs and strengths of responses to perturbations (as system complication increases, the signs of global responses are not always easily determined; for example, response may change sign more than once as time evolves); (c) beyond concentration dynamics, sensitivities revealing further details about the intricate dynamics and the effects of the cross-talks; (d) ranking of vulnerability of nodes of a biological network using integrated sensitivity-a first step toward the identification of drug targets; (e) reduced sensitivity serving as a measure of the stability or robustness of pathways. Our results indicate that the role of the PI3K branch in the coupled pathways is to enhance the robustness of the MAPK pathway. More importantly, they demonstrate that time-dependent sensitivity analysis can be a valuable tool in system biology.

Mitogen-Activated Protein Kinases↗

Continuous hybridoma bioreactor: sensitivity analysis and optimal control.

Animal cell culture has already established itself as a mature technology able to make a wide range of valuable products, the actual focus being to find the competitive bioreactor design and operating conditions for increasing production. A complex analysis, implying sensitivity calculus and optimal control computation, is done for a system composed of a continuous perfectly mixed bioreactor, with cell recirculation, a cell separator, a mixer and a purge. The bioreactor's sensitivity to the control parameters is measured by a new concept, entropic density, developed from the notion of Shannon entropy. An optimization procedure based on a genetic-algorithms approach is applied for the computation of the inlet flow profile in time, which guarantees optimum monoclonal-antibody production. Our studies, including the present one, proved that the best approach to obtain high production is to use a hybrid operating sequence: fed-batch mode followed by the continuous mode.

Antibodies, Monoclonal↗

A sensitivity analysis of a randomized controlled trial of zinc in treatment of falciparum malaria in children.

BACKGROUND: The randomized trial has long been recognized as a means to assess the efficacy of new interventions, because the investigator can reduce or eliminate many sources of error. As such, clinical trials often do not include quantitative assessments of the extent that systematic error could affect their results. We examined the impact of different sources of bias on a randomized controlled trial of the efficacy of zinc as an adjuvant to malaria therapy in reducing time to total parasite clearance. METHODS: Using data from a previously published study, we identified two sources of bias and used the sensitivity analysis technique developed by Lash and Fink to assess the impact of each source of bias on the outcome. RESULTS: After correcting for each source of bias and reincorporating random error into our results, the point estimate of effect comparing those who received placebo to those who received zinc changed slightly (SMR changed from 0.92 to 0.90) but the 95% interval increased 22% (changing from 0.73-1.16 in the conventional analysis to 0.65-1.26 in the sensitivity analysis). CONCLUSIONS: The findings of this sensitivity analysis serve as a reminder that the frequentist confidence interval underestimates the total error, even in a randomized controlled trial. Authors of randomized controlled trial investigations ought to conduct a complete assessment of the impact of potential sources of bias in their studies. CONSORT guidelines for reporting trial results should be updated to encourage authors to assess the impact of non-random errors on their studies.

Antimalarials↗

Using sensitivity analysis to validate the predictions of a biomechanical model of bite forces.

Biomechanical modelling has become a very popular technique for investigating functional anatomy. Modern computer simulation packages make producing such models straightforward and it is tempting to take the results produced at face value. However the predictions of a simulation are only valid when both the model and the input parameters are accurate and little work has been done to verify this. In this paper a model of the human jaw is produced and a sensitivity analysis is performed to validate the results. The model is built using the ADAMS multibody dynamic simulation package incorporating the major occlusive muscles of mastication (temporalis, masseter, medial and lateral pterygoids) as well as a highly mobile temporomandibular joint. This model is used to predict the peak three-dimensional bite forces at each teeth location, joint reaction forces, and the contributions made by each individual muscle. The results for occlusive bite-force (1080N at M1) match those previously published suggesting the model is valid. The sensitivity analysis was performed by sampling the input parameters from likely ranges and running the simulation many times rather than using single, best estimate values. This analysis shows that the magnitudes of the peak retractive forces on the lower teeth were highly sensitive to the chosen origin (and hence fibre direction) of the temporalis and masseter muscles as well as the laxity of the TMJ. Peak protrusive force was also sensitive to the masseter origin. These result shows that the model is insufficiently complex to estimate these values reliably although the much lower sensitivity values obtained for the bite forces in the other directions and also for the joint reaction forces suggest that these predictions are sound. Without the sensitivity analysis it would not have been possible to identify these weaknesses which strongly supports the use of sensitivity analysis as a validation technique for biomechanical modelling.

Anatomy↗

Sensitivity analysis in health economic and pharmacoeconomic studies. An appraisal of the literature.

The objective of this study was to analyse the extent of reporting of sensitivity analyses in the health economics, medical and pharmacy literature between journal types and over time. 90 articles were chosen from each of the bodies of literature on health economics, medicine and pharmacy. MEDLINE, EMBASE and International Pharmaceutical Abstracts were searched for English-language economic studies published between 1989 and 1993. The studies chosen for inclusion had to be original articles published in one of the selected journals between January 1989 and December 1993, involving a comparison between drugs, treatments or services, and evaluating both costs and outcomes. 123 articles initially met these criteria; however, 16 were inappropriate, 17 were randomised out, leaving 90 studies (73%) that were used (30 from each literature group). Data were extracted independently by 5 raters using a validated checklist. Inter-rater reliability was assessed by calculating kappa. 53 of the 90 articles (59%) conducted sensitivity analyses. 39 (74%) stated explicitly that a sensitivity analysis was being performed; this was noted in the Methods section of 35 papers (67%). 80% of health economics journals, 70% of medical journals and 20% of pharmacy journals conducted sensitivity analyses. Despite the fact that all published pharmacoeconomic guidelines suggest the use of sensitivity analysis, only 59% of studies between 1989 and 1993 did so. Improvement is required, especially in the pharmacy literature. No time trends in the conduct of sensitivity analyses were detected. However, the sample may not have been sufficient to detect such trends. Pharmacoeconomic guidelines should provide more details on preferred methods of sensitivity analysis and on desired parameters.

Economics, Pharmaceutical↗

Sensitivity analysis of a nonlinear lumped parameter model of HIV infection dynamics.

A formal sensitivity analysis is performed on a delay differential equation model for the viral dynamics of an in vivo HIV infection during protease inhibitor therapy. We present results of both a differential analysis as well as a principle component based analysis and provide evidence that suggests the exact times at which specific parameters have the most influence over the solution. We offer insight into the pairwise mathematical relationships between the productively infected T-cell death rate delta, the viral plasma clearance rate c, and the time delay tau between infection and viral production as they relate to the viral dynamics. The results support the claim that the presence of a nonzero delay has a major impact on the model dynamics. Lastly, we comment upon the inadequacies of an alternative principle component based analysis.

Computer Simulation↗