Assurance methods for designing a clinical trial with a delayed treatment effect.

An assurance calculation is a Bayesian alternative to a power calculation. One may be performed to aid the planning of a clinical trial, specifically setting the sample size or to support decisions about whether or not to perform a study. Immuno-oncology is a rapidly evolving area in the development of anticancer drugs. A common phenomenon that arises in trials of such drugs is one of delayed treatment effects, that is, there is a delay in the separation of the survival curves. To calculate assurance for a trial in which a delayed treatment effect is likely to be present, uncertainty about key parameters needs to be considered. If uncertainty is not considered, the number of patients recruited may not be enough to ensure we have adequate statistical power to detect a clinically relevant treatment effect and the risk of an unsuccessful trial is increased. We present a new elicitation technique for when a delayed treatment effect is likely and show how to compute assurance using these elicited prior distributions. We provide an example to illustrate how this can be used in practice and develop open-source software to implement our methods. Our methodology has the potential to improve the success rate and efficiency of Phase III trials in immuno-oncology and for other treatments where a delayed treatment effect is expected to occur.

Calibrating cardiac electrophysiology models using latent Gaussian processes on atrial manifolds.

Models of electrical excitation and recovery in the heart have become increasingly detailed, but have yet to be used routinely in the clinical setting to guide personalized intervention in patients. One of the main challenges is calibrating models from the limited measurements that can be made in a patient during a standard clinical procedure. In this work, we propose a novel framework for the probabilistic calibration of electrophysiology parameters on the left atrium of the heart using local measurements of cardiac excitability. Parameter fields are represented as Gaussian processes on manifolds and are linked to measurements via surrogate functions that map from local parameter values to measurements. The posterior distribution of parameter fields is then obtained. We show that our method can recover parameter fields used to generate localised synthetic measurements of effective refractory period. Our methodology is applicable to other measurement types collected with clinical protocols, and more generally for calibration where model parameters vary over a manifold.

Response (minimum clinically relevant change) in ASD symptoms after an intervention according to CARS-2: consensus from an expert elicitation procedure.

The lack of consensual measures to monitor core change in Autism Spectrum Disorder (ASD) or response to interventions leads to difficulty to prove intervention efficacy on ASD core symptoms. There are no universally accepted outcome measures developed for measuring changes in core symptoms. However, the CARS (Childhood Autism Rating Scale) is one of the outcomes recommended in the EMA Guideline on the clinical development of medicinal products for the treatment of ASD. Unfortunately, there is currently no consensus on the response definition for CARS among individuals with ASD. The aim of this elicitation process was to determine an appropriate definition of a response on the CARS2 scale for interventions in patients with Autism Spectrum Disorder (ASD). An elicitation process was conducted following the Sheffield Elicitation Framework (SHELF). Five experts in the field of ASD and two experts in expert knowledge elicitation participated in an 1-day elicitation workshop. Experts in ASD were previously trained in the SHELF elicitation process and received a dossier of scientific evidence concerning the topic. The response definition was set as the mean clinically relevant improvement averaged over all patients, levels of functioning, age groups and clinicians. Based on the scientific evidence and expert judgment, a normal probability distribution was agreed to represent the state of knowledge of this response with expected value 4.03 and standard deviation 0.664. Considering the remaining uncertainty of the estimation and the available literature, a CARS-2 improvement of 4.5 points has been defined as a threshold to conclude to a response after an intervention. A CARS-2 improvement of 4.5 points could be used to evaluate interventions' meaningfulness in indivudals. This initial finding represents an important new benchmark and may aid decision makers in evaluating the efficacy of interventions in ASD.

Corrigendum: Bayesian Calibration of Electrophysiology Models Using Restitution Curve Emulators.

[This corrects the article DOI: 10.3389/fphys.2021.693015.].

Bayesian Calibration of Electrophysiology Models Using Restitution Curve Emulators.

Calibration of cardiac electrophysiology models is a fundamental aspect of model personalization for predicting the outcomes of cardiac therapies, simulation testing of device performance for a range of phenotypes, and for fundamental research into cardiac function. Restitution curves provide information on tissue function and can be measured using clinically feasible measurement protocols. We introduce novel "restitution curve emulators" as probabilistic models for performing model exploration, sensitivity analysis, and Bayesian calibration to noisy data. These emulators are built by decomposing restitution curves using principal component analysis and modeling the resulting coordinates with respect to model parameters using Gaussian processes. Restitution curve emulators can be used to study parameter identifiability via sensitivity analysis of restitution curve components and rapid inference of the posterior distribution of model parameters given noisy measurements. Posterior uncertainty about parameters is critical for making predictions from calibrated models, since many parameter settings can be consistent with measured data and yet produce very different model behaviors under conditions not effectively probed by the measurement protocols. Restitution curve emulators are therefore promising probabilistic tools for calibrating electrophysiology models.

Short to long term outcomes of 154 cemented total hip arthroplasties in ankylosing spondylitis.

BACKGROUND: Long-term outcome of Total Hip arthroplasty (THA) in Ankylosing Spondylitis (AS) remains unreported. Literature suggests a higher overall failure rate in ankylosing spondylitis as compared to osteoarthritis. Concern has been expressed regarding joint survival, given that recipients are generally young. The results of cemented THA in patients with ankylosing spondylitis were studied to determine the utility of THA for these patients. METHODS: Consecutive series of 96 patients (77 males (80%) and 19 females (20%)) with ankylosing spondylitis who underwent 154 cemented THAs at a tertiary referral orthopaedic centre between January 1990-September 2015 were retrospectively analyzed for clinical and radiological outcomes; 58 patients (60.4%) underwent bilateral surgery. RESULTS: Mean age at surgery was 48 years. Average follow up was 12.8 (2.1-24.8) years. 95% of the patients had a good or excellent post-operative outcome.Out of the total 154 hips operated on, 11% (17 hips) developed post-operative complications. Overall, 15 hips (9.7%) required a revision of the procedure, with the most common indication being aseptic loosening of the acetabulum. Average time to revision was 8.5 years (2-15). Survivorship analysis revealed probability of survival of both components at the end of 10 years, with revision due to any reason as the end point to be 92% (with 95% confidence intervals).21 hips (14%) developed heterotopic ossification post-operatively, of which 4 patients (2%) had clinically significant ossification (Brooker III or IV). CONCLUSION: This is one of the largest series of patients with ankylosing spondylitis with long term follow up available. Cemented THA in patients with ankylosing spondylitis provided consistently good and predictable long term results, with low rate of complications and revisions.

Assurance for clinical trial design with normally distributed outcomes: Eliciting uncertainty about variances.

The assurance method is growing in popularity in clinical trial planning. The method involves eliciting a prior distribution for the treatment effect, and then calculating the probability that a proposed trial will produce a "successful" outcome. For normally distributed observations, uncertainty about the variance of the normal distribution also needs to be accounted for, but there is little guidance in the literature on how to elicit a distribution for a variance parameter. We present a simple elicitation method, and illustrate how the elicited distribution is incorporated within an assurance calculation. We also consider multi-stage trials, where a decision to proceed with a larger trial will follow from the outcome of a smaller trial; we illustrate the role of the elicited distribution in assessing the information provided by a proposed smaller trial. Free software is available for implementing our methods.

Gaussian process manifold interpolation for probabilistic atrial activation maps and uncertain conduction velocity.

In patients with atrial fibrillation, local activation time (LAT) maps are routinely used for characterizing patient pathophysiology. The gradient of LAT maps can be used to calculate conduction velocity (CV), which directly relates to material conductivity and may provide an important measure of atrial substrate properties. Including uncertainty in CV calculations would help with interpreting the reliability of these measurements. Here, we build upon a recent insight into reduced-rank Gaussian processes (GPs) to perform probabilistic interpolation of uncertain LAT directly on human atrial manifolds. Our Gaussian process manifold interpolation (GPMI) method accounts for the topology of the atrium, and allows for calculation of statistics for predicted CV. We demonstrate our method on two clinical cases, and perform validation against a simulated ground truth. CV uncertainty depends on data density, wave propagation direction and CV magnitude. GPMI is suitable for probabilistic interpolation of other uncertain quantities on non-Euclidean manifolds. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Interventions to reduce the risk of surgically transmitted Creutzfeldt-Jakob disease: a cost-effective modelling review.

BACKGROUND: Creutzfeldt-Jakob disease is a fatal neurological disease caused by abnormal infectious proteins called prions. Prions that are present on surgical instruments cannot be completely deactivated; therefore, patients who are subsequently operated on using these instruments may become infected. This can result in surgically transmitted Creutzfeldt-Jakob disease. OBJECTIVE: To update literature reviews, consultation with experts and economic modelling published in 2006, and to provide the cost-effectiveness of strategies to reduce the risk of surgically transmitted Creutzfeldt-Jakob disease. METHODS: Eight systematic reviews were undertaken for clinical parameters. One review of cost-effectiveness was undertaken. Electronic databases including MEDLINE and EMBASE were searched from 2005 to 2017. Expert elicitation sessions were undertaken. An advisory committee, convened by the National Institute for Health and Care Excellence to produce guidance, provided an additional source of information. A mathematical model was updated focusing on brain and posterior eye surgery and neuroendoscopy. The model simulated both patients and instrument sets. Assuming that there were potentially 15 cases of surgically transmitted Creutzfeldt-Jakob disease between 2005 and 2018, approximate Bayesian computation was used to obtain samples from the posterior distribution of the model parameters to generate results. Heuristics were used to improve computational efficiency. The modelling conformed to the National Institute for Health and Care Excellence reference case. The strategies evaluated included neither keeping instruments moist nor prohibiting set migration; ensuring that instruments were kept moist; prohibiting instrument migration between sets; and employing single-use instruments. Threshold analyses were undertaken to establish prices at which single-use sets or completely effective decontamination solutions would be cost-effective. RESULTS: A total of 169 papers were identified for the clinical review. The evidence from published literature was not deemed sufficiently strong to take precedence over the distributions obtained from expert elicitation. Forty-eight papers were identified in the review of cost-effectiveness. The previous modelling structure was revised to add the possibility of misclassifying surgically transmitted Creutzfeldt-Jakob disease as another neurodegenerative disease, and assuming that all patients were susceptible to infection. Keeping instruments moist was estimated to reduce the risk of surgically transmitted Creutzfeldt-Jakob disease cases and associated costs. Based on probabilistic sensitivity analyses, keeping instruments moist was estimated to on average result in 2.36 (range 0-47) surgically transmitted Creutzfeldt-Jakob disease cases (across England) caused by infection occurring between 2019 and 2023. Prohibiting set migration or employing single-use instruments reduced the estimated risk of surgically transmitted Creutzfeldt-Jakob disease cases further, but at considerable cost. The estimated costs per quality-adjusted life-year gained of these strategies in addition to keeping instruments moist were in excess of £1M. It was estimated that single-use instrument sets (currently £350-500) or completely effective cleaning solutions would need to cost approximately £12 per patient to be cost-effective using a £30,000 per quality-adjusted life-year gained value. LIMITATIONS: As no direct published evidence to implicate surgery as a cause of Creutzfeldt-Jakob disease has been found since 2005, the estimations of potential cases from elicitation are still speculative. A particular source of uncertainty was in the number of potential surgically transmitted Creutzfeldt-Jakob disease cases that may have occurred between 2005 and 2018. CONCLUSIONS: Keeping instruments moist is estimated to reduce the risk of surgically transmitted Creutzfeldt-Jakob disease cases and associated costs. Further surgical management strategies can reduce the risks of surgically transmitted Creutzfeldt-Jakob disease but have considerable associated costs. STUDY REGISTRATION: This study is registered as PROSPERO CRD42017071807. FUNDING: This project was funded by the National Institute for Health Research (NIHR) Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 24, No. 11. See the NIHR Journals Library website for further project information.

The aims of this report were to summarise evidence relating to surgically transmitted Creutzfeldt­Jakob disease and to explore the value for money of strategies to reduce the chance of any future surgically transmitted Creutzfeldt­Jakob disease cases. Current recommendations include keeping sets of surgical instruments together for high-risk operations and using separate instruments for people born after 1996. The project involved reviewing published papers, speaking with experts and building a computer model. The literature reviews found that Creutzfeldt­Jakob disease occurs in around 1­2 per million people and that no definite cases of surgically transmitted Creutzfeldt­Jakob disease have been observed since the 1970s. The reviews also looked for information on the possibility of patients being infected with Creutzfeldt­Jakob disease after having surgery on high-risk tissues, such as the brain and the back of the eye. They found that there was a great deal of uncertainty regarding who might have Creutzfeldt­Jakob disease, but not yet have symptoms, as well as the risk of transmission and the ability of strategies to reduce this risk. The computer model aimed to estimate value for money of different strategies to reduce the risks of surgically transmitted Creutzfeldt­Jakob disease. However, the reviews found that some of the numbers needed for the model were not known, so experts were asked to estimate this information instead along with the range of possible values. This information included the effectiveness of different cleaning practices and the chances of infected tissue being transmitted between patients undergoing high-risk surgery. The model found that keeping surgical instruments moist prior to cleaning was likely to save money and reduce the chance of future surgically transmitted Creutzfeldt­Jakob disease cases. However, additional measures, such as using only sets of single-use instruments, ensuring that instruments were kept together in their sets or using separate instruments for those born after 1996, appeared to be poor value for money.

Quantifying atrial anatomy uncertainty from clinical data and its impact on electro-physiology simulation predictions.

Patient-specific computational models of structure and function are increasingly being used to diagnose disease and predict how a patient will respond to therapy. Models of anatomy are often derived after segmentation of clinical images or from mapping systems which are affected by image artefacts, resolution and contrast. Quantifying the impact of uncertain anatomy on model predictions is important, as models are increasingly used in clinical practice where decisions need to be made regardless of image quality. We use a Bayesian probabilistic approach to estimate the anatomy and to quantify the uncertainty about the shape of the left atrium derived from Cardiac Magnetic Resonance images. We show that we can quantify uncertain shape, encode uncertainty about the left atrial shape due to imaging artefacts, and quantify the effect of uncertain shape on simulations of left atrial activation times.

Probabilistic Interpolation of Uncertain Local Activation Times on Human Atrial Manifolds.

OBJECTIVE: Local activation time (LAT) mapping of the atria is important for targeted treatment of atrial arrhythmias, but current methods do not interpolate on the atrial manifold and neglect uncertainties associated with LAT observations. In this paper, we describe novel methods to, first, quantify uncertainties in LAT arising from bipolar electrogram analysis and assignment of electrode recordings to the anatomical mesh, second, interpolate uncertain LAT measurements directly on left atrial manifolds to obtain complete probabilistic activation maps, and finally, interpolate LAT jointly across both the manifold and different S1-S2 pacing protocols. METHODS: A modified center of mass approach was used to process bipolar electrograms, yielding a LAT estimate and error distribution from the electrogram morphology. An error distribution for assigning measurements to the anatomical mesh was estimated. Probabilistic LAT maps were produced by interpolating on a left atrial manifold using Gaussian Markov random fields, taking into account observation errors and characterizing LAT predictions by their mean and standard deviation. This approach was extended to interpolate across S1-S2 pacing protocols. RESULTS: We evaluated our approach using recordings from three patients undergoing atrial ablation. Cross-validation showed consistent and accurate prediction of LAT observations both at different locations on the left atrium and for different S1-S2 intervals. SIGNIFICANCE: Interpolation of scalar and vector fields across anatomical structures from point measurements is a challenging problem in biomedical engineering, compounded by uncertainties in measurements and meshes. New methods and approaches are required, and in this paper, we have demonstrated an effective method for probabilistic interpolation of uncertain LAT.

Choice of time horizon critical in estimating costs and effects of changes to HIV programmes.

BACKGROUND: Uganda changed its antiretroviral therapy guidelines in 2014, increasing the CD4 threshold for antiretroviral therapy initiation from 350 cells/µl to 500 cells/µl. We investigate what effect this change in policy is likely to have on HIV incidence, morbidity, and programme costs, and estimate the cost-effectiveness of the change over different time horizons. METHODS: We used a complex individual-based model of HIV transmission and antiretroviral therapy scale-up in Uganda. 100 model fits were generated by fitting the model to 51 demographic, sexual behaviour, and epidemiological calibration targets, varying 96 input parameters, using history matching with model emulation. An additional 19 cost and disability weight parameters were varied during the analysis of the model results. For each model fit, the model was run to 2030, with and without the change in threshold to 500 cells/µl. RESULTS: The change in threshold led to a 9.7% (90% plausible range: 4.3%-15.0%) reduction in incidence in 2030, and averted 278,944 (118,452-502,790) DALYs, at a total cost of $28M (-$142M to +$195M). The cost per disability adjusted life year (DALY) averted fell over time, from $3238 (-$125 to +$29,969) in 2014 to $100 (-$499 to +$785) in 2030. The change in threshold was cost-effective (cost <3×Uganda's per capita GDP per DALY averted) by 2018, and highly cost-effective (cost

Incorporating Genuine Prior Information about Between-Study Heterogeneity in Random Effects Pairwise and Network Meta-analyses.

BACKGROUND: Pairwise and network meta-analyses using fixed effect and random effects models are commonly applied to synthesize evidence from randomized controlled trials. The models differ in their assumptions and the interpretation of the results. The model choice depends on the objective of the analysis and knowledge of the included studies. Fixed effect models are often used because there are too few studies with which to estimate the between-study SD from the data alone. OBJECTIVES: The aim of this study was to propose a framework for eliciting an informative prior distribution for the between-study SD in a Bayesian random effects meta-analysis model to genuinely represent heterogeneity when data are sparse. METHODS: We developed an elicitation method using external information, such as empirical evidence and expert beliefs, on the "range" of treatment effects to infer the prior distribution for the between-study SD. We also developed the method to be implemented in R. RESULTS: The 3-stage elicitation approach allows uncertainty to be represented by a genuine prior distribution to avoid making misleading inferences. It is flexible to what judgments an expert can provide and is applicable to all types of outcome measures for which a treatment effect can be constructed on an additive scale. CONCLUSIONS: The choice between using a fixed effect or random effects meta-analysis model depends on the inferences required and not on the number of available studies. Our elicitation framework captures external evidence about heterogeneity and overcomes the assumption that studies are estimating the same treatment effect, thereby improving the quality of inferences in decision making.

Improving ART programme retention and viral suppression are key to maximising impact of treatment as prevention - a modelling study.

BACKGROUND: UNAIDS calls for fewer than 500,000 new HIV infections/year by 2020, with treatment-as-prevention being a key part of their strategy for achieving the target. A better understanding of the contribution to transmission of people at different stages of the care pathway can help focus intervention services at populations where they may have the greatest effect. We investigate this using Uganda as a case study. METHODS: An individual-based HIV/ART model was fitted using history matching. 100 model fits were generated to account for uncertainties in sexual behaviour, HIV epidemiology, and ART coverage up to 2015 in Uganda. A number of different ART scale-up intervention scenarios were simulated between 2016 and 2030. The incidence and proportion of transmission over time from people with primary infection, post-primary ART-naïve infection, and people currently or previously on ART was calculated. RESULTS: In all scenarios, the proportion of transmission by ART-naïve people decreases, from 70% (61%-79%) in 2015 to between 23% (15%-40%) and 47% (35%-61%) in 2030. The proportion of transmission by people on ART increases from 7.8% (3.5%-13%) to between 14% (7.0%-24%) and 38% (21%-55%). The proportion of transmission by ART dropouts increases from 22% (15%-33%) to between 31% (23%-43%) and 56% (43%-70%). CONCLUSIONS: People who are currently or previously on ART are likely to play an increasingly large role in transmission as ART coverage increases in Uganda. Improving retention on ART, and ensuring that people on ART remain virally suppressed, will be key in reducing HIV incidence in Uganda.

Universal test, treat, and keep: improving ART retention is key in cost-effective HIV control in Uganda.

BACKGROUND: With ambitious new UNAIDS targets to end AIDS by 2030, and new WHO treatment guidelines, there is increased interest in the best way to scale-up ART coverage. We investigate the cost-effectiveness of various ART scale-up options in Uganda. METHODS: Individual-based HIV/ART model of Uganda, calibrated using history matching. 22 ART scale-up strategies were simulated from 2016 to 2030, comprising different combinations of six single interventions (1. increased HIV testing rates, 2. no CD4 threshold for ART initiation, 3. improved ART retention, 4. increased ART restart rates, 5. improved linkage to care, 6. improved pre-ART care). The incremental net monetary benefit (NMB) of each intervention was calculated, for a wide range of different willingness/ability to pay (WTP) per DALY averted (health-service perspective, 3% discount rate). RESULTS: For all WTP thresholds above $210, interventions including removing the CD4 threshold were likely to be most cost-effective. At a WTP of $715 (1 × per-capita-GDP) interventions to improve linkage to and retention/re-enrolment in HIV care were highly likely to be more cost-effective than interventions to increase rates of HIV testing. At higher WTP (> ~ $1690), the most cost-effective option was 'Universal Test, Treat, and Keep' (UTTK), which combines interventions 1-5 detailed above. CONCLUSIONS: Our results support new WHO guidelines to remove the CD4 threshold for ART initiation in Uganda. With additional resources, this could be supplemented with interventions aimed at improving linkage to and/or retention in HIV care. To achieve the greatest reductions in HIV incidence, a UTTK policy should be implemented.

Estimating the Expected Value of Sample Information Using the Probabilistic Sensitivity Analysis Sample: A Fast, Nonparametric Regression-Based Method.

Health economic decision-analytic models are used to estimate the expected net benefits of competing decision options. The true values of the input parameters of such models are rarely known with certainty, and it is often useful to quantify the value to the decision maker of reducing uncertainty through collecting new data. In the context of a particular decision problem, the value of a proposed research design can be quantified by its expected value of sample information (EVSI). EVSI is commonly estimated via a 2-level Monte Carlo procedure in which plausible data sets are generated in an outer loop, and then, conditional on these, the parameters of the decision model are updated via Bayes rule and sampled in an inner loop. At each iteration of the inner loop, the decision model is evaluated. This is computationally demanding and may be difficult if the posterior distribution of the model parameters conditional on sampled data is hard to sample from. We describe a fast nonparametric regression-based method for estimating per-patient EVSI that requires only the probabilistic sensitivity analysis sample (i.e., the set of samples drawn from the joint distribution of the parameters and the corresponding net benefits). The method avoids the need to sample from the posterior distributions of the parameters and avoids the need to rerun the model. The only requirement is that sample data sets can be generated. The method is applicable with a model of any complexity and with any specification of model parameter distribution. We demonstrate in a case study the superior efficiency of the regression method over the 2-level Monte Carlo method.

Bayesian history matching of complex infectious disease models using emulation: a tutorial and a case study on HIV in Uganda.

Advances in scientific computing have allowed the development of complex models that are being routinely applied to problems in disease epidemiology, public health and decision making. The utility of these models depends in part on how well they can reproduce empirical data. However, fitting such models to real world data is greatly hindered both by large numbers of input and output parameters, and by long run times, such that many modelling studies lack a formal calibration methodology. We present a novel method that has the potential to improve the calibration of complex infectious disease models (hereafter called simulators). We present this in the form of a tutorial and a case study where we history match a dynamic, event-driven, individual-based stochastic HIV simulator, using extensive demographic, behavioural and epidemiological data available from Uganda. The tutorial describes history matching and emulation. History matching is an iterative procedure that reduces the simulator's input space by identifying and discarding areas that are unlikely to provide a good match to the empirical data. History matching relies on the computational efficiency of a Bayesian representation of the simulator, known as an emulator. Emulators mimic the simulator's behaviour, but are often several orders of magnitude faster to evaluate. In the case study, we use a 22 input simulator, fitting its 18 outputs simultaneously. After 9 iterations of history matching, a non-implausible region of the simulator input space was identified that was 10(11) times smaller than the original input space. Simulator evaluations made within this region were found to have a 65% probability of fitting all 18 outputs. History matching and emulation are useful additions to the toolbox of infectious disease modellers. Further research is required to explicitly address the stochastic nature of the simulator as well as to account for correlations between outputs.

Assurance calculations for planning clinical trials with time-to-event outcomes.

We consider the use of the assurance method in clinical trial planning. In the assurance method, which is an alternative to a power calculation, we calculate the probability of a clinical trial resulting in a successful outcome, via eliciting a prior probability distribution about the relevant treatment effect. This is typically a hybrid Bayesian-frequentist procedure, in that it is usually assumed that the trial data will be analysed using a frequentist hypothesis test, so that the prior distribution is only used to calculate the probability of observing the desired outcome in the frequentist test. We argue that assessing the probability of a successful clinical trial is a useful part of the trial planning process. We develop assurance methods to accommodate survival outcome measures, assuming both parametric and nonparametric models. We also develop prior elicitation procedures for each survival model so that the assurance calculations can be performed more easily and reliably. We have made free software available for implementing our methods.

Estimating multiparameter partial expected value of perfect information from a probabilistic sensitivity analysis sample: a nonparametric regression approach.

The partial expected value of perfect information (EVPI) quantifies the expected benefit of learning the values of uncertain parameters in a decision model. Partial EVPI is commonly estimated via a 2-level Monte Carlo procedure in which parameters of interest are sampled in an outer loop, and then conditional on these, the remaining parameters are sampled in an inner loop. This is computationally demanding and may be difficult if correlation between input parameters results in conditional distributions that are hard to sample from. We describe a novel nonparametric regression-based method for estimating partial EVPI that requires only the probabilistic sensitivity analysis sample (i.e., the set of samples drawn from the joint distribution of the parameters and the corresponding net benefits). The method is applicable in a model of any complexity and with any specification of input parameter distribution. We describe the implementation of the method via 2 nonparametric regression modeling approaches, the Generalized Additive Model and the Gaussian process. We demonstrate in 2 case studies the superior efficiency of the regression method over the 2-level Monte Carlo method. R code is made available to implement the method.