High-Order Deterministic Sensitivity Analysis and Uncertainty Quantification: Review and New Developments

This work reviews the state-of-the-art methodologies for the deterministic sensitivity analysis of nonlinear systems and deterministic quantification of uncertainties induced in model responses by uncertainties in the model parameters. The need for computing high-order sensitivities is underscored by presenting an analytically solvable model of neutron scattering in a hydrogenous medium, for which all of the response’s relative sensitivities have the same absolute value of unity. It is shown that the wider the distribution of model parameters, the higher the order of sensitivities needed to achieve a desired level of accuracy in representing the response and in computing the response’s expectation, variance, skewness and kurtosis. This work also presents new mathematical expressions that extend to the sixth-order of the current state-of-the-art fourth-order formulas for computing fourth-order correlations among computed model response and model parameters. Another novelty presented in this work is the mathematical framework of the 3rd-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (3rd-CASAM-N), which enables the most efficient computation of the exact expressions of the 1st-, 2nd- and 3rd-order functional derivatives (“sensitivities”) of a model’s response to the underlying model parameters, including imprecisely known initial, boundary and/or interface conditions. The 2nd- and 3rd-level adjoint functions are computed using the same forward and adjoint computer solvers as used for solving the original forward and adjoint systems. Comparisons between the CPU times are also presented for an OECD/NEA reactor physics benchmark, highlighting the fact that finite-difference schemes would not only provide approximate values for the respective sensitivities (in contradistinction to the 3rd-CASAM-N, which provides exact expressions for the sensitivities) but would simply be unfeasible for computing sensitivities of an order higher than first-order. Ongoing work will generalize the 3rd-CASAM-N to a higher order while aiming to overcome the curse of dimensionality.

Value of Perampanel as Adjunctive Treatment for Partial-Onset Seizures in Epilepsy: Cost-Effectiveness and Budget Impact Analysis

Introduction: China has ~6 million patients with active epilepsy every year, around 60% of whom suffer from partial-onset seizures. Perampanel (PER) is a novel anti-epileptic drug for partial-onset seizures. PER has been included in the latest Chinese National Reimbursement Drug List (NRDL) in 2020. However, there is still a lack of evaluation evidence on the value of PER in China.Methods: This study selected a health system perspective. A Markov model was established to simulate the lifelong transition of different response levels and calculate the number of seizures in Chinese patients. Based on the utility value and mortality risk, the life years and quality-adjusted life years (QALYs) of patients using PER vs. lacosamide (LCM) were estimated. Efficacy data were derived from clinical trials and the literature. Cost data (in US dollars) included drug costs and medical service costs. A lifetime horizon was adopted. Health outcomes and costs were discounted at an annual discount rate of 5%. Deterministic sensitivity analysis, probability sensitivity analysis, and scenario analysis were performed. The impact of the inclusion of PER in the NRDL on the medical insurance budget over 3 years (2021–2023) was also estimated.Results: Cost-effectiveness analysis indicates that 8 mg/day of PER increases QALYs by 0.054 and saves costs by $2,390 compared with 400 mg/day of LCM. 4 mg/day of PER increases QALYs by 0.010 and saves costs by $860 compared with 200 mg/day of LCM. Deterministic sensitivity analysis reveals that utility value and the extreme discount rate are the factors with the greatest impact on the incremental cost-effectiveness ratio. Probabilistic sensitivity analysis and scenario analysis show that the results are robust. Budget impact analysis indicates that after inclusion of PER in the NRDL, the incremental budget would be $1.28, $2.83, and $4.56 million from 2021 to 2023, respectively, but covering more eligible epileptic patients in the same time (1,918, 4,287, and 8,983, respectively).Conclusion: PER (8 or 4 mg/day) is of relatively high value as an add-on therapeutic regimen for partial-onset seizures in China because of its dominate advantage of cost-effectiveness over LCM and acceptable budget impact.

Cost-effectiveness of atezolizumab monotherapy versus pembrolizumab monotherapy for first-line (1L) treatment of metastatic non-small cell lung cancer (mNSCLC).

e18847 Background: Atezolizumab monotherapy is indicated as 1L treatment for mNSCLC patients with high programmed death ligand-1 (PD-L1) expression (≥ 50%) and without epidermal growth factor receptor or anaplastic lymphoma kinase mutations. This analysis assessed the cost-effectiveness of 1L atezolizumab monotherapy vs. pembrolizumab monotherapy for mNSCLC patients with high PD-L1 expression from a US third-party payer perspective. Methods: A Markov model with progression-free, progressive disease (PD), and death states was developed in Microsoft Excel to compare clinical and cost outcomes of atezolizumab monotherapy vs. pembrolizumab monotherapy. Efficacy, safety, and utility data were derived from systematic reviews and indirect comparisons of the IMpower110, Keynote-024, and Keynote-042 trials. Product prescribing information and clinical trials informed dosing and administration. Wholesale acquisition cost (WAC, accessed in January 2021) for drugs were used while other cost inputs were derived from publicly available fee schedules and peer-reviewed literature. The key outcome of interest was the incremental cost-effectiveness ratio (ICER) expressed as cost per quality-adjusted life-year (QALY) gained. Deterministic sensitivity analysis with 20% variation and probabilistic sensitivity analyses (PSA) were performed to address uncertainties around input parameters. Results: In the base case, 1L atezolizumab monotherapy was projected to increase life expectancy for patients by 0.60 life-years (4.35 vs. 3.75) and 0.47 QALYs (3.46 vs. 2.98) over pembrolizumab monotherapy at an incremental cost of $27,947 (mean total cost: $396,811 vs. $368,864), resulting in an ICER of $58,841/QALY gained. Results of the deterministic sensitivity analysis were most sensitive to changes in discount rates for costs and care costs in the PD state. The PSA showed that the probability of atezolizumab being cost-effective at willingness-to-pay thresholds of $100,000 and $150,000 was 41% and 49%, respectively. Conclusions: First-line atezolizumab monotherapy had 0.6 life-years and 0.47 QALYs gained compared with pembrolizumab monotherapy and was estimated to be cost-effective (ICER $58,841/QALY). As the ICER falls below the US cost-effectiveness thresholds ( < $100,000-$150,000/QALY), clinicians and payers should consider atezolizumab monotherapy as a cost-effective 1L option for mNSCLC patients with high PD-L1 expression.

Markov decision analysis of neoadjuvant treatment pathway versus surgery first pathway for resectable pancreatic cancer.

456 Background: Surgery first (SF) versus neoadjuvant approach (NAT) to management of potentially resectable pancreatic ductal adenocarcinoma (PDAC) is controversial. This study is unique in utilizing institutional data to offer Markov decision-analysis of overall treatment pathways for resectable PDAC. Methods: An advanced Markov decision analysis model was constructed and populated with data from a retrospective institutional database. Patients presenting with resectable PDAC from 2008-2012 were included in the SF arm. Those presenting with resectable PDAC from 2012-2016 and treated within NAT pathway populated the NAT arm. Model uncertainties were tested with one and two-way deterministic sensitivity analysis and probabilistic Monte Carlo sensitivity analysis set to 1000 cycles with variables altered between highest and lowest observed values. Results: NAT pathway gave an additional 0.58 QALMs (22.43 vs. 21.85 QALMs). Monte Carlo analysis reported indifference between treatment strategies. One-way deterministic sensitivity analysis showed that probability of resection in the SF pathway must be greater than 0.82, or below 0.72 in NAT pathway, and probability of receiving adjuvant therapy above 0.6 to alter pathway superiority. Two-way deterministic sensitivity analysis demonstrated treatment superiority depended on resection rate in each pathway and receiving adjuvant therapy in SF pathway. Markov cohort analysis demonstrated superiority of neoadjuvant pathway (Table). Conclusions: Optimal treatment pathway remains debatable on an intention-to-treat Markov decision analysis. Markov cohort analysis of treatment received demonstrated benefit with NAT pathway. [Table: see text]