Standard Parametric Models Research Articles

An Evaluation of an Algorithm for the Selection of Flexible Survival Models for Cancer Immunotherapies: Pass or Fail?

Accurately extrapolating survival beyond trial follow-up is essential in a health technology assessment where model choice often substantially impacts estimates of clinical and cost effectiveness. Evidence suggests standard parametric models often provide poor fits to long-term data from immuno-oncology trials. Palmer et al. developed an algorithm to aid the selection of more flexible survival models for these interventions. We assess the usability of the algorithm, identify areas for improvement and evaluate whether it effectively identifies models capable of accurate extrapolation. We applied the Palmer algorithm to the CheckMate-649 trial, which investigated nivolumab plus chemotherapy versus chemotherapy alone in patients with gastroesophageal adenocarcinoma. We evaluated the algorithm's performance by comparing survival estimates from identified models using the 12-month data cut to survival observed in the 48-month data cut. The Palmer algorithm offers a systematic procedure for model selection, encouraging detailed analyses and ensuring that crucial stages in the selection process are not overlooked. In our study, a range of models were identified as potentially appropriate for extrapolating survival, but only flexible parametric non-mixture cure models provided extrapolations that were plausible and accurately predicted subsequently observed survival. The algorithm could be improved with minor additions around the specification of hazard plots and setting out plausibility criteria. The Palmer algorithm provides a systematic framework for identifying suitable survival models, and for defining plausibility criteria for extrapolation validity. Using the algorithm ensures that model selection is based on explicit justification and evidence, which could reduce discordance in health technology appraisals.

When the tide wanes: A study of post systemic collapse portfolio management

This study applies the Black–Litterman model to portfolio management in a post-crisis scenario, where standard parametric models often fail due to market irrationality and investor overreactions. The research focuses on the performance of surviving firms, identifying that over-performing stocks tend to outperform in the medium- to long-term, while under-performing stocks exhibit stronger short-term returns as the market corrects its initial overreaction. The study specifically adjusts views within the Black–Litterman framework using only the top and bottom quartiles of stocks, which experience the most significant shifts during a crisis. By controlling for firm size and book-to-market ratios, consistent with the Fama-French three-factor model, the research demonstrates that adjusting portfolio weights with the Black–Litterman model can achieve substantially higher returns with lower downside risk during recovery periods. These findings have significant implications for portfolio managers seeking to optimize returns in volatile, post-crisis markets.

General Population Mortality Adjustment in Survival Extrapolation of Cancer Trials: Exploring Plausibility and Implications for Cost-Effectiveness Analyses in HER2-Positive Breast Cancer in Sweden.

In economic evaluations of novel therapies, assessing lifetime effects based on trial data often necessitates survival extrapolation, with the choice of model affecting outcomes. The aim of this study was to assess accuracy and variability between alternative approaches to survival extrapolation. Data on HER2-positive breast cancer patients from the Swedish National Breast Cancer Register were used to fit standard parametric distribution (SPD) models and excess hazard (EH) models adjusting the survival projections based on general population mortality (GPM). Models were fitted using 6-y data for stage I and II, 4-y data for stage III, and 2-y data for stage IV cancer reflecting an early data cutoff while maintaining sufficient events for comparison of model estimates with actual long-term outcomes. We compared model projections of 15-y survival and restricted mean survival time (RMST) to 15-y registry data and explored the variability between models in extrapolations of long-term survival. Among 11,224 patients compared with the observed registry 15-y RMST estimates across the disease stages, EH cure models provided the most accurate estimates in patients with stage I to III cancer, whereas EH models without cure most closely matched survival in patients with stage IV cancer, in which cure assumption was less plausible. The Akaike information criterion-averaged model projections varied as follows: -8.2% to +5.3% for SPD models, -4.9% to +5.2% for the EH model without a cure assumption, and -19.3% to -0.2% for the EH model with a cure assumption. EH models significantly reduced between-model variance in the predicted RMSTs over a 50-y time horizon compared with SPD models. EH models may be considered as alternatives to SPD models to produce more accurate and plausible survival extrapolation that accounts for general population mortality. Excess hazard (EH) methods have been suggested as an approach to incorporate background mortality rates in economic evaluation using survival extrapolation.We highlight that EH models with or without a cure assumption can produce more accurate survival projections and significantly reduce between-model variability in comparison with standard parametric distribution models across cancer stages.EH models may be a preferred modeling method to reduce model uncertainty in health economic modeling since models that would otherwise have produced implausible extrapolations are constrained by the EH framework.Reduced uncertainty in economic evaluations will enhance the application of evidence-based health care decision making.

A Bayesian flexible model for testing Granger causality

A new Bayesian hypothesis testing procedure for evaluating the Granger causality between two or more time series is proposed. The test is based on a flexible model for the joint evolution of multiple series, where a latent binary matrix indicates whether there is a Granger-causal relationship between such time series. The model is specified through a dependent Geometric stick-breaking process that generalizes the standard parametric Gaussian vector autoregression model, whereas the prior distribution of the latent matrix ensures a multiple testing correction. A Monte Carlo simulation study is provided for comparing the robustness of the proposed hypothesis test with state-of-the-art alternatives. The results show that this proposal performs better than competing approaches. Finally, the new test is applied to real economic data.

Cloud computing and extensive margins of exports: Evidence for manufacturing firms from 27 EU countries

<p class="MsoNormal" style="margin-top: 10pt; text-align: justify;"><span lang="EN-US" style="font-family: 'times new roman', times, serif; font-size: 14pt;">The use of cloud computing by firms can be expected to go hand in hand with higher productivity, more innovations, and lower costs, and, therefore, should be positively related to export activities. Empirical evidence on the link between cloud computing and exports, however, is missing. This paper uses firm level data for manufacturing enterprises from the 27 member countries of the European Union taken from the Flash Eurobarometer 486 survey conducted in February – May 2020 to investigate this link. Applying standard parametric econometric models and a new machine-learning estimator, Kernel-Regularized Least Squares (KRLS), we find that firms which use cloud computing do more often export, do more often export to various destinations all over the world, and do export to more different destinations. The estimated cloud computing premium for extensive margins of exports is statistically highly significant after controlling for firm size, firm age, patents, and country. Furthermore, the size of this premium can be considered to be large. Extensive margins of exports and the use of cloud computing are positively related.</span></p>

Comparing Survival Extrapolation within All-Cause and Relative Survival Frameworks by Standard Parametric Models and Flexible Parametric Spline Models Using the Swedish Cancer Registry.

In health technology assessment, restricted mean survival time and life expectancy are commonly evaluated. Parametric models are typically used for extrapolation. Spline models using a relative survival framework have been shown to estimate life expectancy of cancer patients more reliably; however, more research is needed to assess spline models using an all-cause survival framework and standard parametric models using a relative survival framework. To assess survival extrapolation using standard parametric models and spline models within relative survival and all-cause survival frameworks. From the Swedish Cancer Registry, we identified patients diagnosed with 5 types of cancer (colon, breast, melanoma, prostate, and chronic myeloid leukemia) between 1981 and 1990 with follow-up until 2020. Patients were categorized into 15 cancer cohorts by cancer and age group (18-59, 60-69, and 70-99 y). We right-censored the follow-up at 2, 3, 5, and 10 y and fitted the parametric models within an all-cause and a relative survival framework to extrapolate to 10 y and lifetime in comparison with the observed Kaplan-Meier survival estimates. All cohorts were modeled with 6 standard parametric models (exponential, Weibull, Gompertz, log-logistic, log-normal, and generalized gamma) and 3 spline models (on hazard, odds, and normal scales). For predicting 10-y survival, spline models generally performed better than standard parametric models. However, using an all-cause or a relative survival framework did not show any distinct difference. For lifetime survival, extrapolating from a relative survival framework agreed better with the observed survival, particularly using spline models. For extrapolation to 10 y, we recommend spline models. For extrapolation to lifetime, we suggest extrapolating in a relative survival framework, especially using spline models. For survival extrapolation to 10 y, spline models generally performed better than standard parametric models did. However, using an all-cause or a relative survival framework showed no distinct difference under the same parametric model.Survival extrapolation to lifetime within a relative survival framework agreed well with the observed data, especially using spline models.Extrapolating parametric models within an all-cause survival framework may overestimate survival proportions at lifetime; models for the relative survival approach may underestimate instead.

Challenges with Estimating Long-Term Overall Survival in Extensive Stage Small-Cell Lung Cancer: A Validation-Based Case Study.

The study aimed to explore methods and highlight the challenges of extrapolating the overall survival (OS) of immunotherapy-based treatment in first-line extensive stage small-cell lung cancer (ES-SCLC). Standard parametric survival models, spline models, landmark models, mixture and non-mixture cure models, and Markov models were fitted to 2-year data of the CASPIAN Phase 3 randomised trial of PD-L1 inhibitor durvalumab added to platinum-based chemotherapy (NCT03043872). Extrapolations were compared with updated 3-year data from the same trial and the plausibility of long-term estimates assessed. All models used provided a reasonable fit to the observed Kaplan-Meier (K-M) survival data. The model which provided the best fit to the updated CASPIAN data was the mixture cure model. In contrast, the landmark analysis provided the least accurate fit to model survival. Estimated mean OS differed substantially across models and ranged from (in years) 1.41 (landmark model) to 4.81 (mixture cure model) for durvalumab plus etoposide and platinum and from 1.01 (landmark model) to 2.00 (mixture cure model) for etoposide and platinum. While most models may provide a good fit to K-M data, it is crucial to assess beyond the statistical goodness-of-fit and consider the clinical plausibility of the long-term predictions. The more complex cure models demonstrated the best predictive ability at 3 years, potentially providing a better representation of the underlying method of action of immunotherapy; however, consideration of the models' clinical plausibility and cure assumptions need further research and validation. Our findings underscore the significance of adopting a clinical perspective when selecting the most appropriate approach to model long-term survival, particularly when considering the use of more complex models.

Cost-effectiveness of pembrolizumab for previously treated MSI-H/dMMR solid tumours in the UK

Objectives Patients with previously treated microsatellite instability-high (MSI-H)/mismatch repair deficient (dMMR) tumours have limited chemotherapeutic treatment options. Pembrolizumab received approval from the EMA in 2022 for the treatment of colorectal, endometrial, gastric, small intestine, and biliary MSI-H/dMMR tumour types. This approval was supported by data from the KEYNOTE-164 and KEYNOTE-158 clinical trials. This study evaluated the cost-effectiveness of pembrolizumab compared with standard of care (SoC) for previously treated MSI-H/dMMR solid tumours in line with the approved EMA label from a UK healthcare payer perspective. Methods A multi-tumour partitioned survival model was built consisting of pre-progression, progressed disease, and dead health states. Pembrolizumab survival outcomes were extrapolated using Bayesian hierarchical models (BHMs) fitted to pooled data from KEYNOTE-164 and KEYNOTE-158. Comparator outcomes were informed by published sources. Tumour sites were modelled independently and then combined, weighted by tumour site distribution. A SoC comparator was used to formulate the overall cost-effectiveness result with pembrolizumab as the intervention. SoC comprised a weighted average of the comparators by tumour site based on market share. Drug acquisition, administration, adverse events, monitoring, subsequent treatment, end-of-life costs, and testing costs were included. Sensitivity and scenario analyses were performed, including modelling pembrolizumab efficacy using standard parametric survival models. Results Pembrolizumab, at list price, was associated with £129,469 in total costs, 8.30 LYs, and 3.88 QALYs across the pooled tumour sites. SoC was associated with £28,222 in total costs, 1.14 LYs, and 0.72 QALYs across the pooled tumour sites. This yields an incremental cost-effectiveness ratio (ICER) of £32,085 per QALY. Results were robust to sensitivity and scenario analyses. Conclusions This model demonstrates pembrolizumab provides a valuable new alternative therapy for UK patients with MSH-H/dMMR cancer at the cost of £32,085 per QALY, with confidential discounts anticipated to improve cost-effectiveness further.

Statistical Challenges from Trials of Potentially Curative Treatments: Validation of Cure Assumptions When Analyzing Zuma-7 Follow-up Data of Axi-Cel and Standard of Care Therapy

Introduction: ZUMA-7 is the largest randomized controlled trial (RCT) for chimeric antigen receptor (CAR) T-cell therapy which compared axicabtagene ciloleucel (Axi-cel) to standard of care (SoC) including autologous stem cell transplant (ASCT) for the treatment of relapsed or refractory DLBCL. Both arms of ZUMA-7 contained potentially curative treatments; however, differences in the treatment completion rate (94% received axi-cel and 36% received ASCT) and timing to receive definitive treatment led to differences in the extent and timing of cure. Furthermore, 57% of the SoC arm received potentially curative CAR-T therapies in subsequent lines of therapy leading to a delayed cure in that fraction of the population. The resulting event-free survival (EFS) and overall survival (OS) curves can pose challenges in interpretation and extrapolation for the purpose of simulations of long-term treatment effects and cost-effectiveness. Mixture cure modeling (MCM) has been suggested as a superior method to evaluate treatments of a curative nature to allow for part of the population to achieve long-term remission. This method has been shown to be useful both in designing and powering clinical studies of curative therapies but also for extrapolation of long-term outcomes in simulation studies. However previous iterations of this method did not account for differences in timing of curative therapies. ZUMA-7 had two pivotal analyses separated by nearly 2-years of follow-up: a primary EFS (datacut 1) and a primary OS analyses (data cut 2). The aim of this study was to use the two data cuts of ZUMA-7 to validate MCM in 2L LBCL and describe differences that may have arisen due to treatment specific timing and extent of cure. Methods: Overall survival individual patient-level data from the ZUMA-7 trial for axi-cel and SoC from both data cut 1 (median follow-up: 24.9 months) and data cut 2 (median follow-up: 47.2 months) were used in this analysis. Three different parametric modeling approaches were applied and compared in both data cuts: standard parametric model, spline-based model, and MCMs. Modeling approaches were evaluated for plausibility across a range of metrics, across the two data cuts, including visual fit, plausibility of long-term estimates, statistical goodness of fit, inspection of hazard plots, point-estimate accuracy, and conditional survival estimates. Additionality, the ability of the early data cut extrapolation to predict the actual data was assessed by comparing the model predictions with the latest KM estimator in both trial arms. Differences between trial arms were evaluated. Results: Cure-based and spline models provided the best fit based on the percentage inaccuracy of extrapolations fitted with data cut 1 in comparison to 5-year OS Kaplan-Meier estimates confirmed by data cut 2. In the axi-cel treatment arm, the percentage inaccuracy range between 2% and 27% (Figure 1). Based on data cut 1, cure fractions ranged considerably across the MCM extrapolation forms considered for both treatment arms (range: 24-54% [Figure 2] and 35-49% for axi-cel and SoC, respectively). Notably, the range of cure fractions narrowed considerably based on extrapolations performed on the more mature data cut 2 (range: 50-54% [Figure 2] and 41-50% for axi-cel and SoC, respectively). Overall, the uncertainty in the estimate of cure fractions based on MCMs was reduced from data cut 1 to data cut 2 for axi-cel vs. SoC, suggesting clinical input is needed to validate early extrapolations using less mature data cuts. Conclusion: Our analysis suggests that MCMs are helpful in making accurate predictions of survival based on immature data when a plateau in the survival curve is clinically plausible. However, this analysis also highlights the importance of considering clinical plausibility to guide specific curve selection in the presence of immature survival data, as there was a high degree of variability in the early extrapolations which was reduced with the longer-term follow-up. The ability to reliably extrapolate from early data may improve clinical decision making and reduce delays in patient access to potentially lifesaving treatments as more mature follow-up data are being collected.

Evaluation of Flexible Parametric Relative Survival Approaches for Enforcing Long-Term Constraints When Extrapolating All-Cause Survival

ObjectivesParametric models are used to estimate the lifetime benefit of an intervention beyond the range of trial follow-up. Recent recommendations have suggested more flexible survival approaches and the use of external data when extrapolating. Both of these can be realized by using flexible parametric relative survival modeling. The overall aim of this article is to introduce and contrast various approaches for applying constraints on the long-term disease-related (excess) mortality including cure models and evaluate the consequent implications for extrapolation. MethodsWe describe flexible parametric relative survival modeling approaches. We then introduce various options for constraining the long-term excess mortality and compare the performance of each method in simulated data. These methods include fitting a standard flexible parametric relative survival model, enforcing statistical cure, and forcing the long-term excess mortality to converge to a constant. We simulate various scenarios, including where statistical cure is reasonable and where the long-term excess mortality persists. ResultsThe compared approaches showed similar survival fits within the follow-up period. However, when extrapolating the all-cause survival beyond trial follow-up, there is variation depending on the assumption made about the long-term excess mortality. Altering the time point from which the excess mortality is constrained enables further flexibility. ConclusionsThe various constraints can lead to applying explicit assumptions when extrapolating, which could lead to more plausible survival extrapolations. The inclusion of general population mortality directly into the model-building process, which is possible for all considered approaches, should be adopted more widely in survival extrapolation in health technology assessment.

Cost-effectiveness analysis of adding transarterial chemoembolisation to lenvatinib as first-line treatment for advanced hepatocellular carcinoma in China

ObjectiveThe objective of this study was to evaluate the comparative cost-effectiveness of lenvatinib (LEN) plus transarterial chemoembolisation (TACE) (LEN-TACE) and LEN alone to treat advanced hepatocellular carcinoma (HCC) from the...

Retrospective Comparison of Survival Projections for CAR T-Cell Therapies in Large B-Cell Lymphoma.

Durable remission has been observed in patients with relapsed or refractory (R/R) large B-cell lymphoma (LBCL) treated with chimeric antigen receptor (CAR) T-cell therapy. Consequently, hazard functions for overall survival (OS) are often complex, requiring the use of flexible methods for extrapolations. We aimed to retrospectively compare the predictive accuracy of different survival extrapolation methods and evaluate the validity of goodness-of-fit (GOF) criteria-based model selection for CAR T-cell therapies in R/R LBCL. OS data were sourced from JULIET, ZUMA-1, and TRANSCEND NHL 001. Standard parametric, mixture cure, cubic spline, and mixture models were fit to multiple database locks (DBLs), with varying follow-up durations. GOF was assessed using the Akaike information criterion and Bayesian information criterion. Predictive accuracy was calculated as the mean absolute error (MAE) relative to OS observed in the most mature DBL. For all studies, mixture cure and cubic spline models provided the best predictive accuracy for the least mature DBL (MAE 0.013‒0.085 and 0.014‒0.128, respectively). The predictive accuracy of the standard parametric and mixture models showed larger variation (MAE 0.024‒0.162 and 0.013‒0.176, respectively). With increasing data maturity, the predictive accuracy of standard parametric models remained poor. Correlation between GOF criteria and predictive accuracy was low, particularly for the least mature DBL. Our analyses demonstrated that mixture cure and cubic spline models provide the most accurate survival extrapolations of CAR T-cell therapies in LBCL. Furthermore, GOF should not be the only criteria used when selecting the optimal survival model.

Conditional probability and probability updating

The conditional probability formula is supposed to reflect the correct updating of probability assignments when new information is incorporated. Starting from a non-atomic probability measure, it is proved that the conditional probability formula provides the only transformed probability measure satisfying a “minimum requirement” relational assumption. This result applies to the standard Bayesian parametric model.

MSR53 Bayesian Parametric Mixture Survival Models in Immuno-Oncology Applications: Leveraging Control Arm Observations to Model Heterogeneous Response in the Experimental Arm

Heterogeneous response to an intervention is a common feature of survival patterns in randomized clinical trials (RCTs) of immuno-oncology therapies. This effect is usually inadequately represented by standard parametric models. Instead, it is desirable to employ parametric mixture models (PMMs), which represent the cohort as a combination of two latent subpopulations with distinct survival curves. However, classical PMMs are often too complex to parameterize reliably given the limited observations in RCT data.

MSR74 Comparison of Cure Versus Standard Parametric Models Using Advanced Melanoma Data

As melanoma starts spreading to various parts of the body from where it started, it is known as advanced melanoma. This study compares the results of the mixture and non-mixture cure models with the standard parametric models while estimating the long-term survival probability of the patients treated with nivolumab.

MSR29 Application of Bayesian Multi-Parameter Evidence Synthesis to Achieve Clinical Plausibility of Lifetime Survival Extrapolations in First-Line Advanced Non-Small Cell Lung Cancer (aNSCLC)

Lifetime overall survival (OS) extrapolations are required to estimate important differences in costs and benefits between comparators in health economic models. Bayesian multi-parameter evidence synthesis (B-MPES) models for aNSCLC patients receiving second-line nivolumab have previously demonstrated clinically reasonable and stable estimates for long-term OS. Here, we investigate the plausibility of B-MPES predictions for OS in the CheckMate 227 Part 1 trial of nivolumab plus ipilimumab (NIVO+IPI) in aNSCLC patients in the first-line setting and compare with uninformed standard parametric models (SPMs).

Extrapolating empirical long-term survival data: the impact of updated follow-up data and parametric extrapolation methods on survival estimates in multiple myeloma

BackgroundIn economic evaluations, survival is often extrapolated to smooth out the Kaplan-Meier estimate and because the available data (e.g., from randomized controlled trials) are often right censored. Validation of the accuracy of extrapolated results can depend on the length of follow-up and the assumptions made about the survival hazard. Here, we analyze the accuracy of different extrapolation techniques while varying the data cut-off to estimate long-term survival in newly diagnosed multiple myeloma (MM) patients.MethodsEmpirical data were available from a randomized controlled trial and a registry for MM patients treated with melphalan + prednisone, thalidomide, and bortezomib- based regimens. Standard parametric and spline models were fitted while artificially reducing follow-up by introducing database locks. The maximum follow-up for these locks varied from 3 to 13 years. Extrapolated (conditional) restricted mean survival time (RMST) was compared to the Kaplan-Meier RMST and models were selected according to statistical tests, and visual fit.ResultsFor all treatments, the RMST error decreased when follow-up and the absolute number of events increased, and censoring decreased. The decline in RMST error was highest when maximum follow-up exceeded six years. However, even when censoring is low there can still be considerable deviations in the extrapolated RMST conditional on survival until extrapolation when compared to the KM-estimate.ConclusionsWe demonstrate that both standard parametric and spline models could be worthy candidates when extrapolating survival for the populations examined. Nevertheless, researchers and decision makers should be wary of uncertainty in results even when censoring has decreased, and the number of events has increased.

Cost-Effectiveness Analysis of Biomarker Testing to Guide First-Line PARP Inhibitor Maintenance for Patients with Advanced Ovarian Cancer After Response to First-Line Platinum Chemotherapy in the USA.

Poly(ADP-ribose) polymerase inhibitor maintenance treatments are available for platinum-sensitive advanced ovarian cancer. Olaparib (O) is available for BRCA mutation patients or in combination with bevacizumab (O+B) for patients with homologous recombination deficiency (HRD+); niraparib (N) is available for all patients. This study aimed to evaluate the cost effectiveness of biomarker testing and maintenance treatments(mTx) with poly(ADP-ribose) polymerase inhibitor in platinum-sensitive advanced ovarian cancer in the USA. Ten strategies were evaluated (S1-S10), representing biomarker testing (none, BRCA or HRD), and mTx (O, O+B, Nor B). PAOLA-1 data were used to build a model estimating progression-free survival (PFS), second PFS (PFS2) and overall survival for O+B. PFS was modelled through mixture cure models; PFS2 and overall survival were modelled by standard parametric models. Hazard ratios of PFS for O+B versus B, N and O were obtained from the literature to estimate PFS for B, N and O. PFS2 and OS for B, N and O were informed by PFS benefits. S2 (no testing, B) had the lowest cost while S10 (HRD testing, O+B for HRD+ and B for HRD-) had the highest quality-adjusted life-years (QALYs). All niraparib strategies were dominated. S2, S4 (BRCA testing, O for BRCA+ and B for BRCA-), S6 (BRCA testing, olaparib plus bevacizumab for BRCA+ and bevacizumab for BRCA-) and S10 were the non-dominated strategies with an incremental cost-effectiveness ratio of $29,095/QALY, $33,786/QALY and $52,948/QALY for S4 versus S2, S6 versus S4 and S10 versus S6, respectively. Homologous recombination deficiency testing followed by O+B for HRD+ and B for HRD- is a highly cost-effective strategy for patients with platinum-sensitive advanced ovarian cancer. A HRD biomarker-guided approach provides most QALYs with good economic value.

Economic evaluation of toripalimab combined with chemotherapy in the treatment of non-small cell lung cancer.

The CHOICE-01 trial showed that toripalimab plus chemotherapy achieved satisfactory outcomes compared with chemotherapy in patients with advanced non-small cell lung cancer (NSCLC) who were negative for driver genes, but the economics of this regimen is unclear. Therefore, this study aimed to evaluate the cost-effectiveness of toripalimab in combination with chemotherapy in advanced NSCLC with negative driver genes from the perspective of the Chinese healthcare system. A three-state partitioned survival model was developed to simulate the costs and outcomes associated with adding toripalimab to first-line chemotherapy. The clinical data in the model came from the CHOICE-01 trial, only direct medical costs were included, and utility values were referred to the literature. Four models were applied to explore the differences in the results of fitting and extrapolating K-M curves from different models, and cost-effectiveness subgroup analysis was performed. The incremental cost-effectiveness ratio (ICER) was used as the main outcome measure. Sensitivity analysis was performed to assess the impact of parameter uncertainty on the model. The baseline analysis showed that toripalimab coupled with chemotherapy cost $21,052 more than chemotherapy ($43,197 vs. $22,145) and also gained 0.71 QALYs more (1.75 QALYs vs. 1.03 QALYs), with an ICER of $29,478/QALYs. At the current willingness-to-pay threshold ($35,108/QALY), the extra cost was well worth it. The results of fitting and extrapolating the survival curves using other models were consistent with the results of the standard parametric model. Subgroup analysis demonstrated that the addition of toripalimab to chemotherapy was economical. Sensitivity analysis showed that the utility values of PD and PFS stages had the greatest impact on the model. From the viewpoint of the Chinese healthcare system, toripalimab combined with chemotherapy in the treatment of advanced NSCLC with negative driver genes was likely to be cost-effective compared with chemotherapy.

Impact of Extrapolation Model Choices on the Structural Uncertainty in Economic Evaluations for Cancer Immunotherapy: A Case Study of Checkmate067.

The aim of this study was to compare the performance of different extrapolation modeling techniques and analyze their impact on structural uncertainties in the economic evaluations of cancer immunotherapy. The individual patient data was reconstructed through published Checkmate067 Kaplan Meier curves. Standard parametric models and six flexible techniques were tested, including fractional polynomial, restricted cubic splines, Royston-Parmar models, generalized additive models, parametric mixture models, and mixture cure models. Mean square errors (MSE) and bias from raw survival plots were used to test the model fitness and extrapolation performance. Variability of estimated incremental cost-effectiveness ratios (ICERs) from different models was used to inform the structural uncertainty in economic evaluations. All indicators were analyzed and compared under cut-offs of 3 years and 6.5 years, respectively, to further discuss model impact under different data maturity. R Codes for reproducing this study can be found on GitHub. The flexible techniques in general performed better than standard parametric models with smaller MSE irrespective of the data maturity. Survival outcomes projected by long-term extrapolation using immature data differed from those with mature data. Although a best-performing model was not found because several models had very similar MSE in this case, the variability of modeled ICERs significantly increased when prolonging simulation cycles. Flexible techniques show better performance in the case of Checkmate067, regardless of data maturity. Model choices affect ICERs of cancer immunotherapy, especially when dealing with immature survival data. When researchers lack evidence to identify the 'right' model, we recommend identifying and revealing the model impacts on structural uncertainty.