A Guide to Selecting Flexible Survival Models to Inform Economic Evaluations of Cancer Immunotherapies

Mixture and Non-mixture Cure Models for Health Technology Assessment: What You Need to Know

There is increasing interest in the use of cure modelling to inform health technology assessment (HTA) due to the development of new treatments that appear to offer the potential for cure in some patients. However, cure models are often not included in evidence dossiers submitted to HTA agencies, and they are relatively rarely relied upon to inform decision-making. This is likely due to a lack of understanding of how cure models work, what they assume, and how reliable they are. In this tutorial we explain why and when cure models may be useful for HTA, describe the key characteristics of mixture and non-mixture cure models, and demonstrate their use in a range of scenarios, providing Stata code. We highlight key issues that must be taken into account by analysts when fitting these models and by reviewers and decision-makers when interpreting their predictions. In particular, we note that flexible parametric non-mixture cure models have not been used in HTA, but they offer advantages that make them well suited to an HTA context when a cure assumption is valid but follow-up is limited.

Tackling Challenges in Assessing the Economic Value of Tumor-Agnostic Therapies: A Cost-Effectiveness Analysis of Pembrolizumab as a Case Study

OBJECTIVES

Assessing the value of tumor-agnostic drugs (TAD) is challenging given the potential variability in treatment effects, trials with small sample sizes, different standards of care (SoC), and lack of comparative data from single-arm basket trials. Our study developed and applied novel methods to assess the value of pembrolizumab compared with SoC to inform coverage decisions.

METHODS

We developed a partitioned survival model to evaluate the cost-utility of pembrolizumab for previously treated patients with 8 advanced or metastatic microsatellite instability-high or mismatch repair-deficient cancers from a US commercial payer perspective. Efficacy of pembrolizumab was based on data from trials directly or with adjustment using Bayesian hierarchical models. Eight chemotherapy-based external control arms were constructed from the TriNetX electronic health record databases. Tumor-specific health-state utility values were applied. All costs were adjusted to 2022 US dollars.

RESULTS

At a lifetime horizon, pembrolizumab was associated with increased effectiveness compared with chemotherapies in colorectal (quality-adjusted life years [QALYs]: +0.64, life years [LYs]: +0.64), endometrial (QALYs: +3.79, LYs: +5.47), and small intestine cancers (QALYs: +1.73, LYs: +2.48), but not for patients with metastatic gastric, cholangiocarcinoma, pancreatic, ovarian, and brain cancers. Incremental cost-effectiveness ratios varied substantially across tumor types. Pembrolizumab was found to be cost-effective in treating colorectal and endometrial cancers (incremental cost-effectiveness ratios: $121 967 and $139 257, respectively), and not cost-effective for other assessed cancers at a $150 000 willingness-to-pay/QALY threshold, compared with SoC chemotherapies.

CONCLUSIONS

The cost-effectiveness of TADs can vary by cancers. Using analytic tools such as external controls and Bayesian hierarchical models can tackle several challenges in assessing the value of TADs and uncertainties from basket trials.

Assessing the Performance of Alternative Methods for Estimating Long-Term Survival Benefit of Immuno-oncology Therapies

OBJECTIVES

This study aimed to determine the accuracy and consistency of established methods of extrapolating mean survival for immuno-oncology (IO) therapies, the extent of any systematic biases in estimating long-term clinical benefit, what influences the magnitude of any bias, and the potential implications for health technology assessment.

METHODS

A targeted literature search was conducted to identify published long-term follow-up from clinical trials of immune-checkpoint inhibitors. Earlier published results were identified and Kaplan-Meier estimates for short- and long-term follow-up were digitized and converted to pseudo-individual patient data using an established algorithm. Six standard parametric, 5 flexible parametric, and 2 mixture-cure models (MCMs) were used to extrapolate long-term survival. Mean and restricted mean survival time (RMST) were estimated and compared between short- and long-term follow-up.

RESULTS

Predicted RMST from extrapolation of early data underestimated observed RMST in long-term follow-up for 184 of 271 extrapolations. All models except the MCMs frequently underestimated observed RMST. Mean survival estimates increased with longer follow-up in 196 of 270 extrapolations. The increase exceeded 20% in 122 extrapolations. Log-logistic and log-normal models showed the smallest change with additional follow-up. MCM performance varied substantially with functional form.

CONCLUSIONS

Standard and flexible parametric models frequently underestimate mean survival for IO treatments. Log-logistic and log-normal models may be the most pragmatic and parsimonious solutions for estimating IO mean survival from immature data. Flexible parametric models may be preferred when the data used in health technology assessment are more mature. MCMs fitted to immature data produce unreliable results and are not recommended.

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

Objective

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).

Methods

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.

Results

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.

Conclusion

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.

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

BACKGROUND

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.

OBJECTIVES

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.

METHODS

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.

RESULTS

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.

CONCLUSIONS

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.

Cost-effectiveness analysis of serplulimab as first-line treatment for advanced esophageal squamous cell carcinoma

Objective: To evaluate the cost-effectiveness of serplulimab as first-line treatment for patients with advanced esophageal squamous cell carcinoma from the perspective of the Chinese healthcare system. Materials & methods: A partitioned survival model was created to evaluate costs and health outcomes. The model's robustness was evaluated using one-way and probabilistic sensitivity analyses. Results: Serplulimab demonstrated an incremental cost-effectiveness ratio of $104,537.375/quality-adjusted life-year in the overall population group. Subgroup analysis showed that serplulimab had incremental cost-effectiveness ratios of $261,750.496/quality-adjusted life-year and $68,107.997/quality-adjusted life-year in the populations with PD-L1 1 ≤ combined positive score <10 and PD-L1 combined positive score ≥10, respectively. Conclusion: Incremental cost-effectiveness ratios of serplulimab therapy were found to exceed the willingness-to-pay threshold of $37,304.34. Thus, serplulimab is not cost-effective compared with chemotherapy as a first-line treatment for esophageal squamous cell carcinoma patients.

General-Purpose Methods for Simulating Survival Data for Expected Value of Sample Information Calculations

BACKGROUND

Expected value of sample information (EVSI) quantifies the expected value to a decision maker of reducing uncertainty by collecting additional data. EVSI calculations require simulating plausible data sets, typically achieved by evaluating quantile functions at random uniform numbers using standard inverse transform sampling (ITS). This is straightforward when closed-form expressions for the quantile function are available, such as for standard parametric survival models, but these are often unavailable when assuming treatment effect waning and for flexible survival models. In these circumstances, the standard ITS method could be implemented by numerically evaluating the quantile functions at each iteration in a probabilistic analysis, but this greatly increases the computational burden. Thus, our study aims to develop general-purpose methods that standardize and reduce the computational burden of the EVSI data-simulation step for survival data.

METHODS

We developed a discrete sampling method and an interpolated ITS method for simulating survival data from a probabilistic sample of survival probabilities over discrete time units. We compared the general-purpose and standard ITS methods using an illustrative partitioned survival model with and without adjustment for treatment effect waning.

RESULTS

The discrete sampling and interpolated ITS methods agree closely with the standard ITS method, with the added benefit of a greatly reduced computational cost in the scenario with adjustment for treatment effect waning.

CONCLUSIONS

We present general-purpose methods for simulating survival data from a probabilistic sample of survival probabilities that greatly reduce the computational burden of the EVSI data-simulation step when we assume treatment effect waning or use flexible survival models. The implementation of our data-simulation methods is identical across all possible survival models and can easily be automated from standard probabilistic decision analyses.

HIGHLIGHTS

Expected value of sample information (EVSI) quantifies the expected value to a decision maker of reducing uncertainty through a given data collection exercise, such as a randomized clinical trial. In this article, we address the problem of computing EVSI when we assume treatment effect waning or use flexible survival models, by developing general-purpose methods that standardize and reduce the computational burden of the EVSI data-generation step for survival data.We developed 2 methods for simulating survival data from a probabilistic sample of survival probabilities over discrete time units, a discrete sampling method and an interpolated inverse transform sampling method, which can be combined with a recently proposed nonparametric EVSI method to accurately estimate EVSI for collecting survival data.Our general-purpose data-simulation methods greatly reduce the computational burden of the EVSI data-simulation step when we assume treatment effect waning or use flexible survival models. The implementation of our data-simulation methods is identical across all possible survival models and can therefore easily be automated from standard probabilistic decision analyses.

Impact of Extrapolation Model Choices on the Structural Uncertainty in Economic Evaluations for Cancer Immunotherapy: A Case Study of Checkmate 067

OBJECTIVES

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.

METHODS

The individual patient data was reconstructed through published Checkmate 067 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.

RESULTS

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.

CONCLUSIONS

Flexible techniques show better performance in the case of Checkmate 067, 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.

Cost-Effectiveness of Blinatumomab in Pediatric Patients with High-Risk First-Relapse B-Cell Precursor Acute Lymphoblastic Leukemia in France

BACKGROUND

Based on the results of the phase III randomized 20120215 trial, the European Medicines Agency granted the approval of blinatumomab for the treatment of pediatric patients with high-risk first-relapsed Philadelphia chromosome-negative B-cell precursor acute lymphoblastic leukemia (ALL). In France, blinatumomab received reimbursement for this indication in May 2022. This analysis assessed the cost effectiveness of blinatumomab compared with high-risk consolidation chemotherapy (HC3) in this indication from a French healthcare and societal perspective.

METHODS

A partitioned survival model with three health states (event-free, post-event and death) was developed to estimate life-years (LYs), quality-adjusted life-years (QALYs) and costs over a lifetime horizon. Patients who were alive after 5 years were considered to be cured. An excess mortality rate was applied to capture the late effects of cancer therapy. Utility values were based on the TOWER trial using French tariffs, and cost input data were identified from French national public health sources. The model was validated by clinical experts.

RESULTS

Treatment with blinatumomab over HC3 was estimated to provide gains of 8.39 LYs and 7.16 QALYs. Total healthcare costs for blinatumomab and HC3 were estimated to be €154,326 and €102,028, respectively, resulting in an increment of €52,298. The incremental cost-effectiveness ratio was estimated to be €7308 per QALY gained from a healthcare perspective. Results were robust to sensitivity analyses, including analysis from the societal perspective.

CONCLUSIONS

Blinatumomab administered as part of consolidation therapy in pediatric patients with high-risk first-relapsed ALL is cost effective compared with HC3 from the French healthcare and societal perspective.

Cost-Effectiveness of First-Line Pembrolizumab Monotherapy Versus Chemotherapy in High Programmed Death-Ligand 1 Advanced Non-Small Cell Lung Cancer in the Irish Healthcare Setting

OBJECTIVES

This study aimed to assess the cost-effectiveness of pembrolizumab monotherapy in the first-line treatment of advanced non-small cell lung cancer (NSCLC) in adults whose tumors expressed programmed death-ligand 1 (PD-L1) with a tumor proportion score (TPS) ≥ 50% in the Irish healthcare setting.

METHODS

Effectiveness inputs were derived from the 5-year analysis of KEYNOTE-024 phase III clinical trial. The intervention was pembrolizumab monotherapy; the comparator was a weighted average of the 5 chemotherapy regimens from the trial. The population included those with previously untreated advanced PD-L1 TPS ≥ 50% NSCLC. A de novo partitioned survival model was developed. Survival modeling was done using Bayesian model averaging on fitted parametric functions. Costs included drug acquisition, treatment initiation, administration and monitoring, adverse events, subsequent treatments, and terminal care. Costs and health state utilities were sourced from the literature and Irish sources. The model had a 20-year time horizon. The perspective taken was the Health Service Executive. A 4% discount rate was applied. Outcomes were expressed as an incremental cost-effectiveness ratio (ICER), measured in terms of incremental costs per quality-adjusted life-year (QALY). Probabilistic sensitivity analysis and 1-way sensitivity analyses were conducted.

RESULTS

The model estimated a base case ICER of €54 237 per QALY. The probabilistic sensitivity analysis estimated an average ICER of €54 568 per QALY and a 11% probability of cost-effectiveness at the Irish cost-effectiveness threshold of €45 000 per QALY.

CONCLUSION

At the current list price, first-line pembrolizumab monotherapy is not considered cost-effective for the treatment of advanced PD-L1 TPS ≥ 50% NSCLC in the Irish healthcare setting.

Comparison of statistical methods for extrapolating survival in previously untreated diffuse large B-cell lymphoma: results based on the POLARIX study

OBJECTIVE

The ongoing Phase III randomized POLARIX study (GO39942; NCT03274492) demonstrated significantly improved progression-free survival (PFS) with polatuzumab vedotin plus rituximab, cyclophosphamide, doxorubicin and prednisone (Pola-R-CHP) versus rituximab plus cyclophosphamide, doxorubicin, vincristine, and prednisone (R-CHOP) in patients with previously untreated diffuse large B-cell lymphoma (DLBCL). We compared statistical methodologies to extrapolate long-term PFS data from POLARIX.

MATERIALS AND METHODS

This analysis explored four different approaches to extrapolate the POLARIX data: standard parametric survival, mixture-cure, landmark, and spline models. The resulting extrapolation curves were validated via comparison with the corresponding Kaplan-Meier (KM) curves from POLARIX and the POLARIX-like population of the Phase III GOYA study (NCT01287741; R-CHOP arm).

RESULTS

The R-CHOP PFS KM curve from the GOYA validation set was well aligned with the POLARIX KM curve. As we anticipated that PFS in POLARIX would evolve similarly to that of GOYA, the data from GOYA were used to externally validate the extrapolated modelling results. While all four statistical methods were able to fit the data to the POLARIX KM curve, the mixture-cure model was the most accurate in predicting long-term PFS in the GOYA external validation set. In the mixture-cure model, generalized gamma distribution estimated 64% (95% confidence intervals [CI]: 56-71%) of patients to have long-term remission in the R-CHOP arm of POLARIX and GOYA, and 75% (95% CI: 70-79%) in the Pola-R-CHP arm of POLARIX. A limitation of this study was the comparison of the statistical models only in the PFS KM curves, since it was not possible to determine which statistical method was more appropriate to extrapolate the overall survival KM curves.

CONCLUSIONS

Within this analysis, the mixture-cure model provided the best prediction of long-term outcomes from the primary PFS analysis of the POLARIX study.