Generalized Linear Models for Flexible Parametric Modeling of the Hazard Function

Cost-utility of sintilimab plus chemotherapy vs chemotherapy as first-line treatment of advanced gastric or gastroesophageal junction cancer in China

OBJECTIVES

ORIENT-16, a phase III clinical trial conducted at 62 hospitals in China, reported that add-on sintilimab (Sin) to chemotherapy (Chemo) had favorable efficacy (p < 0.05) for patients with advanced HER2-negative gastric or gastroesophageal junction cancer (GC/GEJC). This study aimed to evaluate the cost-utility of the Sin+Chemo based on results of ORIENT-16 from the perspective of Chinese healthcare payers.

METHODS

A three-state partitioned survival model was developed to simulate the 10-year life expectancy and total healthcare costs for patients with advanced HER2-negative GC/GEJC. Primary measure outcomes were: cost, quality-adjusted life-years (QALYs), and incremental cost-utility ratios (ICURs). Sensitivity/scenario analyses were conducted to assess the model robustness.

RESULTS

In all patients, Sin+Chemo vs Chemo increased costs by $6,472, additionally providing 0.61 QALYs, resulting in an ICUR of $10,610/QALY. While, in PD-L1 combined positive score ≥ 5 cohort, the ICUR was $9,738/QALYs. The ICUR was most sensitive to the utility of progression-free survival. The probabilistic sensitivity analysis showed that add-on Sin had a 100% probability of being cost-effective at a willingness-to-pay threshold of $18,625/QALY gained.

CONCLUSIONS

Sin+Chemo is a cost-effective first-line treatment option for advanced HER2-negative GC/GEJC in China.

CLINICAL TRIAL REGISTRATION

ORIENT-16, www.clinicaltrials.gov, identifier is NCT03745170.

Using Age-Specific Rates for Parametric Survival Function Estimation in Simulation Models

PURPOSE

To describe a procedure for incorporating parametric functions into individual-level simulation models to sample time to event when age-specific rates are available but not the individual data.

METHODS

Using age-specific event rates, regression analysis was used to parametrize parametric survival distributions (Weibull, Gompertz, log-normal, and log-logistic), select the best fit using the R2 statistic, and apply the corresponding formula to assign random times to events in simulation models. We used stroke rates in the Spanish population to illustrate our procedure.

RESULTS

The 3 selected survival functions (Gompertz, Weibull, and log-normal) had a good fit to the data up to 85 y of age. We selected Gompertz distribution as the best-fitting distribution due to its goodness of fit.

CONCLUSIONS

Our work provides a simple procedure for incorporating parametric risk functions into simulation models without individual-level data.

HIGHLIGHTS

We describe the procedure for sampling times to event for individual-level simulation models as a function of age from parametric survival functions when age-specific rates are available but not the individual dataWe used linear regression to estimate age-specific hazard functions, obtaining estimates of parameter uncertainty.Our approach allows incorporating parameter (second-order) uncertainty in individual-level simulation models needed for probabilistic sensitivity analysis in the absence of individual-level survival data.

Sotorasib versus Docetaxel for treatment of US and Chinese patients with advanced non-small-cell lung cancer with KRAS p.G12C-mutated: A cost-effectiveness analysis to inform drug pricing

BACKGROUND

The cost-effectiveness of sotorasib and its reasonable price in the United States (US) and China remain unknown. Our objective was to estimate the price at which sotorasib could be economical as second-line treatment for advanced non-small-cell lung cancer patients with Kirsten rat sarcoma viral oncogene homolog p.G12C-mutation in 2 countries.

METHODS

We conducted an economic evaluation from the perspective of US and Chinese payers. To analyze US patients, we built a partitioned survival model. However, since we lacked Asian-specific overall survival data, we created a state transition model for the Chinese patients. We obtained patients' baseline characteristics and clinical data from CodeBreaK200, while utilities and costs were gathered from public databases and published literature. We calculated costs (US dollar), life years, quality-adjusted life years (QALYs), and incremental cost-effectiveness ratios. We conducted price simulation to guide pricing strategies. Additionally, we assessed the reliability of our results through sensitivity analyses, scenario analyses, and subgroup analyses.

RESULTS

The incremental cost-effectiveness ratios of sotorasib compared to docetaxel were $1501,852 per quality-adjusted life-years (QALY) in the US and $469,106/QALY in China, respectively, which meant sotorasib was unlikely to be economical at the currently available price of $20,878 (240 × 120 mg) in both countries. Price simulation results revealed that sotorasib would be preferred at a price lower than $1400 at the willingness-to-pay threshold of $37,376 in China and a price lower than $2220 at the willingness-to-pay threshold of $150,000 in the US. Sensitivity, scenario, and subgroup analyses showed that these conclusions were generally robust, the model was most sensitive to the utilities of progression-free survival and post-progression survival.

CONCLUSIONS

Sotorasib could potentially be a cost-effective therapy in the US and China following price reductions. Our evidence-based pricing strategy can assist decision-makers and clinicians in making optimal decisions. However, further analysis of budget impact and affordability is needed.

Extending Beyond Bagust and Beale: Fully Parametric Piecewise Exponential Models for Extrapolation of Survival Outcomes in Health Technology Assessment

OBJECTIVES

When extrapolating time-to-event data the Bagust and Beale (B&B) approach uses the Kaplan-Meier survival function until a manually chosen time point, after which a constant hazard is assumed. This study demonstrates an objective statistical approach to estimate this time point.

METHODS

We estimate piecewise exponential models (PEMs), whereby the hazard function is partitioned into segments each with constant hazards. The boundaries of these segments are known as change points. Our approach determines the location and number of change points in PEMs from which the hazard in the final segment is used to model long-term survival. We reviewed previous applications of the B&B approach in National Institute for Health and Care Excellence Technology Appraisals (TAs) completed between July 2011 and June 2017. The time points after which constant hazards were assumed were compared between PEMs and the B&B approaches. When further survival data were published following the original TA, we compared these updated estimates to predicted survival from the PEM and other parametric models adjusted for general population mortality.

RESULTS

Six of the 59 TAs in this review considered the B&B approach. There was general agreement between the location of time points identified through the PEM and the B&B approaches. In 2 of the identified TAs the best fitting model to the data was a no-change-point model. Of the 3 TAs for which further survival data became available, PEM provided the closest prediction for survival outcomes in 2 TAs.

CONCLUSIONS

PEMs are useful for survival extrapolation when a long-term constant hazard trend for the disease is clinically plausible.

Cost-effectiveness analysis of atezolizumab in patients with non-small-cell lung cancer ineligible for treatment with a platinum-containing regimen: a United Kingdom health care perspective

Background

Cost-effectiveness of atezolizumab, as a treatment for advanced non-small-cell lung cancer (NSCLC) patients who cannot receive a platinum-containing regimen,was still unknown. Our objective was to evaluate the cost-effectiveness of atezolizumab vs. chemotherapy in this indication from the perspective of UK healthcare system.

Methods

From the global, randomised, open-label, phase III IPSOS trial, clinical inputs and patient characteristics were obtained. A partitioned survival model with three health states was built: Progression-free survival, progressed disease and death. A lifetime time horizon was applied, with an annual discount rate of 3.5%. Additionally, the willingness-to-pay threshold of £50,000/QALY was utilized. Primary outcomes were quality-adjusted life-year (QALY), costs, and incremental cost-effectiveness ratio (ICER). Sensitivity, scenario, and subgroup analyses were used to assess the reliability of base-case results. Price simulations were carried out in order to provide information for the pricing strategy at specific willingness-to-pay threshold.

Results

In the base-case analysis, atezolizumab resulted in a gain of 0.28 QALYs and an ICER of £94,873/QALY compared to chemotherapy, demonstrating no cost-effectiveness. Price simulation results revealed that atezolizumab would be preferred at a price lower than £2,215 (a reduction of 41.8%) at the willingness-to-pay threshold of £50,000. Sensitivity, scenario and subgroup analyses revealed these conclusions were generally robust, the model was most sensitive to the price of atezolizumab and subsequent medication. Furthermore, atezolizumab was found to be more cost-effective for patients displaying a positive PD-L1 expression, with an ICER of £72,098/QALY as compared to chemotherapy.

Conclusion

Atezolizumab is not cost-effective for patients with advanced NSCLC ineligible for platinum-containing regimen, potential price reduction is necessary.

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.

A Comparison of Alternative Network Meta-Analysis Methods in the Presence of Nonproportional Hazards: A Case Study in First-Line Advanced or Metastatic Renal Cell Carcinoma

OBJECTIVES

Network meta-analysis (NMA) of time-to-event outcomes based on constant hazard ratios can result in biased findings when the proportional hazards (PHs) assumption does not hold in a subset of trials. We aimed to summarize the published non-PH NMA methods for time-to-event outcomes, demonstrate their application, and compare their results.

METHODS

The following non-PH NMA methods were compared through an illustrative case study in oncology of 4 randomized controlled trials in terms of progression-free survival and overall survival: (1) 1-step or (2) 2-step multivariate NMAs based on traditional survival distributions or fractional polynomials, (3) NMAs with restricted cubic splines for baseline hazard, and (4) restricted mean survival NMA.

RESULTS

For progression-free survival, the PH assumption did not hold across trials and non-PH NMA methods better reflected the relative treatment effects over time. The most flexible models (fractional polynomials and restricted cubic splines) fit better to the data than the other approaches. Estimated hazard ratios obtained with different non-PH NMA methods were similar at 5 years of follow-up but differed thereafter in the extrapolations. Although there was no strong evidence of PH violation for overall survival, non-PH NMA methods captured this uncertainty in the relative treatment effects over time.

CONCLUSIONS

When the PH assumption is questionable in a subset of the randomized controlled trials, we recommend assessing alternative non-PH NMA methods to estimate relative treatment effects for time-to-event outcomes. We propose a transparent and explicit stepwise model selection process considering model fit, external constraints, and clinical validity. Given inherent uncertainty, sensitivity analyses are suggested.

Serplulimab Plus Chemotherapy vs Chemotherapy for Treatment of US and Chinese Patients with Extensive-Stage Small-Cell Lung Cancer: A Cost-Effectiveness Analysis to Inform Drug Pricing

BACKGROUND

Serplulimab is a potential valuable therapy, while patients, physicians, and decision-makers are uncertain about the cost-effectiveness of this novel drug and its corresponding reasonable price. This study aimed to simulate the price at which serplulimab was cost-effective as first-line therapy for United States (US) and Chinese extensive-stage small-cell lung cancer (ES-SCLC) patients.

METHODS

In this economic evaluation, a partitioned survival model was constructed from the perspective of US and Chinese payers. Baseline characteristics of patients and critical clinical data were obtained from ASTRUM-005. Costs and utilities were collected from open-access databases and published literature. Cumulative costs (in US dollars), life years, quality-adjusted life years (QALYs), and incremental cost-effectiveness ratios (ICERs) were measured and compared. Price simulation was conducted to inform the pricing strategy at the given willingness-to-pay (WTP) threshold. The robustness of the model was assessed via sensitivity analyses and scenario analyses; subgroup analyses were also included.

RESULTS

Base-case analysis indicated that serplulimab ($818.16/100 mg) would be cost-effective in the US at the WTP threshold of $150,000, with improved effectiveness of 0.61 QALYs and an additional cost of $64,918 (ICER $106,757). Serplulimab ($818.16/100 mg, patient assistance program considered) was cost-effective in China, with improved effectiveness of 0.58 QALYs and an increased overall cost of $19,369 (ICER $33,392). The price simulation results indicated that serplulimab was favored in the US when the price was less than $762.11/100 mg and $1261.57/100 mg at the WTP threshold of $100,000 and $150,000, respectively; it was cost-effective at the WTP threshold of $38,184 when the price was less than $373.37/100 mg in China. Sensitivity analyses revealed that the above results were stable. Subgroup analysis results indicated an overall trend for subgroups with better survival advantages to have a higher probability of cost-effectiveness, despite serplulimab not being cost-effective in some subgroups.

CONCLUSIONS

Serplulimab might be a valuable and cost-effective therapy in both the US and China. The evidence-based pricing strategy provided by this study could benefit decision-makers in making optimal decisions and clinicians in general clinical practice. More evidence about the budget impact and affordability for patients is needed.

Toripalimab plus chemotherapy vs. chemotherapy in patients with advanced non-small-cell lung cancer: A cost-effectiveness analysis

Background: The potency and safety of toripalimab combination with chemotherapy (TC) as the first-line therapy for advanced non-small cell lung cancer (NSCLC) have been demonstrated in the CHOICE-01 study. Our research explored whether TC was cost-effective compared to chemotherapy alone from the Chinese payer perspective. Materials and methods: Clinical parameters were obtained from a randomized, multicenter, registrational, placebo-controlled, double-blind, phase III trial. Standard fee databases and previously published literature were used to determine costs and utilities. A Markov model with three mutually exclusive health statuses (progression-free survival (PFS), disease progression, and death) was used to predict the disease course. The costs and utilities were discounted at 5% per annum. The main endpoints of the model included cost, quality-adjusted life years (QALYs), and incremental cost-effectiveness ratio (ICER). Univariate and probabilistic sensitivity analyses were performed to investigate the uncertainty. Subgroup analyses were performed to verify the cost-effectiveness of TC in patients with squamous and non-squamous cancer. Results: TC combination therapy yielded an incremental 0.54 QALYs with an incremental cost of $11,777, compared to chemotherapy, giving rise to ICERs of $21,811.76/QALY. Probabilistic sensitivity analysis revealed that TC was not favorable at 1 time GDP per capita. With a prespecified willingness-to-pay threshold (WTP) of three times the GDP per capita, combined treatment had a 100% probability of being cost-effective and had substantial cost-effectiveness in advanced NSCLC. Probabilistic sensitivity analyses showed that TC was more likely to be accepted with a WTP threshold higher than $22,195 in NSCLC. Univariate sensitivity analysis showed that the utility of PFS state, crossover proportions of the chemotherapy arm, cost per cycle of pemetrexed treatment, and discount rate were the dominant influencing factors. Subgroup analyses found that in patients with squamous NSCLC, the ICER was $14,966.09/QALY. In the non-squamous NSCLC, ICER raised to $23,836.27/QALY. ICERs were sensitive to the variance of the PFS state utility. TC was more likely to be accepted when WTP increases exceeded $14,908 in the squamous NSCLC subgroup and $23,409 in the non-squamous NSCLC subgroup. Conclusion: From the perspective of the Chinese healthcare system, TC may be cost-effective in individuals with previously untreated advanced NSCLC at the prespecified WTP threshold compared to chemotherapy, and more significant in individuals with squamous NSCLC, which will provide evidence for clinicians to make the best decisions in general clinical practice.

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

OBJECTIVES

Parametric models are routinely used to estimate the benefit of cancer drugs beyond trial follow-up. The advent of immune checkpoint inhibitors has challenged this paradigm, and emerging evidence suggests that more flexible survival models, which can better capture the shapes of complex hazard functions, might be needed for these interventions. Nevertheless, there is a need for an algorithm to help analysts decide whether flexible models are required and, if so, which should be chosen for testing. This position article has been produced to bridge this gap.

METHODS

A virtual advisory board comprising 7 international experts with in-depth knowledge of survival analysis and health technology assessment was held in summer 2021. The experts discussed 24 questions across 6 topics: the current survival model selection procedure, data maturity, heterogeneity of treatment effect, cure and mortality, external evidence, and additions to existing guidelines. Their responses culminated in an algorithm to inform selection of flexible survival models.

RESULTS

The algorithm consists of 8 steps and 4 questions. Key elements include the systematic identification of relevant external data, using clinical expert input at multiple points in the selection process, considering the future and the observed hazard functions, assessing the potential for long-term survivorship, and presenting results from all plausible models.

CONCLUSIONS

This algorithm provides a systematic, evidence-based approach to justify the selection of survival extrapolation models for cancer immunotherapies. If followed, it should reduce the risk of selecting inappropriate models, partially addressing a key area of uncertainty in the economic evaluation of these agents.

Benzodiazepine-related dementia risks and protopathic biases revealed by multiple-kernel learning with electronic medical records

Objectives

To simultaneously estimate how the risk of incident dementia nonlinearly varies with the administration period and cumulative dose of benzodiazepines, the duration of disorders with an indication for benzodiazepines, and other potential confounders, with the goal of settling the controversy over the role of benzodiazepines in the development of dementia.

Methods

The classical hazard model was extended using the techniques of multiple-kernel learning. Regularised maximum-likelihood estimation, including determination of hyperparameter values with 10-fold cross-validation, bootstrap goodness-of-fit test, and bootstrap estimation of confidence intervals, was applied to cohorts retrospectively extracted from electronic medical records of our university hospitals between 1 November 2004 and 31 July 2020. The analysis was mainly focused on 8160 patients aged 40 or older with new onset of insomnia, affective disorders, or anxiety disorders, who were followed up for 4.10 ± 3.47 years.

Results

Besides previously reported risk associations, we detected significant nonlinear risk variations over 2-4 years attributable to the duration of insomnia and anxiety disorders, and to the administration period of short-acting benzodiazepines. After nonlinear adjustment for potential confounders, we observed no significant risk associations with long-term use of benzodiazepines.

Conclusions

The pattern of the detected nonlinear risk variations suggested reverse causation and confounding. Their putative bias effects over 2-4 years suggested similar biases in previously reported results. These results, together with the lack of significant risk associations with long-term use of benzodiazepines, suggested the need to reconsider previous results and methods for future analysis.

Cost-effectiveness analysis of sintilimab vs. placebo in combination with chemotherapy as first-line therapy for local advanced or metastatic oesophageal squamous cell carcinoma

Objective

Results of Orient 15 indicated the health benefits to patients with local advanced or metastatic oesophageal squamous cell carcinoma (OSCC). This study aimed to evaluate the cost-effectiveness of sintilimab plus chemotherapy in treating OSCC from the perspective of Chinese healthcare system.

Methods

A partitioned survival model was constructed to evaluate the cost-effectiveness of sintilimab plus chemotherapy vs. chemotherapy in treating OSCC. Baseline characteristics of patients and key clinical data were extracted from Orient 15. Costs and utilities were collected from published studies and open-access databases. Costs, quality-adjusted life-years (QALYs), life-years gained, and incremental cost-effectiveness ratios (ICER) were chosen as economic outcome indicators. We also performed sensitivity analyses and subgroup analyses to verify the stability of results.

Results

Combination therapy provided additional 0.84 QALYs and 1.46 life-years with an incremental cost of $25,565.48 than chemotherapy, which had an ICER of $30,409.44 per QALY. The probabilistic sensitivity analysis indicated that combination therapy had a 98.8% probability of cost-effectiveness at the willingness-to-pay threshold (WTP) of $38,184 per QALY. Deterministic sensitivity analysis showed that model outcomes were sensitive to the utilities of progression-free survival and progression disease. The subgroup analysis revealed that combination therapy was cost-effective in patients with high expression of PD-L1 and several specific subgroups.

Conclusion

In this economic evaluation, sintilimab plus chemotherapy was likely to be cost-effective compared with chemotherapy in the first-line therapy of advanced OSCC from the perspective of Chinese healthcare system. Our findings may provide evidence for clinicians to make optimal decisions in clinical practice and for decision-makers to evaluate the cost-effectiveness of sintilimab.

A systematic review and network meta-analysis of first-line immune checkpoint inhibitor combination therapies in patients with advanced non-squamous non-small cell lung cancer

Introduction

Clinical evidence suggests that first-line immune checkpoint inhibitor (ICI) combination therapies can improve survival in patients with advanced non-squamous non-small cell lung cancer (nsq-NSCLC). However, the optimal strategy remains unknown without a systematic comparison of their long-term effects.

Methods

We performed a systematic review and network meta-analysis by retrieving up-to-date literature from PubMed® (National Library of Medicine, Bethesda, MD, USA), Embase® (Elsevier, Amsterdam, Netherlands), MEDLINE® (National Library of Medicine), ClinicalTrials.gov (National Library of Medicine), and major international conference publications. Published studies and abstracts comparing first-line ICI combination therapies with other treatments for patients with advanced nsq-NSCLC were included. Restricted mean survival time (RMST) was measured over 12 months for progression-free survival (PFS) and 18 months for overall survival (OS), and the Royston–Parmar model was used to extrapolate and compare data for the long-term outcomes.

Results

We included a total of 11 trials involving 12 therapies and 6,130 patients. Pembrolizumab plus chemotherapy exhibited the best overall survival (OS) benefit at both 18 and 60 months [RMST = 2.95, 95% confidence interval (CI) 1.96 to 3.97; life-years gained over a 5-year period = 2.18 years]. Nivolumab plus bevacizumab plus chemotherapy was found to present the best progression-free survival (PFS) benefit at 12 months (RMST 3.02, 95% CI 2.11 to 3.91), whereas atezolizumab plus bevacizumab plus chemotherapy showed the best PFS benefit at 36 months (life-years gained over 3 years = 1.22 years). Subgroup analyses showed that among patients with programmed death-ligand 1 (PD-L1) expression ≥ 50%, atezolizumab plus chemotherapy and nivolumab plus ipilimumab resulted in superior OS benefits at 18 and 60 months, respectively. Among patients with PD-L1 expression&lt; 1%, pembrolizumab plus chemotherapy was associated with OS benefits at both 18 and 60 months. Sintilimab plus chemotherapy was associated with relatively fewer grade ≥ 3 adverse events than other ICI combination therapies.

Conclusion

Our results show that ICI combination therapies showed better survival benefits than chemotherapy. Pembrolizumab plus chemotherapy could provide the best OS benefits to patients with advanced nsq-NSCLC, whereas atezolizumab plus bevacizumab plus chemotherapy could bring the best PFS benefits. The optimal ICI combination therapy varies depending on PD-L1 expression level.

Systematic Review Registration

https://www.crd.york.ac.uk/PROSPERO/display_record.php?RecordID=325005, identifier CRD42022325005.

Cost-effectiveness analysis of camrelizumab plus chemotherapy as first-line treatment for advanced squamous NSCLC in China

Objective

Results of CameL-sq has revealed the clinical benefits to patients with advanced squamous non-small-cell lung cancer (sq-NSCLC). This study aims to evaluate the cost-effectiveness of camrelizumab plus chemotherapy to treat sq-NSCLC from the perspective of the Chinese healthcare system.

Methods

We used a partitioned survival model with a lifetime horizon to evaluate the cost-effectiveness of camrelizumab plus chemotherapy vs. chemotherapy in treating sq-NSCLC. Baseline characteristics of patients and key clinical data were extracted from CameL-sq. Costs and utilities were collected from the open-access database and published literature. Costs, quality-adjusted life-years (QALYs), life-years gained, and incremental cost-effectiveness ratios (ICERs) were chosen as economic outcome indicators. We also performed a sensitivity analysis, subgroup analysis, and scenario analysis to verify the stability of the basic analysis results and explore the results under different scenarios.

Results

Combination therapy added 0.47 QALYS and 0.91 life-years with an incremental cost of $6,347.81 compared with chemotherapy, which had an ICER of $13,572 per QALY. The probabilistic sensitivity analysis indicated that camrelizumab plus chemotherapy had a 37.8% probability of cost-effectiveness at a willingness-to-pay threshold (WTP) of 1 time GDP per capital. When WTP was set as 3 times GDP per capital, combination therapy had significant cost-effectiveness. Deterministic sensitivity analysis showed that cost of the best supportive care was the factor with the greatest influence. The subgroup analysis found that combination therapy was associated with cost-effectiveness in several subgroups, namely, patients with disease stage IIIB/IIIC and with PD-L1 tumor proportion score ≤ 1%. Scenario analysis showed that ICER was positively correlated with the price of camrelizumab.

Conclusion

In this economic evaluation, camrelizumab plus chemotherapy was unlikely to be cost-effective compared with chemotherapy in the first line therapy of sq-NSCLC from a perspective of the Chinese healthcare system. Reducing the price of camrelizumab and tailoring treatments based on individual patient factors might improve the cost-effectiveness. Our findings may provide evidence for clinicians in making optimal decisions in general clinical practice.

Dynamic and Flexible Survival Models for Extrapolation of Relative Survival: A Case Study and Simulation Study

BACKGROUND

Extrapolation of survival data is a key task in health technology assessments (HTAs), which may be improved by incorporating general population mortality data via relative survival models. Dynamic survival models are a promising method for extrapolation that may be expanded to dynamic relative survival models (DRSMs), a novel development presented here. There are currently neither examples of dynamic models in HTA nor comparisons of DRSMs with other relative survival models when used for survival extrapolation.

METHODS

An existing appraisal, for which there had been disagreement over the approach to survival extrapolation, was chosen and the health economic model recreated. The sensitivity of estimates of cost-effectiveness to different model choices (standard survival models, DSMs, and DRSMs) and specifications was examined. The appraisal informed a simulation study to evaluate DRSMs with relative survival models based on both standard and spline-based (flexible) models.

RESULTS

Dynamic models provided insight into the behavior of the trend in the hazard function and how it may vary during the extrapolated phase. DRSMs led to extrapolations with improved plausibility for which model choice may be based on clinical input. In the simulation study, the flexible and dynamic relative survival models performed similarly and provided highly variable extrapolations.

LIMITATIONS

Further experience with these models is required to identify settings when they are most useful, and they provide sufficiently accurate extrapolations.

CONCLUSIONS

Dynamic models provide a flexible and attractive method for extrapolating survival data and facilitate the use of clinical input for model choice. Flexible and dynamic relative survival models make few structural assumptions and can improve extrapolation plausibility, but further research is required into methods for reducing the variability in extrapolations.

Methods for Extrapolating Survival Analyses for the Economic Evaluation of Advanced Therapy Medicinal Products

There are two significant challenges for analysts conducting economic evaluations of advanced therapy medicinal products (ATMPs): (i) estimating long-term treatment effects in the absence of mature clinical data, and (ii) capturing potentially complex hazard functions. This review identifies and critiques a variety of methods that can be used to overcome these challenges. The narrative review is informed by a rapid literature review of methods used for the extrapolation of survival analyses in the economic evaluation of ATMPs. There are several methods that are more suitable than traditional parametric survival modelling approaches for capturing complex hazard functions, including, cure-mixture models and restricted cubic spline models. In the absence of mature clinical data, analysts may augment clinical trial data with data from other sources to aid extrapolation, however, the relative merits of employing methods for including data from different sources is not well understood. Given the high and potentially irrecoverable costs of making incorrect decisions concerning the reimbursement or commissioning of ATMPs, it is important that economic evaluations are correctly specified, and that both parameter and structural uncertainty associated with survival extrapolations are considered. Value of information analyses allow for this uncertainty to be expressed explicitly, and in monetary terms.

Incorporating external trial data to improve survival extrapolations: a pilot study of the COU-AA-301 trial

Survival extrapolation plays a key role within cost effectiveness analysis and is often subject to substantial uncertainty. Use of external data to improve extrapolations has been identified as a key research priority. We present findings from a pilot study using data from the COU-AA-301 trial of abiraterone acetate for metastatic castration-resistant prostate cancer, to explore how external trial data may be incorporated into survival extrapolations. External trial data were identified via a targeted search of technology assessment reports. Four methods using external data were compared to simple parametric models (SPMs): informal reference to external data to select appropriate SPMs, piecewise models with, and without, hazard ratio adjustment, and Bayesian models fitted with a prior on the shape parameter(s). Survival and hazard plots were compared, and summary metrics (point estimate accuracy and restricted mean survival time) were calculated. Without consideration of external data, several SPMs may have been selected as the ‘best-fitting’ model. The range of survival probability estimates was generally reduced when external data were included in model estimation, and external hazard plots aided model selection. Different methods yielded varied results, even with the same data source, highlighting potential issues when integrating external trial data within model estimation. By using external trial data, the most (in)appropriate models may be more easily identified. However, benefits of using external data are contingent upon their applicability to the research question, and the choice of method can have a large impact on extrapolations.

Comparing current and emerging practice models for the extrapolation of survival data: a simulation study and case-study

BACKGROUND

Estimates of future survival can be a key evidence source when deciding if a medical treatment should be funded. Current practice is to use standard parametric models for generating extrapolations. Several emerging, more flexible, survival models are available which can provide improved within-sample fit. This study aimed to assess if these emerging practice models also provided improved extrapolations.

METHODS

Both a simulation study and a case-study were used to assess the goodness of fit of five classes of survival model. These were: current practice models, Royston Parmar models (RPMs), Fractional polynomials (FPs), Generalised additive models (GAMs), and Dynamic survival models (DSMs). The simulation study used a mixture-Weibull model as the data-generating mechanism with varying lengths of follow-up and sample sizes. The case-study was long-term follow-up of a prostate cancer trial. For both studies, models were fit to an early data-cut of the data, and extrapolations compared to the known long-term follow-up.

RESULTS

The emerging practice models provided better within-sample fit than current practice models. For data-rich simulation scenarios (large sample sizes or long follow-up), the GAMs and DSMs provided improved extrapolations compared with current practice. Extrapolations from FPs were always very poor whilst those from RPMs were similar to current practice. With short follow-up all the models struggled to provide useful extrapolations. In the case-study all the models provided very similar estimates, but extrapolations were all poor as no model was able to capture a turning-point during the extrapolated period.

CONCLUSIONS

Good within-sample fit does not guarantee good extrapolation performance. Both GAMs and DSMs may be considered as candidate extrapolation models in addition to current practice. Further research into when these flexible models are most useful, and the role of external evidence to improve extrapolations is required.

The Extrapolation Performance of Survival Models for Data With a Cure Fraction: A Simulation Study

OBJECTIVES

Curative treatments can result in complex hazard functions. The use of standard survival models may result in poor extrapolations. Several models for data which may have a cure fraction are available, but comparisons of their extrapolation performance are lacking. A simulation study was performed to assess the performance of models with and without a cure fraction when fit to data with a cure fraction.

METHODS

Data were simulated from a Weibull cure model, with 9 scenarios corresponding to different lengths of follow-up and sample sizes. Cure and noncure versions of standard parametric, Royston-Parmar, and dynamic survival models were considered along with noncure fractional polynomial and generalized additive models. The mean-squared error and bias in estimates of the hazard function were estimated.

RESULTS

With the shortest follow-up, none of the cure models provided good extrapolations. Performance improved with increasing follow-up, except for the misspecified standard parametric cure model (lognormal). The performance of the flexible cure models was similar to that of the correctly specified cure model. Accurate estimates of the cured fraction were not necessary for accurate hazard estimates. Models without a cure fraction provided markedly worse extrapolations.

CONCLUSIONS

For curative treatments, failure to model the cured fraction can lead to very poor extrapolations. Cure models provide improved extrapolations, but with immature data there may be insufficient evidence to choose between cure and noncure models, emphasizing the importance of clinical knowledge for model choice. Dynamic cure fraction models were robust to model misspecification, but standard parametric cure models were not.

Comparison of the performances of survival analysis regression models for analysis of conception modes and risk of type-1 diabetes among 1985-2015 Swedish birth cohort

The goal is to examine the risk of conception mode-type-1 diabetes using different survival analysis modelling approaches and examine if there are differentials in the risk of type-1 diabetes between children from fresh and frozen-thawed embryo transfers. We aimed to compare the performances and fitness of different survival analysis regression models with the Cox proportional hazard (CPH) model used in an earlier study. The effect of conception modes and other prognostic factors on type-1 diabetes among children conceived either spontaneously or by assisted reproductive technology (ART) and its sub-groups was modelled in the earlier study. We used the information on all singleton children from the Swedish Medical Birth Register hosted by the Swedish National Board of Health and Welfare, 1985 to 2015. The main explanatory variable was the mode of conception. We applied the CPH, parametric and flexible parametric survival regression (FPSR) models to the data at 5% significance level. Loglikelihood, Akaike and Bayesian information criteria were used to assess model fit. Among the 3,138,540 singletons, 47,938 (1.5%) were conceived through ART (11,211 frozen-thawed transfer and 36,727 fresh embryo transfer). In total, 18,118 (0.58%) of the children had type-1 diabetes, higher among (0.58%) those conceived spontaneously than the ART-conceived (0.42%). The median (Interquartile range (IQR)) age at onset of type-1 diabetes among spontaneously conceived children was 10 (14-6) years, 8(5-12) for ART, 6 (4-10) years for frozen-thawed embryo transfer and 9 (5-12) years for fresh embryo transfer. The estimates from the CPH, FPSR and parametric PH models are similar. There was no significant difference in the risk of type-1 diabetes among ART- and spontaneously conceived children; FPSR: (adjusted Hazard Ratio (aHR) = 1.070; 95% Confidence Interval (CI):0.929-1.232, p = 0.346) vs CPH: (aHR = 1.068; 95%CI: 0.927-1.230, p = 0.361). A sub-analysis showed that the adjusted hazard of type-1 diabetes was 37% (aHR = 1.368; 95%CI: 1.013-1.847, p = 0.041) higher among children from frozen-thawed embryo transfer than among children from spontaneous conception. The hazard of type-1 diabetes was higher among children whose mothers do not smoke (aHR = 1.296; 95%CI:1.240-1.354, p<0.001) and of diabetic mothers (aHR = 6.419; 95%CI:5.852-7.041, p<0.001) and fathers (aHR = 8.808; 95%CI:8.221-9.437, p<0.001). The estimates from the CPH, parametric models and the FPSR model were close. This is an indication that the models performed similarly and any of them can be used to model the data. We couldn't establish that ART increases the risk of type-1 diabetes except when it is subdivided into its two subtypes. There is evidence of a greater risk of type-1 diabetes when conception is through frozen-thawed transfer.

Performance evaluation of survival regression models in analysing Swedish dental implant complication data with frailty

The use of inappropriate methods for estimating the effects of covariates in survival data with frailty leads to erroneous conclusions in medical research. This study evaluated the performance of 13 survival regression models in assessing the factors associated with the timing of complications in implant-supported dental restorations in a Swedish cohort. Data were obtained from randomly selected cohort (n = 596) of Swedish patients provided with dental restorations supported in 2003. Patients were evaluated over 9 years of implant loss, peri-implantitis or technical complications. Best Model was identified using goodness, AIC and BIC. The loglikelihood, the AIC and BIC were consistently lower in flexible parametric model with frailty (df = 2) than other models. Adjusted hazard of implant complications was 45% (adjusted Hazard Ratio (aHR) = 1.449; 95% Confidence Interval (CI): 1.153-1.821, p = 0.001) higher among patients with periodontitis. While controlling for other variables, the hazard of implant complications was about 5 times (aHR = 4.641; 95% CI: 2.911-7.401, p<0.001) and 2 times (aHR = 2.338; 95% CI: 1.553-3.519, p<0.001) higher among patients with full- and partial-jaw restorations than those with single crowns. Flexible parametric survival model with frailty are the most suitable for modelling implant complications among the studied patients.

How Uncertain is the Survival Extrapolation? A Study of the Impact of Different Parametric Survival Models on Extrapolated Uncertainty About Hazard Functions, Lifetime Mean Survival and Cost Effectiveness

BACKGROUND AND OBJECTIVE

The extrapolation of estimated hazard functions can be an important part of cost-effectiveness analyses. Given limited follow-up time in the sample data, it may be expected that the uncertainty in estimates of hazards increases the further into the future they are extrapolated. The objective of this study was to illustrate how the choice of parametric survival model impacts on estimates of uncertainty about extrapolated hazard functions and lifetime mean survival.

METHODS

We examined seven commonly used parametric survival models and described analytical expressions and approximation methods (delta and multivariate normal) for estimating uncertainty. We illustrate the multivariate normal method using case studies based on four representative hypothetical datasets reflecting hazard functions commonly encountered in clinical practice (constant, increasing, decreasing, or unimodal), along with a hypothetical cost-effectiveness analysis.

RESULTS

Depending on the survival model chosen, the uncertainty in extrapolated hazard functions could be constant, increasing or decreasing over time for the case studies. Estimates of uncertainty in mean survival showed a large variation (up to sevenfold) for each case study. The magnitude of uncertainty in estimates of cost effectiveness, as measured using the incremental cost per quality-adjusted life-year gained, varied threefold across plausible models. Differences in estimates of uncertainty were observed even when models provided near-identical point estimates.

CONCLUSIONS

Survival model choice can have a significant impact on estimates of uncertainty of extrapolated hazard functions, mean survival and cost effectiveness, even when point estimates were similar. We provide good practice recommendations for analysts and decision makers, emphasizing the importance of considering the plausibility of estimates of uncertainty in the extrapolated period as a complementary part of the model selection process.