Extrapolating Survival Data Using Historical Trial-Based a Priori Distributions

Use of external data to inform overall survival extrapolation in NICE technology appraisals for oncology drugs

AIM

To assess use of external evidence for overall survival (OS) estimation in oncology single-technology appraisals (STAs) by the National Institute for Health and Care Excellence (NICE).

METHODS

STAs for oncology drugs appraised by NICE between January 2021 and March 2023 were identified. For each eligible STA, OS extrapolation methods used, the rationale for using external data, the source and type of data, and information on acceptance by the evidence review group (ERG) and the appraisal committee were extracted.

RESULTS

Initially, 215 STAs were identified, of which 82 were eligible for the study. Of these, 32 STAs used external data for OS extrapolation, including trial data (44%), real-world data (47%), clinical opinion (25%), meta-analysis (1%) and previous STA (1%). External data were used more frequently in state-transition models for post-event transitions and cure assumptions, and in partitioned-survival models to replace pivotal trial OS, inform long-term survival estimates or to estimate OS based on surrogacy analysis. Sensitivity analyses on use of external data was explored in 16 (50%) of the STAs. The committee accepted use of external data in half of the analysed STAs, acknowledging uncertainty in OS extrapolation.

LIMITATIONS

The analysis was limited to the STAs published between 2021 and 2023 and publicly available materials on the NICE website.

CONCLUSION

This study provides an overview of external data used to estimate OS in oncology STAs conducted by NICE in recent years. External data, including trial data, real-world data and clinical opinions, were incorporated into recent oncology STAs at various modelling stages. ERGs and appraisal committees were generally accepting of the use of external data. However, it is crucial to conduct a sensitivity analysis and provide a justification for the methods and data source selection.

Defining Biological and Clinical Plausibility: The DICSA Framework for Protocolized Assessment in Survival Extrapolations Across Therapeutic Areas

BACKGROUND

Numerous health technology assessment guidance documents emphasize the importance of biological/clinical plausibility of modeled lifetime incremental survival without clearly defining it.

OBJECTIVES

This paper defines biologically and clinically plausible lifetime survival extrapolations and proposes a framework to systematically assess this by comparing survival expectations estimated premodeling, with the final modeled survival extrapolations. This framework is embedded in a survival extrapolation protocol template, which ensures that both the expectations and extrapolations are based on unified, comprehensive evidence.

METHODS

A targeted review was conducted of 29 guidance documents from National Institute for Health and Care Excellence, Pharmaceutical Benefits Advisory Committee, Haute Autorité de Santé, Canada's Drug Agency, and European joint clinical assessment, focusing on survival analysis, evidence synthesis, cost-effectiveness modeling methods, and use of observational data.

RESULTS

Survival extrapolations are biologically/clinically plausible when "predicted survival estimates that fall within the range considered plausible a-priori, obtained using a-priori justified methodology." These a priori expectations should utilize the totality of evidence available and take into account local target setting (i.e., survival-influencing aspects such as patient population, treatment pathway, and country). Pre-protocolized biologically/clinically plausible survival extrapolation was operationalized in a five-step DICSA approach: (1) Describe the target setting as defined by all relevant treatment and disease aspects that influence survival; (2) collect Information from relevant sources; (3) Compare survival-influencing aspects across information sources; (4) Set pre-protocolized survival expectations and plausible ranges; and (5) Assess how trial-based extrapolations align with the set expectations by comparing modeled survival extrapolations to the range of values a priori considered to be plausible.

CONCLUSION

The definition of plausibility of survival extrapolations, the operationalization of its assessment, and the corresponding extrapolation protocol template can contribute to the transparent development of biologically/clinically plausible survival extrapolations.

Slipping Away: Slippage in Hazard Ratios Over Datacuts and Its Impact on Immuno-oncology Combination Economic Evaluations

OBJECTIVES

This study examines the impact of slippage in hazard ratios (tending toward the null over subsequent datacuts) for overall survival for combination treatment with a PD-(L)-1 inhibitor and a tyrosine kinase inhibitor in advanced renal cell carcinoma.

METHODS

Four trials' Kaplan-Meier curves were digitized over several datacuts and fitted with standard parametric curves. Accuracy and consistency of early data projections were calculated versus observed restricted mean survival time and fitted lifetime survival from the longest follow-up datacut. The change in economically justifiable price (eJP) was calculated fitting the same curve to both arms, using an assumed average utility of 0.7 and willingness-to-pay threshold of £30 000 per quality-adjusted life-year. The eJP represents the lifetime justifiable price increment for the new treatment, including differences in drug-, administration-, and disease-related costs.

RESULTS

Slippage in hazard ratios was observed in trials with longer follow-up, potentially influenced by subsequent PD-(L)-1 use after tyrosine kinase inhibitor monotherapy, early stoppage of PD-(L)-1, and development of resistance. Lognormal and log-logistic curves were more likely to overpredict the observed result; Gompertz and gamma underpredicted. Statistical measures of goodness of fit did not select the curves that resulted in the RMST closest to what was observed in the final data cut. Large differences in incremental mean life-years were observed between even the penultimate and final datacuts for most of the fitted curves, meaningfully affecting the eJP.

CONCLUSIONS

This work demonstrates the challenge in predicting treatment benefits with novel therapies using immature data. Incorporating information on the impact of subsequent treatment is likely to play a key role in improving predictions.

Cost-Effectiveness of Semaglutide in Patients With Obesity and Cardiovascular Disease

BACKGROUND

Randomized clinical trials have shown that semaglutide is associated with a clinically relevant reduction in body weight and a lower risk of adverse cardiovascular events in those who are overweight or obese with a history of cardiovascular disease but no diabetes. The objective of this study was to assess the cost-effectiveness of semaglutide for this indication.

METHODS

A decision analytic Markov model was used to compare the lifetime benefits and costs of semaglutide 2.4-mg subcutaneous weekly vs standard care in a hypothetical cohort of patients who were overweight or obese with preexisting cardiovascular disease (and no diabetes) from the health care payer perspective. Our model included ischemic stroke, heart failure hospitalization and/or urgent visit or myocardial infarction, and death over monthly transition cycles. Model outcomes included costs (2023 CAD$), quality-adjusted life years (QALYs), and incremental cost-effectiveness ratios.

RESULTS

Base case analysis showed that the incremental cost-effectiveness ratio for semaglutide compared with standard care was $72,962 per QALY gained with a 14% likelihood of cost-effectiveness adopting a $50,000 per QALY gained willingness to pay threshold. Factors with the greatest influence on cost-effectiveness were medication efficacy on mortality and medication cost. When the price of semaglutide was reduced by 50%, it was economically attractive at $37,190 per QALY gained with an 80% likelihood of cost-effectiveness at a $50,000 per QALY threshold.

CONCLUSIONS

Semaglutide might be a cost-effective option for the publicly funded health care system contingent on initial pricing. Considering the candidate population-patients who are overweight or obese with preexisting cardiovascular disease-policymakers should consider the budget effect of funding semaglutide and weigh it against other ways scarce health care dollars might be used.

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.

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

OBJECTIVES

Parametric 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.

METHODS

We 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.

RESULTS

The 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.

CONCLUSIONS

The 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.

Extrapolation of Survival Data Using a Bayesian Approach: A Case Study Leveraging External Data from Cilta-Cel Therapy in Multiple Myeloma

INTRODUCTION

Extrapolating long-term overall survival (OS) from shorter-term clinical trial data is key to health technology assessment in oncology. However, extrapolation using conventional methods is often subject to uncertainty. Using ciltacabtagene autoleucel (cilta-cel), a chimeric antigen receptor T-cell therapy for multiple myeloma, we used a flexible Bayesian approach to demonstrate use of external longer-term data to reduce the uncertainty in long-term extrapolation.

METHODS

The pivotal CARTITUDE-1 trial (NCT03548207) provided the primary efficacy data for cilta-cel, including a 12-month median follow-up snapshot of OS. Longer-term (48-month median follow-up) survival data from the phase I LEGEND-2 study (NCT03090659) were also available. Twelve-month CARTITUDE-1 OS data were extrapolated in two ways: (1) conventional survival models with standard parametric distributions (uninformed), and (2) Bayesian survival models whose shape prior was informed from 48-month LEGEND-2 data. For validation, extrapolations from 12-month CARTITUDE-1 data were compared with observed 28-month CARTITUDE-1 data.

RESULTS

Extrapolations of the 12-month CARTITUDE-1 data using conventional uninformed parametric models were highly variable. Using informative priors from the 48-month LEGEND-2 dataset, the ranges of projected OS at different timepoints were consistently narrower. Area differences between the extrapolation curves and the 28-month CARTITUDE-1 data were generally lower in informed Bayesian models, except for the uninformed log-normal model, which had the lowest difference.

CONCLUSIONS

Informed Bayesian survival models reduced variation of long-term projections and provided similar projections as the uninformed log-normal model. Bayesian models generated a narrower and more plausible range of OS projections from 12-month data that aligned with observed 28-month data.

TRIAL REGISTRATION

CARTITUDE-1 ClinicalTrials.gov identifier, NCT03548207. LEGEND-2 ClinicalTrials.gov identifier, NCT03090659, registered retrospectively on 27 March 2017, and ChiCTR-ONH-17012285.

A Systematic Review of Methods to Incorporate External Evidence into Trial-Based Survival Extrapolations for Health Technology Assessment

BACKGROUND

External evidence is commonly used to inform survival modeling for health technology assessment (HTA). While there are a range of methodological approaches that have been proposed, it is unclear which methods could be used and how they compare.

PURPOSE

This review aims to identify, describe, and categorize established methods to incorporate external evidence into survival extrapolation for HTA.

DATA SOURCES

Embase, MEDLINE, EconLit, and Web of Science databases were searched to identify published methodological studies, supplemented by hand searching and citation tracking.

STUDY SELECTION

Eligible studies were required to present a novel extrapolation approach incorporating external evidence (i.e., data or information) within survival model estimation.

DATA EXTRACTION

Studies were classified according to how the external evidence was integrated as a part of model fitting. Information was extracted concerning the model-fitting process, key requirements, assumptions, software, application contexts, and presentation of comparisons with, or validation against, other methods.

DATA SYNTHESIS

Across 18 methods identified from 22 studies, themes included use of informative prior(s) (n = 5), piecewise (n = 7), and general population adjustment (n = 9), plus a variety of "other" (n = 8) approaches. Most methods were applied in cancer populations (n = 13). No studies compared or validated their method against another method that also incorporated external evidence.

LIMITATIONS

As only studies with a specific methodological objective were included, methods proposed as part of another study type (e.g., an economic evaluation) were excluded from this review.

CONCLUSIONS

Several methods were identified in this review, with common themes based on typical data sources and analytical approaches. Of note, no evidence was found comparing the identified methods to one another, and so an assessment of different methods would be a useful area for further research.HighlightsThis review aims to identify methods that have been used to incorporate external evidence into survival extrapolations, focusing on those that may be used to inform health technology assessment.We found a range of different approaches, including piecewise methods, Bayesian methods using informative priors, and general population adjustment methods, as well as a variety of "other" approaches.No studies attempted to compare the performance of alternative methods for incorporating external evidence with respect to the accuracy of survival predictions. Further research investigating this would be valuable.

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.

Blended Survival Curves: A New Approach to Extrapolation for Time-to-Event Outcomes from Clinical Trials in Health Technology Assessment

BACKGROUND

Survival extrapolation is essential in cost-effectiveness analysis to quantify the lifetime survival benefit associated with a new intervention, due to the restricted duration of randomized controlled trials (RCTs). Current approaches of extrapolation often assume that the treatment effect observed in the trial can continue indefinitely, which is unrealistic and may have a huge impact on decisions for resource allocation.

OBJECTIVE

We introduce a novel methodology as a possible solution to alleviate the problem of survival extrapolation with heavily censored data from clinical trials.

METHOD

The main idea is to mix a flexible model (e.g., Cox semiparametric) to fit as well as possible the observed data and a parametric model encoding assumptions on the expected behavior of underlying long-term survival. The two are "blended" into a single survival curve that is identical with the Cox model over the range of observed times and gradually approaching the parametric model over the extrapolation period based on a weight function. The weight function regulates the way two survival curves are blended, determining how the internal and external sources contribute to the estimated survival over time.

RESULTS

A 4-y follow-up RCT of rituximab in combination with fludarabine and cyclophosphamide versus fludarabine and cyclophosphamide alone for the first-line treatment of chronic lymphocytic leukemia is used to illustrate the method.

CONCLUSION

Long-term extrapolation from immature trial data may lead to significantly different estimates with various modelling assumptions. The blending approach provides sufficient flexibility, allowing a wide range of plausible scenarios to be considered as well as the inclusion of external information, based, for example, on hard data or expert opinion. Both internal and external validity can be carefully examined.

HIGHLIGHTS

Interim analyses of trials with limited follow-up are often subject to high degrees of administrative censoring, which may result in implausible long-term extrapolations using standard approaches.In this article, we present an innovative methodology based on "blending" survival curves to relax the traditional proportional hazard assumption and simultaneously incorporate external information to guide the extrapolation.The blended method provides a simple and powerful framework to allow a careful consideration of a wide range of plausible scenarios, accounting for model fit to the short-term data as well as the plausibility of long-term extrapolations.

Alert-driven vs scheduled remote monitoring of implantable cardiac defibrillators: A cost-consequence analysis from the TRUST trial

BACKGROUND

Alert-driven remote patient monitoring (RPM) or fully virtual care without routine evaluations may reduce clinic workload and promote more efficient resource allocation, principally by diminishing nonactionable patient encounters.

OBJECTIVE

The purpose of this study was to conduct a cost-consequence analysis to compare 3 postimplant implantable cardioverter-defibrillator (ICD) follow-up strategies: (1) in-person evaluation (IPE) only; (2) RPM-conventional (hybrid of IPE and RPM); and (3) RPM-alert (alert-based ICD follow-up).

METHODS

We constructed a decision-analytic Markov model to estimate the costs and benefits of the 3 strategies over a 2-year time horizon from the perspective of the US Medicare payer. Aggregate and patient-level data from the TRUST (Lumos-T Safely RedUceS RouTine Office Device Follow-up) randomized clinical trial informed clinical effectiveness model inputs. TRUST randomized 1339 patients 2:1 to conventional RPM or IPE alone, and found that RPM was safe and reduced the number of nonactionable encounters. Cost data were obtained from the published literature. The primary outcome was incremental cost.

RESULTS

Mean cumulative follow-up costs per patient were $12,688 in the IPE group, $12,001 in the RPM-conventional group, and $11,011 in the RPM-alert group. Compared to the IPE group, both the RPM-conventional and RPM-alert groups were associated with lower incremental costs of -$687 (95% confidence interval [CI] -$2138 to +$638) and -$1,677 (95% CI -$3134 to -$304), respectively. Therefore, the RPM-alert strategy was most cost-effective, with an estimated cost-savings in 99% of simulations.

CONCLUSIONS

Alert-driven RPM was economically attractive and, if patient outcomes and safety are comparable to those of conventional RPM, may be the preferred strategy for ICD follow-up.

Bayesian hierarchical model-based network meta-analysis to overcome survival extrapolation challenges caused by data immaturity

Aim: This research evaluated standard Weibull mixture cure (WMC) network meta-analysis (NMA) with Bayesian hierarchical (BH) WMC NMA to inform long-term survival of therapies. Materials & methods: Four trials in previously treated metastatic non-small-cell lung cancer with PD-L1 >1% were used comparing docetaxel with nivolumab, pembrolizumab and atezolizumab. Cure parameters related to a certain treatment class were assumed to share a common distribution. Results: Standard WMC NMA predicted cure rates were 0.03 (0.01; 0.07), 0.18 (0.12; 0.24), 0.07 (0.02; 0.15) and 0.03 (0.00; 0.09) for docetaxel, nivolumab, pembrolizumab and atezolizumab, respectively, with corresponding incremental life years (LY) of 3.11 (1.65; 4.66), 1.06 (0.41; 2.37) and 0.42 (-0.57; 1.68). The Bayesian hierarchical-WMC-NMA rates were 0.06 (0.03; 0.10), 0.17 (0.11; 0.23), 0.12 (0.05; 0.20) and 0.12 (0.03; 0.23), respectively, with incremental LY of 2.35 (1.04; 3.93), 1.67 (0.68; 2.96) and 1.36 (-0.05; 3.64). Conclusion: BH-WMC-NMA impacts incremental mean LYs and cost-effectiveness ratios, potentially affecting reimbursement decisions.

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.

Structured expert elicitation to inform long-term survival extrapolations using alternative parametric distributions: a case study of CAR T therapy for relapsed/ refractory multiple myeloma

Background

Our aim was to extend traditional parametric models used to extrapolate survival in cost-effectiveness analyses (CEAs) by integrating individual-level patient data (IPD) from a clinical trial with estimates from experts regarding long-term survival. This was illustrated using a case study evaluating survival of patients with triple-class exposed relapsed/refractory multiple myeloma treated with the chimeric antigen receptor (CAR) T cell therapy idecabtagene vicleucel (ide-cel, bb2121) in KarMMa (a phase 2, single-arm trial).

Methods

The distribution of patients expected to be alive at 3, 5, and 10 years given the observed survival from KarMMa (13.3 months of follow-up) was elicited from 6 experts using the SHeffield ELicitation Framework. Quantities of interest were elicited from each expert individually, which informed the consensus elicitation including all experts. Estimates for each time point were assumed to follow a truncated normal distribution. These distributions were incorporated into survival models, which constrained the expected survival based on standard survival distributions informed by IPD from KarMMa.

Results

Models for ide-cel that combined KarMMa data with expert opinion were more consistent in terms of survival as well as mean survival at 10 years (survival point estimates under different parametric models were 29–33% at 3 years, 5–17% at 5 years, and 0–6% at 10 years) versus models with KarMMa data alone (11–39% at 3 years, 0–25% at 5 years, and 0–11% at 10 years).

Conclusion

This case study demonstrates a transparent approach to integrate IPD from trials with expert opinion using traditional parametric distributions to ensure long-term survival extrapolations are clinically plausible.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-022-01745-z.

Bayesian Modeling of COVID-19 to Classify the Infection and Death Rates in a Specific Duration: The Case of Algerian Provinces

COVID-19 causes acute respiratory illness in humans. The direct consequence of the spread of the virus is the need to find appropriate and effective solutions to reduce its spread. Similar to other countries, the pandemic has spread in Algeria, with noticeable variation in mortality and infection rates between regions. We aimed to estimate the proportion of people who died or became infected with SARS-CoV-2 in each provinces using a Bayesian approach. The estimation parameters were determined using a binomial distribution along with an a priori distribution, and the results had a high degree of accuracy. The Bayesian model was applied during the third wave (1 January-15 August 2021), in all Algerian's provinces. For spatial analysis of duration, geographical maps were used. Our findings show that Tissemsilt, Ain Defla, Illizi, El Taref, and Ghardaia (Mean = 0.001) are the least affected provinces in terms of COVID-19 mortality. The results also indicate that Tizi Ouzou (Mean = 0.0694), Boumerdes (Mean = 0.0520), Annaba (Mean = 0.0483), Tipaza (Mean = 0.0524), and Tebessa (Mean = 0.0264) are more susceptible to infection, as they were ranked in terms of the level of corona infections among the 48 provinces of the country. Their susceptibility seems mainly due to the population density in these provinces. Additionally, it was observed that northeast Algeria, where the population is concentrated, has the highest infection rate. Factors affecting mortality due to COVID-19 do not necessarily depend on the spread of the pandemic. The proposed Bayesian model resulted in being useful for monitoring the pandemic to estimate and compare the risks between provinces. This statistical inference can provide a reasonable basis for describing future pandemics in other world geographical areas.

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.

Cost-Effectiveness of Coronary Artery Bypass Surgery Versus Medicine in Ischemic Cardiomyopathy: The STICH Randomized Clinical Trial

BACKGROUND

The STICH Randomized Clinical Trial (Surgical Treatment for Ischemic Heart Failure) demonstrated that coronary artery bypass grafting (CABG) reduced all-cause mortality rates out to 10 years compared with medical therapy alone (MED) in patients with ischemic cardiomyopathy and reduced left ventricular function (ejection fraction ≤35%). We examined the economic implications of these results.

METHODS

We used a decision-analytic patient-level simulation model to estimate the lifetime costs and benefits of CABG and MED using patient-level resource use and clinical data collected in the STICH trial. Patient-level costs were calculated by applying externally derived US cost weights to resource use counts during trial follow-up. A 3% discount rate was applied to both future costs and benefits. The primary outcome was the incremental cost-effectiveness ratio assessed from the US health care sector perspective.

RESULTS

For the CABG arm, we estimated 6.53 quality-adjusted life-years (95% CI, 5.70-7.53) and a lifetime cost of $140 059 (95% CI, $106 401 to $180 992). For the MED arm, the corresponding estimates were 5.52 (95% CI, 5.06-6.09) quality-adjusted life-years and $74 894 lifetime cost (95% CI, $58 372 to $93 541). The incremental cost-effectiveness ratio for CABG compared with MED was $63 989 per quality-adjusted life-year gained. At a societal willingness-to-pay threshold of $100 000 per quality-adjusted life-year gained, CABG was found to be economically favorable compared with MED in 87% of microsimulations.

CONCLUSIONS

In the STICH trial, in patients with ischemic cardiomyopathy and reduced left ventricular function, CABG was economically attractive relative to MED at current benchmarks for value in the United States.

REGISTRATION

URL: https://www.

CLINICALTRIALS

gov; Unique identifier: NCT00023595.

Using Data on Survival with Idiopathic Pulmonary Fibrosis to Estimate Survival with Other Types of Progressive Fibrosis Interstitial Lung Disease: A Bayesian Framework

INTRODUCTION

Among the various types of progressive fibrosing interstitial lung diseases (PF-ILDs), substantial survival data exist for idiopathic pulmonary fibrosis (IPF) but not for other types. This hinders evidence-based decisions about treatment and management, as well as the economic modelling needed to justify research into new treatments and reimbursement approvals. Given the clinical similarities between IPF and other PF-ILDs, we reasoned that patient survival data from four major IPF trials could be used to estimate long-term survival in other PF-ILDs.

METHODS

We used propensity score matching to match patients with IPF taking either nintedanib or placebo in the TOMORROW, INPULSIS-1, INPULSIS-2 and INPULSIS-ON trials to patients with PF-ILDs other than IPF in the INBUILD trial. Seven models were fitted to the survival data for the matched patients with IPF, and the three best-fitting models were used to generate informative priors in a Bayesian framework to extrapolate patient survival of the INBUILD population.

RESULTS

After propensity score matching, the analysis included data from 1099 patients with IPF (640 nintedanib patients; 459 placebo patients) and 654 patients with other PF-ILDs (326 nintedanib patients; 328 placebo patients). Gamma, log-logistic and Weibull models best fit the survival of the matched patients with IPF. All three models led to consistent Bayesian estimates of survival for the matched patients with other PF-ILDs, with median rates of overall survival ranging from 6.34 to 6.50 years after starting nintedanib. The corresponding control group survival estimates were 3.42 to 3.76 years.

CONCLUSION

We provide the first estimates of long-term overall survival for patients with PF-ILDs other than IPF, and our analysis suggests that nintedanib may prolong their survival. Our Bayesian approach to estimating survival of one disease based on clinical trial data from a similar disease may help inform economic modelling of rare, orphan and newly defined disorders.

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.

Heterogeneity in Survival with Immune Checkpoint Inhibitors and Its Implications for Survival Extrapolations: A Case Study in Advanced Melanoma

Background

Survival heterogeneity and limited trial follow-up present challenges for estimating lifetime benefits of oncology therapies. This study used CheckMate 067 (NCT01844505) extended follow-up data to assess the predictive accuracy of standard parametric and flexible models in estimating the long-term overall survival benefit of nivolumab plus ipilimumab (an immune checkpoint inhibitor combination) in advanced melanoma.

Methods

Six sets of survival models (standard parametric, piecewise, cubic spline, mixture cure, parametric mixture, and landmark response models) were independently fitted to overall survival data for treatments in CheckMate 067 (nivolumab plus ipilimumab, nivolumab, and ipilimumab) using successive data cuts (28, 40, 52, and 60 mo). Standard parametric models allow survival extrapolation in the absence of a complex hazard. Piecewise and cubic spline models allow additional flexibility in fitting the hazard function. Mixture cure, parametric mixture, and landmark response models provide flexibility by explicitly incorporating survival heterogeneity. Sixty-month follow-up data, external ipilimumab data, and clinical expert opinion were used to evaluate model estimation accuracy. Lifetime survival projections were compared using a 5% discount rate.

Results

Standard parametric, piecewise, and cubic spline models underestimated overall survival at 60 mo for the 28-mo data cut. Compared with other models, mixture cure, parametric mixture, and landmark response models provided more accurate long-term overall survival estimates versus external data, higher mean survival benefit over 20 y for the 28-mo data cut, and more consistent 20-y mean overall survival estimates across data cuts.

Conclusion

This case study demonstrates that survival models explicitly incorporating survival heterogeneity showed greater accuracy for early data cuts than standard parametric models did, consistent with similar immune checkpoint inhibitor survival validation studies in advanced melanoma. Research is required to assess generalizability to other tumors and disease stages.

Highlights

Comparison of Parametric Survival Extrapolation Approaches Incorporating General Population Mortality for Adequate Health Technology Assessment of New Oncology Drugs

OBJECTIVES

Survival extrapolation of trial outcomes is required for health economic evaluation. Generally, all-cause mortality (ACM) is modeled using standard parametric distributions, often without distinguishing disease-specific/excess mortality and general population background mortality (GPM). Recent National Institute for Health and Care Excellence guidance (Technical Support Document 21) recommends adding GPM hazards to disease-specific/excess mortality hazards in the log-likelihood function ("internal additive hazards"). This article compares alternative extrapolation approaches with and without GPM adjustment.

METHODS

Survival extrapolations using the internal additive hazards approach (1) are compared to no GPM adjustment (2), applying GPM hazards once ACM hazards drop below GPM hazards (3), adding GPM hazards to ACM hazards (4), and proportional hazards for ACM versus GPM hazards (5). The fit, face validity, mean predicted life-years, and corresponding uncertainty measures are assessed for the active versus control arms of immature and mature (30- and 75-month follow-up) multiple myeloma data and mature (64-month follow-up) breast cancer data.

RESULTS

The 5 approaches yielded considerably different outcomes. Incremental mean predicted life-years vary most in the immature multiple myeloma data set. The lognormal distribution (best statistical fit for approaches 1-4) produces survival increments of 3.5 (95% credible interval: 1.4-5.3), 8.5 (3.1-13.0), 3.5 (1.3-5.4), 2.9 (1.1-4.5), and 1.6 (0.4-2.8) years for approaches 1 to 5, respectively. Approach 1 had the highest face validity for all data sets. Uncertainty over parametric distributions was comparable for GPM-adjusted approaches 1, 3, and 4, and much larger for approach 2.

CONCLUSION

This study highlights the importance of GPM adjustment, and particularly of incorporating GPM hazards in the log-likelihood function of standard parametric distributions.

Data Analysis of the Risks of Type 2 Diabetes Mellitus Complications before Death Using a Data-Driven Modelling Approach: Methodologies and Challenges in Prolonged Diseases

(1) Background: A disease prediction model derived from real-world data is an important tool for managing type 2 diabetes mellitus (T2D). However, an appropriate prediction model for the Asian T2D population has not yet been developed. Hence, this study described construction details of the T2D Holistic Care model via estimating the probability of diabetes-related complications and the time-to-occurrence from a population-based database. (2) Methods: The model was based on the database of a Taiwan pay-for-performance reimbursement scheme for T2D between November 2002 and July 2017. A nonhomogeneous Markov model was applied to simulate multistate (7 main complications and death) transition probability after considering the sequential and repeated difficulties. (3) Results: The Markov model was constructed based on clinical care information from 163,452 patients with T2D, with a mean follow-up time of 5.5 years. After simulating a cohort of 100,000 hypothetical patients over a 10-year time horizon based on selected patient characteristics at baseline, a good predicted complication and mortality rates with a small range of absolute error (0.3–3.2%) were validated in the original cohort. Better and optimal predictabilities were further confirmed compared to the UKPDS Outcomes model and applied the model to other Asian populations, respectively. (4) Contribution: The study provides well-elucidated evidence to apply real-world data to the estimation of the occurrence and time point of major diabetes-related complications over a patient’s lifetime. Further applications in health decision science are encouraged.

Economic Evaluation of Catheter Ablation of Atrial Fibrillation in Patients with Heart Failure With Reduced Ejection Fraction

BACKGROUND

Randomized clinical trials have demonstrated that catheter ablation for atrial fibrillation in patients with heart failure with reduced ejection fraction may improve survival and other cardiovascular outcomes.

METHODS

We constructed a decision-analytic Markov model to estimate the costs and benefits of catheter ablation and medical management in patients with symptomatic heart failure with reduced ejection fraction (left ventricular ejection fraction ≤35%) and atrial fibrillation over a lifetime horizon. Evidence from the published literature informed the model inputs, including clinical effectiveness data from meta-analyses. Probabilistic and deterministic sensitivity analyses were performed. A 3% discount rate was applied to both future costs and benefits. The primary outcome was the incremental cost-effectiveness ratio assessed from the US health care sector perspective.

RESULTS

Catheter ablation was associated with 6.47 (95% CI, 5.89-6.93) quality-adjusted life years (QALYs) and a total cost of $105 657 (95% CI, $55 311-$191 934; 2018 US dollars), compared with 5.30 (95% CI, 5.20-5.39) QALYs and $63 040 (95% CI, $37 624-$102 260) for medical management. The incremental cost-effectiveness ratio for catheter ablation compared with medical management was $38 496 (95% CI, $5583-$117 510) per QALY gained. Model inputs with the greatest variation on incremental cost-effectiveness ratio estimates were the cost of ablation and the effect of catheter ablation on mortality reduction. When assuming a more conservative estimate of the treatment effect of catheter ablation on mortality (hazard ratio of 0.86), the estimated incremental cost-effectiveness ratio was $74 403 per QALY gained. At a willingness-to-pay threshold of $100 000 per QALY gained, atrial fibrillation ablation was found to be economically favorable compared with medical management in 95% of simulations.

CONCLUSIONS

Catheter ablation in patients with heart failure with reduced ejection fraction patients and atrial fibrillation may be considered economically attractive at current benchmarks for societal willingness-to-pay in the United States.