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.

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.

Generalized Linear Models for Flexible Parametric Modeling of the Hazard Function.

Background. Parametric modeling of survival data is important, and reimbursement decisions may depend on the selected distribution. Accurate predictions require sufficiently flexible models to describe adequately the temporal evolution of the hazard function. A rich class of models is available among the framework of generalized linear models (GLMs) and its extensions, but these models are rarely applied to survival data. This article describes the theoretical properties of these more flexible models and compares their performance to standard survival models in a reproducible case study. Methods. We describe how survival data may be analyzed with GLMs and their extensions: fractional polynomials, spline models, generalized additive models, generalized linear mixed (frailty) models, and dynamic survival models. For each, we provide a comparison of the strengths and limitations of these approaches. For the case study, we compare within-sample fit, the plausibility of extrapolations, and extrapolation performance based on data splitting. Results. Viewing standard survival models as GLMs shows that many impose a restrictive assumption of linearity. For the case study, GLMs provided better within-sample fit and more plausible extrapolations. However, they did not improve extrapolation performance. We also provide guidance to aid in choosing between the different approaches based on GLMs and their extensions. Conclusions. The use of GLMs for parametric survival analysis can outperform standard parametric survival models, although the improvements were modest in our case study. This approach is currently seldom used. We provide guidance on both implementing these models and choosing between them. The reproducible case study will help to increase uptake of these models.

Modeling the Economic Impact of Interventions for Older Populations with Multimorbidity: A Method of Linking Multiple Single-Disease Models.

Introduction. Individuals from older populations tend to have more than 1 health condition (multimorbidity). Current approaches to produce economic evidence for clinical guidelines using decision-analytic models typically use a single-disease approach, which may not appropriately reflect the competing risks within a population with multimorbidity. This study aims to demonstrate a proof-of-concept method of modeling multiple conditions in a single decision-analytic model to estimate the impact of multimorbidity on the cost-effectiveness of interventions. Methods. Multiple conditions were modeled within a single decision-analytic model by linking multiple single-disease models. Individual discrete event simulation models were developed to evaluate the cost-effectiveness of preventative interventions for a case study assuming a UK National Health Service perspective. The case study used 3 diseases (heart disease, Alzheimer's disease, and osteoporosis) that were combined within a single linked model. The linked model, with and without correlations between diseases incorporated, simulated the general population aged 45 years and older to compare results in terms of lifetime costs and quality-adjusted life-years (QALYs). Results. The estimated incremental costs and QALYs for health care interventions differed when 3 diseases were modeled simultaneously (£840; 0.234 QALYs) compared with aggregated results from 3 single-disease models (£408; 0.280QALYs). With correlations between diseases additionally incorporated, both absolute and incremental costs and QALY estimates changed in different directions, suggesting that the inclusion of correlations can alter model results. Discussion. Linking multiple single-disease models provides a methodological option for decision analysts who undertake research on populations with multimorbidity. It also has potential for wider applications in informing decisions on commissioning of health care services and long-term priority setting across diseases and health care programs through providing potentially more accurate estimations of the relative cost-effectiveness of interventions.

The Cost-effectiveness of Sequences of Biological Disease-modifying Antirheumatic Drug Treatment in England for Patients with Rheumatoid Arthritis Who Can Tolerate Methotrexate.

OBJECTIVE: To ascertain whether strategies of treatment with a biological disease-modifying antirheumatic drug (bDMARD) are cost-effective in an English setting. Results are presented for those patients with moderate to severe rheumatoid arthritis (RA) and those with severe RA. METHODS: An economic model to assess the cost-effectiveness of 7 bDMARD was developed. A systematic literature review and network metaanalysis was undertaken to establish relative clinical effectiveness. The results were used to populate the model, together with estimates of Health Assessment Questionnaire (HAQ) score following European League Against Rheumatism response; annual costs, and utility, per HAQ band; trajectory of HAQ for patients taking bDMARD; and trajectory of HAQ for patients using nonbiologic therapy (NBT). Results were presented as those associated with the strategy with the median cost-effectiveness. Supplementary analyses were undertaken assessing the change in cost-effectiveness when only patients with the most severe prognoses taking NBT were provided with bDMARD treatment. The costs per quality-adjusted life-year (QALY) values were compared with reported thresholds from the UK National Institute for Health and Care Excellence of £20,000 to £30,000 (US$24,700 to US$37,000). RESULTS: In the primary analyses, the cost per QALY of a bDMARD strategy was £41,600 for patients with severe RA and £51,100 for those with moderate to severe RA. Under the supplementary analyses, the cost per QALY fell to £25,300 for those with severe RA and to £28,500 for those with moderate to severe RA. CONCLUSION: The cost-effectiveness of bDMARD in RA in England is questionable and only meets current accepted levels in subsets of patients with the worst prognoses.

Modelling the cost effectiveness of interventions for osteoporosis: issues to consider.

Expenditure on treating osteoporotic fractures and on preventative intervention is considerable and is likely to rise in forthcoming years due to the association between fracture risk and age. With funders such as the National Institute for Health and Care Excellence and the Pharmaceutical Benefits Advisory Committee explicitly considering cost-effectiveness analyses within the process of producing guidance, it is imperative that economic models are as robust as possible. This article details issues that need to be considered specifically related to health technology assessments of interventions for osteoporosis, and highlights limitations within the current evidence base. A likely direction of impact on cost effectiveness of addressing the key issues has been included alongside a tentative categorization of the level of these impacts. It is likely that cost-effectiveness ratios presented in previous models that did not address the identified issues were favourable to interventions.

Cost-effectiveness of presentation versus delayed troponin testing for acute myocardial infarction.

OBJECTIVES: To estimate the cost-effectiveness of delayed troponin testing for myocardial infarction compared with troponin testing at presentation. DESIGN: Decision analysis modelling of cost-effectiveness using secondary data sources. SETTING: Acute hospitals in the UK. POPULATION: Patients attending hospital with suspected myocardial infarction but a normal or non-diagnostic ECG and no major comorbidities requiring admission. INTERVENTIONS: Delayed troponin testing (10 h after symptom onset) compared with standard and high-sensitivity troponin testing at presentation and no testing. Sensitivity analysis evaluated high-sensitivity troponin testing 3 h after initial assessment. MAIN OUTCOME MEASURES: The incremental cost per quality-adjusted life year (QALY) gained by each strategy, compared with the next most effective alternative, and the probability of each strategy being cost-effective at varying willingness-to-pay per QALY gained. RESULTS: In all scenarios tested, presentation high-sensitivity troponin testing was the most effective strategy with an incremental cost-effectiveness ratio below the £20 000/QALY threshold. 10 h troponin testing was only likely to be cost-effective if a discharge decision could be made as soon as a negative result was available and the £30 000/QALY threshold was used, or if a lower sensitivity estimate for presentation high-sensitivity troponin was assumed. Sensitivity analysis showed that including high-sensitivity troponin testing at presentation and 3 h in the analysis makes this the most cost-effective strategy. CONCLUSIONS: Delayed troponin testing is unlikely to be cost-effective compared with high-sensitivity troponin testing at presentation in most scenarios. Current NICE chest pain guidelines do not promote cost-effective care.

Granulocyte colony-stimulating factors for febrile neutropenia prophylaxis following chemotherapy: systematic review and meta-analysis.

BACKGROUND: Febrile neutropenia (FN) occurs following myelosuppressive chemotherapy and is associated with morbidity, mortality, costs, and chemotherapy reductions and delays. Granulocyte colony-stimulating factors (G-CSFs) stimulate neutrophil production and may reduce FN incidence when given prophylactically following chemotherapy. METHODS: A systematic review and meta-analysis assessed the effectiveness of G-CSFs (pegfilgrastim, filgrastim or lenograstim) in reducing FN incidence in adults undergoing chemotherapy for solid tumours or lymphoma. G-CSFs were compared with no primary G-CSF prophylaxis and with one another. Nine databases were searched in December 2009. Meta-analysis used a random effects model due to heterogeneity. RESULTS: Twenty studies compared primary G-CSF prophylaxis with no primary G-CSF prophylaxis: five studies of pegfilgrastim; ten of filgrastim; and five of lenograstim. All three G-CSFs significantly reduced FN incidence, with relative risks of 0.30 (95% CI: 0.14 to 0.65) for pegfilgrastim, 0.57 (95% CI: 0.48 to 0.69) for filgrastim, and 0.62 (95% CI: 0.44 to 0.88) for lenograstim. Overall, the relative risk of FN for any primary G-CSF prophylaxis versus no primary G-CSF prophylaxis was 0.51 (95% CI: 0.41 to 0.62). In terms of comparisons between different G-CSFs, five studies compared pegfilgrastim with filgrastim. FN incidence was significantly lower for pegfilgrastim than filgrastim, with a relative risk of 0.66 (95% CI: 0.44 to 0.98). CONCLUSIONS: Primary prophylaxis with G-CSFs significantly reduces FN incidence in adults undergoing chemotherapy for solid tumours or lymphoma. Pegfilgrastim reduces FN incidence to a significantly greater extent than filgrastim.

Consistency between direct and indirect trial evidence: is direct evidence always more reliable?

OBJECTIVES: To present a case study involving the reduction in incidence of febrile neutropenia (FN) after chemotherapy with granulocyte colony-stimulating factors (G-CSFs), illustrating difficulties that may arise when following the common preference for direct evidence over indirect evidence. METHODS: Evidence of the efficacy of treatments was identified from two previous systematic reviews. We used Bayesian evidence synthesis to estimate relative treatment effects based on direct evidence, indirect evidence, and both pooled together. We checked for inconsistency between direct and indirect evidence and explored the role of one specific trial using cross-validation. A subsequent review identified further studies not available at the time of the original analysis. We repeated the analyses on the enlarged evidence base. RESULTS: We found substantial inconsistency in the original evidence base. The median odds ratio of FN for primary pegfilgrastim versus no primary G-CSF was 0.06 (95% credible interval: 0.02-0.19) based on direct evidence, but 0.27 (95% credible interval: 0.13-0.53) based on indirect evidence (P value for consistency hypothesis 0.027). The additional trials were consistent with the earlier indirect, rather than the direct, evidence, and there was no inconsistency between direct and indirect estimates in the updated evidence. The earlier inconsistency was due to one trial comparing primary pegfilgrastim with no primary G-CSF. Predictive cross-validation showed that this study was inconsistent with the evidence as a whole and with other trials making this comparison. CONCLUSIONS: Both the Cochrane Handbook and the NICE Methods Guide express a preference for direct evidence. A more robust strategy, which is in line with the accepted principles of evidence synthesis, would be to combine all relevant and appropriate information, whether direct or indirect.

Cost-effectiveness of granulocyte colony-stimulating factor prophylaxis for febrile neutropenia in breast cancer in the United Kingdom.

OBJECTIVE: We report a cost-effectiveness evaluation of granulocyte colony-stimulating factors (G-CSFs) for the prevention of febrile neutropenia (FN) after chemotherapy in the United Kingdom (UK). METHODS: A mathematical model was constructed simulating the experience of women with breast cancer undergoing chemotherapy. Three strategies were modeled: primary prophylaxis (G-CSFs administered in all cycles), secondary prophylaxis (G-CSFs administered in all cycles after an FN event), and no G-CSF prophylaxis. Three G-CSFs were considered: filgrastim, lenograstim, and pegfilgrastim. Costs were taken from UK databases and utility values from published sources. A systematic review provided data on G-CSF efficacy. Probabilistic sensitivity analyses examined the effects of uncertainty in model parameters. RESULTS: In the UK, base-case analysis with a willingness-to-pay (WTP) threshold of £20K per quality-adjusted life year gained and also using list prices, the most cost-effective strategy was primary prophylaxis with pegfilgrastim for a patient with baseline FN risk greater than 38%, secondary prophylaxis with pegfilgrastim for baseline FN risk 11% to 37%, and no G-CSFs for baseline FN risk less than 11%. Using a WTP threshold of £30K and list prices, primary prophylaxis with pegfilgrastim was cost-effective for baseline FN risks greater than 29%. In all analyses, pegfilgrastim dominated filgrastim and lenograstim. Sensitivity analyses demonstrated that higher WTP threshold, younger age, earlier stage at diagnosis, or reduced G-CSF prices result in G-CSF prophylaxis being cost-effective at lower baseline FN risk levels. CONCLUSION: Pegfilgrastim was the most cost-effective G-CSF. The most cost-effective strategy (primary or secondary prophylaxis) was dependent on the FN risk level for an individual patient, patient age and stage at diagnosis, and G-CSF price.

The cost effectiveness of a randomized controlled trial to establish the relative efficacy of vitamin K1 compared with alendronate.

PURPOSE: The authors aimed to evaluate whether vitamin K(1) or alendronate (the recommended treatment in England and Wales for postmenopausal women with a previous fracture) appeared to be the more cost-effective treatment for fracture prevention. Furthermore, expected value of sample information (EVSI) analyses were undertaken to estimate whether a head-to-head trial of alendronate and vitamin K(1) would be considered cost effective. METHOD: A published osteoporosis model structure, populated with data from literature reviews, was used to evaluate the costs and quality-adjusted life-years associated with each intervention being provided to women at high risk of fracture, given current information. A lifetime horizon and a national health service and personal social services cost perspective were used. Observed outcomes from head-to-head randomized controlled trials (RCTs) of predetermined sizes were simulated and synthesized with existing data to formulate posterior distributions, which were used to estimate the more cost-effective treatment given these additional data. The EVSI was estimated and the expected net benefit of sampling (ENBS) calculated by subtracting the proposed trial costs. RESULTS: Given current information, vitamin K(1) is expected to dominate alendronate. However, this was subject to a considerable degree of uncertainty; dominance was reversed when it was assumed that vitamin K(1) had no effect on hip fractures. EVSI analysis indicated that an RCT of 2000 or 5000 women per arm produced high, and comparable, ENBS. These results were maintained in sensitivity analyses. CONCLUSIONS: It is concluded that an RCT recruiting between 2000 and 5000 women per arm to evaluate the relative efficacy of alendronate and vitamin K(1) appears to be cost effective for informing decision making in England and Wales.

The cost-effectiveness of group cognitive behavioral therapy compared with routine primary care for women with postnatal depression in the UK.

OBJECTIVE: To assess the cost-effectiveness of group cognitive behavior therapy (gCBT) in comparison with routine primary care for women with postnatal depression in the UK. METHODS: Our analysis was based on a systematic literature review of the relative clinical effectiveness of gCBT compared with routine primary care and further reviews, supplemented with expert opinion of the likely cost of providing gCBT and the duration of comparative advantage for gCBT. Raw data were used to estimate a statistical relationship between changes in the Edinburgh Postnatal Depression Score (EPDS) values and changes in short-form six dimensions' (SF-6D) values. A mathematical model was constructed, and probabilistic sensitivity analyses were undertaken to estimate the mean cost per quality-adjusted life-year (QALY) and to evaluate the expected value of perfect information (EVPI). RESULTS: The mean cost per QALY from the stochastic analysis was estimated to be pound36,062; however, there was considerable uncertainty around this value. The EVPI was estimated to be greater than pound64 million; the key uncertainties were in the cost per woman of providing treatment and in the statistical relationship between changes in EPDS values and changes in SF-6D values. The expected value of perfect partial information for both of these parameters was in excess of pound25 million. CONCLUSIONS: Given the current information, the use of gCBT does not appear to be cost-effective; however, this decision is uncertain. The value of information analyses conducted indicates that further research to provide robust information on key parameters is needed and appears justified in cost-effective terms.

Carotid artery imaging for secondary stroke prevention: both imaging modality and rapid access to imaging are important.

BACKGROUND AND PURPOSE: Patients with transient ischemic attack require carotid imaging to diagnose carotid stenosis. The differing sensitivity/specificity and availability of carotid imaging methods have created uncertainty over which noninvasive method is best and whether intra-arterial angiography is still required. We evaluated the influence of carotid imaging methods on secondary stroke prevention. METHODS: We modeled the effect of different carotid imaging strategies and timing on endarterectomy workload, stroke, and death at 1 and 5 years. We used all available data on stroke prevention after transient ischemic attack from systematic reviews (carotid imaging, medical and surgical interventions), population-based transient ischemic attack/stroke studies, government statistics, and stroke prevention clinics. RESULTS: Choice of imaging strategy affected speed of assessment, strokes prevented, and endarterectomy workload. The number of strokes prevented at 5 years varied by up to 22 per 1000 patients between imaging strategies for a given time to assessment. Delaying endarterectomy from 14 to approximately 30 days would fail to prevent up to 11 strokes per 1000 patients depending on the imaging strategy. Sensitive fast imaging (eg, ultrasound) was best for patients seen early; specific imaging (eg, CT angiography or contrast-enhanced MR angiography) was best for patients seen late after transient ischemic attack. Intra-arterial angiography conferred no advantage over noninvasive imaging. CONCLUSIONS: Rapid access to sensitive noninvasive carotid imaging prevents most strokes. However, imaging strategies differ in their effect on stroke prevention by as much as 22 per 1000 patients and optimal imaging varies with time after transient ischemic attack TIA. Routine intra-arterial angiography should be avoided.

The cost-effectiveness of bosentan in the United Kingdom for patients with pulmonary arterial hypertension of WHO functional class III.

OBJECTIVES: To assess whether bosentan or no active intervention, in addition to palliative care, is the more cost-effective first-line treatment option for patients with idiopathic pulmonary arterial hypertension (iPAH) or PAH associated with connective tissue disease (PAH-CTD) of WHO functional classification (FC) III in the United Kingdom. METHODS: A cost-utility model simulated the treatment of patients with PAH of FC III. Patients remained on the selected intervention until death or clinical deterioration to FC IV, which would trigger initiation of epoprostenol treatment. The initial first-line treatment choice was assumed to not affect survival, but to affect the time until clinical deterioration, with this assumption being relaxed in sensitivity analyses. The distribution of time to clinical deterioration was estimated from long-term clinical trial databases of bosentan and from published literature. Utility associated with FC was taken from published literature. Costs were sourced from published literature and from specialist PAH centers. The time horizon was that of patients' lifetimes, with costs and benefits discounted at 3.5% per annum. RESULTS: In the base case, bosentan dominated no active intervention because of the longer time to clinical deterioration and therefore the reduced time, per patient, spent in FC IV, which was associated with high costs of epoprostenol and reduced utility. In sensitivity analyses, bosentan was estimated to be more cost-effective than no active intervention, provided that any survival benefit was not greater than 2 years for patients with iPAH and 1 year for those with PAH-CTD. CONCLUSIONS: Bosentan is likely to be a more cost-effective first-line therapy for patients with PAH FC III in the UK than no active intervention.

The cost-effectiveness of an RCT to establish whether 5 or 10 years of bisphosphonate treatment is the better duration for women with a prior fracture.

PURPOSE: Five years of bisphosphonate treatment have proven efficacy in reducing fractures. Concerns exist that long-term bisphosphonate treatment may actually result in an increased number of fractures. This study evaluates, in the context of England and Wales, whether it is cost-effective to conduct a randomized controlled trial (RCT) and what sample size may be optimal to estimate the efficacy of bisphosphonates in fracture prevention beyond 5 years. METHOD: An osteoporosis model was constructed to evaluate the cost-effectiveness of extending bisphosphonate treatment from 5 years to 10 years. Two scenarios were run. The 1st uses long-term efficacy data from published literature, and the 2nd uses distributions elicited from clinical experts. RESULTS: of a proposed RCT were simulated. The expected value of sample information technique was applied to calculate the expected net benefit of sampling from conducting such an RCT at varying levels of participants per arm and to compare this with proposed trial costs. Results. Without further information, the better duration of bisphosphonate treatment was estimated to be 5 years using the published data but 10 years using the elicited expert opinions, although in both cases uncertainty was substantial. The net benefit of sampling was consistently high when between 2000 and 5000 participants per arm were recruited. CONCLUSIONS: An RCT to evaluate the long-term efficacy of bisphosphonates in fracture prevention appears to be cost-effective for informing decision making in England and Wales.