The Impact of Ignoring Population Heterogeneity when Markov Models are Used in Cost-Effectiveness Analysis

Advances in Addressing Patient Heterogeneity in Economic Evaluation: A Review of the Methods Literature

Cost-effectiveness analyses commonly use population or sample averages, which can mask key differences across subgroups and may lead to suboptimal resource allocation. Despite there being several new methods developed over the last decade, there is no recent summary of what methods are available to researchers. This review sought to identify advances in methods for addressing patient heterogeneity in economic evaluations and to provide an overview of these methods. A literature search was conducted using the Econlit, Embase and MEDLINE databases to identify studies published after 2011 (date of a previous review on this topic). Eligible studies needed to have an explicit methodological focus, related to how patient heterogeneity can be accounted for within a full economic evaluation. Sixteen studies were included in the review. Methodologies were varied and included regression techniques, model design and value of information analysis. Recent publications have applied methodologies more commonly used in other fields, such as machine learning and causal forests. Commonly noted challenges associated with considering patient heterogeneity included data availability (e.g., sample size), statistical issues (e.g., risk of false positives) and practical factors (e.g., computation time). A range of methods are available to address patient heterogeneity in economic evaluation, with relevant methods differing according to research question, scope of the economic evaluation and data availability. Researchers need to be aware of the challenges associated with addressing patient heterogeneity (e.g., data availability) to ensure findings are meaningful and robust. Future research is needed to assess whether and how methods are being applied in practice.

A scoping review on patient heterogeneity in economic evaluations of precision medicine based on basket trials

INTRODUCTION

Considerable challenges in the economic evaluation of precision medicines have been mentioned in previous studies. However, they have not addressed how an economic assessment would be conducted based on basket trials (novel studies for evaluation of precision medicine effects) in which the included populations have specific biomarkers and various cancers. Since basket trial populations have remarkable heterogeneity, this study aims to investigate the concept of heterogeneity and specific method(s) for considering it in economic evaluations through guidelines and studies that could be applicable in economic evaluation based on basket trials.

AREA COVERED

We searched PubMed, Web of Science, Scopus, Google Scholar, and Google to find studies and pharmacoeconomics guidelines. The inclusion criteria included subjects of patient heterogeneity and suggested explicit method(s). Thirty-nine guidelines and 43 studies were included and evaluated. None of these materials mentioned disease types in a target population as a factor causing heterogeneity. Moreover, in economic evaluations, patient heterogeneity has been considered with four general approaches subgroup analysis, individual-based models, sensitivity analysis, and regression models.

EXPERT OPINION

Type of disease is not considered a contributing factor in population heterogeneity, and the probable appropriate method for this issue could be individual-based models.

Predicting the Effectiveness of Endemic Infectious Disease Control Interventions: The Impact of Mass Action versus Network Model Structure

BACKGROUND

Analyses of the effectiveness of infectious disease control interventions often rely on dynamic transmission models to simulate intervention effects. We aim to understand how the choice of network or compartmental model can influence estimates of intervention effectiveness in the short and long term for an endemic disease with susceptible and infected states in which infection, once contracted, is lifelong.

METHODS

We consider 4 disease models with different permutations of socially connected network versus unstructured contact (mass-action mixing) model and heterogeneous versus homogeneous disease risk. The models have susceptible and infected populations calibrated to the same long-term equilibrium disease prevalence. We consider a simple intervention with varying levels of coverage and efficacy that reduces transmission probabilities. We measure the rate of prevalence decline over the first 365 d after the intervention, long-term equilibrium prevalence, and long-term effective reproduction ratio at equilibrium.

RESULTS

Prevalence declined up to 10% faster in homogeneous risk models than heterogeneous risk models. When the disease was not eradicated, the long-term equilibrium disease prevalence was higher in mass-action mixing models than in network models by 40% or more. This difference in long-term equilibrium prevalence between network versus mass-action mixing models was greater than that of heterogeneous versus homogeneous risk models (less than 30%); network models tended to have higher effective reproduction ratios than mass-action mixing models for given combinations of intervention coverage and efficacy.

CONCLUSIONS

For interventions with high efficacy and coverage, mass-action mixing models could provide a sufficient estimate of effectiveness, whereas for interventions with low efficacy and coverage, or interventions in which outcomes are measured over short time horizons, predictions from network and mass-action models diverge, highlighting the importance of sensitivity analyses on model structure.

HIGHLIGHTS

• We calibrate 4 models-socially connected network versus unstructured contact (mass-action mixing) model and heterogeneous versus homogeneous disease risk-to 10% preintervention disease prevalence.• We measure the short- and long-term intervention effectiveness of all models using the rate of prevalence decline, long-term equilibrium disease prevalence, and effective reproduction ratio.• Generally, in the short term, prevalence declined faster in the homogeneous risk models than in the heterogeneous risk models.• Generally, in the long term, equilibrium disease prevalence was higher in the mass-action mixing models than in the network models, and the effective reproduction ratio was higher in network models than in the mass-action mixing models.

Using Discretely Integrated Condition Event Simulation To Construct Quantitative Benefit-Risk Models: The Example of Rotavirus Vaccination in France

PURPOSE

Although quantitative benefit-risk models (qBRms) are indisputably valuable tools for gaining comprehensive assessments of health care interventions, they are not systematically used, probably because they lack an integrated framework that provides methodologic structure and harmonization. An alternative that allows all stakeholders to design operational models starting from a standardized framework was recently developed: the discretely integrated condition event (DICE) simulation. The aim of the present work was to assess the feasibility of implementing a qBRm in DICE, using the example of rotavirus vaccination.

METHODS

A model of rotavirus vaccination was designed using DICE and implemented in spreadsheet software with 3 worksheets: Conditions, Events, and Outputs. Conditions held the information in the model; this information changed at Events, and Outputs were special Conditions that stored the results collected during the analysis. A hypothetical French birth cohort was simulated for the assessment of rotavirus vaccination over time. The benefits were estimated for up to 5 years, and the risks in the 7 days following rotavirus vaccination versus no vaccination were assessed, with the results expressed as benefit-risk ratios.

FINDINGS

This qBRm model required 8 Events, 38 Conditions, and 9 Outputs. Two Events cyclically updated the rates of rotavirus gastroenteritis (RVGE) and intussusception (IS) according to age. Vaccination occurred at 2 additional Events, according to the vaccination scheme applied in France, and affected the occurrence of the other Events. Outputs were the numbers of hospitalizations related to RVGE and to IS, and related deaths. The entire model was specified in a small set of tables contained in a 445-KB electronic workbook. Analyses showed that for each IS-related hospitalization or death caused, 1613 (95% credible interval, 1001-2800) RVGE-related hospitalizations and 787 (95% credible interval, 246-2691) RVGE-related deaths would be prevented by vaccination. These results are consistent with those from a published French study using similar inputs but a very different modeling approach.

IMPLICATIONS

A limitation of the DICE approach was the extended run time needed for completing the sensitivity analyses when implemented in the electronic worksheets. DICE provided a user-friendly integrated framework for developing qBRms and should be considered in the development of structured approaches to facilitate benefit-risk assessment.

The Value of Further Research: The Added Value of Individual-Participant Level Data

Judgements based on average cost-effectiveness estimates may disguise significant heterogeneity in net health outcomes. Decisions about coverage of new interventions are often more efficient when they consider between-patient heterogeneity, which is usually operationalized as different selections for different subgroups. While most model-based cost-effectiveness studies are populated with aggregated-level sub-group estimates, individual-level data are recognized as the best source of evidence to produce unbiased and efficient estimates to explore this heterogeneity. This paper extends a previously published framework to assesses the added value of having access to individual-level data, compared to using aggregate-level data only, in the absence/presence of mutually exclusive population subgroups. Supported by a case study on the cost-effectiveness of interventions to increase uptake of smoke-alarms, the extended framework provided a quantification of the benefits foregone of not using individual-level data, pointed to the optimal number of subgroups and where further research should be undertaken. Although not indicating changes in reimbursement decisions, results showed that irrespective of using aggregate or individual-level data, no substantial additional gains are obtained if more than two subgroups are taken into account. However, depending on the evidence type used, different subgroups are revealed as warranting larger research funds. The use of individual-level data, rather than aggregate, may however influence not only the extent to which an appropriate understanding of existing heterogeneity is attained, but, more importantly, it may shape approval decisions for particular population subgroups and judgements of future research.

Validation of a DICE Simulation Against a Discrete Event Simulation Implemented Entirely in Code

BACKGROUND

Modeling is an essential tool for health technology assessment, and various techniques for conceptualizing and implementing such models have been described. Recently, a new method has been proposed-the discretely integrated condition event or DICE simulation-that enables frequently employed approaches to be specified using a common, simple structure that can be entirely contained and executed within widely available spreadsheet software. To assess if a DICE simulation provides equivalent results to an existing discrete event simulation, a comparison was undertaken.

METHODS

A model of osteoporosis and its management programmed entirely in Visual Basic for Applications and made public by the National Institute for Health and Care Excellence (NICE) Decision Support Unit was downloaded and used to guide construction of its DICE version in Microsoft Excel^®. The DICE model was then run using the same inputs and settings, and the results were compared.

RESULTS

The DICE version produced results that are nearly identical to the original ones, with differences that would not affect the decision direction of the incremental cost-effectiveness ratios (<1% discrepancy), despite the stochastic nature of the models.

LIMITATION

The main limitation of the simple DICE version is its slow execution speed.

CONCLUSIONS

DICE simulation did not alter the results and, thus, should provide a valid way to design and implement decision-analytic models without requiring specialized software or custom programming. Additional efforts need to be made to speed up execution.

Risk stratification in compartmental epidemic models: Where to draw the line?

Economic evaluations of infectious disease control interventions frequently use dynamic compartmental epidemic models. Such models capture heterogeneity in risk of infection by stratifying the population into discrete risk groups, thus approximating what is typically continuous variation in risk. An important open question is whether and how different risk stratification choices influence model predictions of intervention effects. We develop equivalent Susceptible-Infected-Susceptible (SIS) dynamic transmission models: an unstratified model, a model stratified into a high-risk and low-risk group, and a model with an arbitrary number of risk groups. Absent intervention, the models produce the same overall prevalence of infected individuals in steady state. We consider an intervention that either reduces the contact rate or increases the disease clearance rate. We develop analytical and numerical results characterizing the models and the effects of the intervention. We find that there exist multiple feasible choices of risk stratification, contact distribution, and within- and between-group contact rates for models that stratify risk. We show analytically and empirically that these choices can generate different estimates of intervention effectiveness, and that these differences can be significant enough to alter conclusions from cost-effectiveness analyses and change policy recommendations. We conclude that the choice of how to discretize risk in compartmental epidemic models can influence predicted effectiveness of interventions. Therefore, analysts should examine multiple alternatives and report the range of results.

The impact of individual-level heterogeneity on estimated infectious disease burden: a simulation study

Background

Disease burden is not evenly distributed within a population; this uneven distribution can be due to individual heterogeneity in progression rates between disease stages. Composite measures of disease burden that are based on disease progression models, such as the disability-adjusted life year (DALY), are widely used to quantify the current and future burden of infectious diseases. Our goal was to investigate to what extent ignoring the presence of heterogeneity could bias DALY computation.

Methods

Simulations using individual-based models for hypothetical infectious diseases with short and long natural histories were run assuming either “population-averaged” progression probabilities between disease stages, or progression probabilities that were influenced by an a priori defined individual-level frailty (i.e., heterogeneity in disease risk) distribution, and DALYs were calculated.

Results

Under the assumption of heterogeneity in transition rates and increasing frailty with age, the short natural history disease model predicted 14% fewer DALYs compared with the homogenous population assumption. Simulations of a long natural history disease indicated that assuming homogeneity in transition rates when heterogeneity was present could overestimate total DALYs, in the present case by 4% (95% quantile interval: 1–8%).

Conclusions

The consequences of ignoring population heterogeneity should be considered when defining transition parameters for natural history models and when interpreting the resulting disease burden estimates.

Electronic supplementary material

The online version of this article (doi:10.1186/s12963-016-0116-y) contains supplementary material, which is available to authorized users.

Cancer Care Coordinators to Improve Tamoxifen Persistence in Breast Cancer: How Heterogeneity in Baseline Prognosis Impacts on Cost-Effectiveness

OBJECTIVES

To assess the cost-effectiveness of a cancer care coordinator (CCC) in helping women with estrogen receptor positive (ER+) early breast cancer persist with tamoxifen for 5 years.

METHODS

We investigated the cost-effectiveness of a CCC across eight breast cancer subtypes, defined by progesterone receptor (PR) status, human epidermal growth factor receptor 2 (HER2) status, and local/regional spread. These subtypes range from excellent to poorer prognoses. The CCC helped in improving tamoxifen persistence by providing information, checking-in by phone, and "troubleshooting" concerns. We constructed a Markov macrosimulation model to estimate health gain (in quality-adjusted life-years or QALYs) and health system costs in New Zealand, compared with no CCC. Participants were modeled until death or till the age of 110 years. Some input parameters (e.g., the impact of a CCC on tamoxifen persistence) had sparse evidence. Therefore, we used estimates with generous uncertainty and conducted sensitivity analyses.

RESULTS

The cost-effectiveness of a CCC for regional ER+/PR-/HER2+ breast cancer (worst prognosis) was NZ $23,400 (US $15,800) per QALY gained, compared with NZ $368,500 (US $248,800) for local ER+/PR+/HER2- breast cancer (best prognosis). Using a cost-effectiveness threshold of NZ $45,000 (US $30,400) per QALY, a CCC would be cost-effective only in the four subtypes with the worst prognoses.

CONCLUSIONS

There is value in investigating cost-effectiveness by different subtypes within a disease. In this example of breast cancer, the poorer the prognosis, the greater the health gains from a CCC and the better the cost-effectiveness. Incorporating heterogeneity in a cost-utility analysis is important and can inform resource allocation decisions. It is also feasible to undertake in practice.

Decision-analytic models: current methodological challenges

Modelers seeking to help inform decisions about insurance (public or private) coverage of the cost of pharmaceuticals or other health care interventions face various methodological challenges. In this review, which is not meant to be comprehensive, we cover those that in our experience are most vexing. The biggest challenge is getting decision makers to trust the model. This is a major problem because most models undergo only cursory validation; our field has lacked the motivation, time, and data to properly validate models intended to inform health care decisions. Without documented, adequate validation, there is little basis for decision makers to have confidence that the model's results are credible and should be used in a health technology appraisal. A fundamental problem for validation is that the models are very artificial and lack sufficient depth to adequately represent the reality they are simulating. Typically, modelers assume that all resources have infinite capacity so any patient needing care receives it immediately; there are no waiting times or queues, contrary to the common experience in actual practice. Moreover, all the patients enter the model simultaneously at time zero rather than over time as happens in actuality; differences between patients are ignored or minimized and structural modeling choices that make little sense (e.g., using states to represent events) are forced by commitment to a technique (and even to specific spreadsheet software!). The resulting structural uncertainty is rarely addressed, because methods are lacking and even probabilistic analysis of parameter uncertainty suffers from weak consideration of correlation and arbitrary distribution choices. Stakeholders must see to it that models are fit for the stated purpose and provide the best possible estimates given available data-the decisions at stake deserve nothing less.

How should we deal with patient heterogeneity in economic evaluation: a systematic review of national pharmacoeconomic guidelines

OBJECTIVE

To review and analyze recommendations from national pharmacoeconomic guidelines with regard to acknowledging patient heterogeneity in economic evaluations.

METHODS

National pharmacoeconomic guidelines were obtained through the ISPOR Web site. Guidance was extracted by using a developed data extraction sheet. Extracted data were divided into subcategories on the basis of consensus meetings.

RESULTS

Of the 26 included guidelines, 20 (77%) advised to identify patient heterogeneity. Most guidelines (77%) provided general methodological advice to acknowledge patient heterogeneity, including justifications for distinguishing subgroups (65%), prespecification of subgroups (42%), or methodology to acknowledge patient heterogeneity (77%). Stratified analysis of cost-effectiveness was most commonly advised (20 guidelines; 77%); however, guidance on the specific application of methods was scarce (9 guidelines; 34%) and generally limited if provided. Guidance to present patient heterogeneity was provided by 15 guidelines (58%), most prominently to describe the definition (31%) and justification (31%) of subgroups.

CONCLUSIONS

The majority of national pharmacoeconomic guidelines provide guidance on acknowledging patient heterogeneity in economic evaluations. However, because guidance is mostly not specific, its usefulness is limited. This may reflect that the importance of acknowledging patient heterogeneity is usually recognized while there is a lack of consensus on specific methods to acknowledge patient heterogeneity. We advise the further development of national pharmacoeconomic guidelines to provide specific guidance on the identification of patient heterogeneity, methods to acknowledge it, and presenting the results. We present a checklist that can assist in formulating these recommendations. This could facilitate the systematic and transparent handling of patient heterogeneity in economic evaluations worldwide.

Acknowledging patient heterogeneity in economic evaluation : a systematic literature review

BACKGROUND AND OBJECTIVE

Patient heterogeneity is the part of variability that can be explained by certain patient characteristics (e.g. age, disease stage). Population reimbursement decisions that acknowledge patient heterogeneity could potentially save money and increase population health. To date, however, economic evaluations pay only limited attention to patient heterogeneity. The objective of the present paper is to provide a comprehensive overview of the current knowledge regarding patient heterogeneity within economic evaluation of healthcare programmes.

METHODS

A systematic literature review was performed to identify methodological papers on the topic of patient heterogeneity in economic evaluation. Data were obtained using a keyword search of the PubMed database and manual searches. Handbooks were also included. Relevant data were extracted regarding potential sources of patient heterogeneity, in which of the input parameters of an economic evaluation these occur, methods to acknowledge patient heterogeneity and specific concerns associated with this acknowledgement.

RESULTS

A total of 20 articles and five handbooks were included. The relevant sources of patient heterogeneity (demographics, preferences and clinical characteristics) and the input parameters where they occurred (baseline risk, treatment effect, health state utility and resource utilization) were combined in a framework. Methods were derived for the design, analysis and presentation phases of an economic evaluation. Concerns related mainly to the danger of false-positive results and equity issues.

CONCLUSION

By systematically reviewing current knowledge regarding patient heterogeneity within economic evaluations of healthcare programmes, we provide guidance for future economic evaluations. Guidance is provided on which sources of patient heterogeneity to consider, how to acknowledge them in economic evaluation and potential concerns. The improved acknowledgement of patient heterogeneity in future economic evaluations may well improve the efficiency of healthcare.

State-Transition Modeling

State-transition modeling (STM) is an intuitive, flexible, and transparent approach of computer-based decision-analytic modeling, including both Markov model cohort simulation as well as individual-based (first-order Monte Carlo) microsimulation. Conceptualizing a decision problem in terms of a set of (health) states and transitions among these states, STM is one of the most widespread modeling techniques in clinical decision analysis, health technology assessment, and health-economic evaluation. STMs have been used in many different populations and diseases, and their applications range from personalized health care strategies to public health programs. Most frequently, state-transition models are used in the evaluation of risk factor interventions, screening, diagnostic procedures, treatment strategies, and disease management programs.

State-transition modeling: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force--3

State-transition modeling is an intuitive, flexible, and transparent approach of computer-based decision-analytic modeling including both Markov model cohort simulation and individual-based (first-order Monte Carlo) microsimulation. Conceptualizing a decision problem in terms of a set of (health) states and transitions among these states, state-transition modeling is one of the most widespread modeling techniques in clinical decision analysis, health technology assessment, and health-economic evaluation. State-transition models have been used in many different populations and diseases, and their applications range from personalized health care strategies to public health programs. Most frequently, state-transition models are used in the evaluation of risk factor interventions, screening, diagnostic procedures, treatment strategies, and disease management programs. The goal of this article was to provide consensus-based guidelines for the application of state-transition models in the context of health care. We structured the best practice recommendations in the following sections: choice of model type (cohort vs. individual-level model), model structure, model parameters, analysis, reporting, and communication. In each of these sections, we give a brief description, address the issues that are of particular relevance to the application of state-transition models, give specific examples from the literature, and provide best practice recommendations for state-transition modeling. These recommendations are directed both to modelers and to users of modeling results such as clinicians, clinical guideline developers, manufacturers, or policymakers.

Population- versus cohort-based modelling approaches

While no single type of model can provide adequate answers under all circumstances, any modelling endeavour should incorporate three fundamental considerations in any decision-making question: the target population, the disease and the intervention characteristics. A target population is likely to be characterized by various types of heterogeneity and a dynamic evolution over time. It is therefore important to adequately capture these population effects on the results of a model. There are essentially two different approaches in modelling a population over time: a cohort-based approach and a population-based approach. In a cohort-based model, a closed group of individuals who have at least one specific characteristic or experience in common over a defined period of time is run through a state transition process. The cohort is generally composed of a hypothetical number of representative or 'average' individuals (i.e. the target population is considered to be a homogeneous group). The population-based approach projects the evolution of the estimated prevalent target population and intends to reflect as much as possible the demographic, epidemiological and clinical characteristics of the prevalent target population relevant for the decision problem. A cohort-based approach is generally used in most published healthcare decision models. However, this choice is rarely discussed by modellers. In this article, we challenge this assumption. To address the underlying decision problem, we affirm it is crucial that modellers consider the characteristics of the target population. Then, they could opt for using the most appropriate approach. Decision makers should also understand the impact on the results of both types of models in order to make informed healthcare decisions.

Bias associated with failing to incorporate dependence on event history in Markov models

PURPOSE

When using state-transition Markov models to simulate risk of recurrent events over time, incorporating dependence on higher numbers of prior episodes can increase model complexity, yet failing to capture this event history may bias model outcomes. This analysis assessed the tradeoffs between model bias and complexity when evaluating risks of recurrent events in Markov models.

METHODS

The authors developed a generic episode/relapse Markov cohort model, defining bias as the percentage change in events prevented with 2 hypothetical interventions (prevention and treatment) when incorporating 0 to 9 prior episodes in relapse risk versus a model with 10 such episodes. Magnitude and sign of bias were evaluated as a function of event and recovery risks, disease-specific mortality, and risk function.

RESULTS

Bias was positive in the base case for a prevention strategy, indicating that failing to fully incorporate dependence on event history overestimated the prevention's predicted impact. For treatment, the bias was negative, indicating an underestimated benefit. Bias approached zero as the number of tracked prior episodes increased, and the average bias over 10 tracked episodes was greater with the exponential compared with linear functions of relapse risk and with treatment compared with prevention strategies. With linear and exponential risk functions, absolute bias reached 33% and 78%, respectively, in prevention and 52% and 85% in treatment.

CONCLUSION

Failing to incorporate dependence on prior event history in subsequent relapse risk in Markov models can greatly affect model outcomes, overestimating the impact of prevention and treatment strategies by up to 85% and underestimating the impact in some treatment models by up to 20%. When at least 4 prior episodes are incorporated, bias does not exceed 26% in prevention or 11% in treatment.

Does one size fit all? Investigating heterogeneity in men's preferences for benign prostatic hyperplasia treatment using mixed logit analysis

In this study, the authors demonstrate how mixed logit analysis of discrete choice experiment (DCE) data can provide information about unobserved preference heterogeneity. Their application investigates unobserved heterogeneity in men's preferences for benign prostatic hyperplasia (BPH) treatment. They use a DCE to elicit preferences for seven characteristics of BPH treatment: time to symptom improvement, sexual and nonsexual treatment side effects, risks of acute urinary retention and surgery, cost of treatment, and reduction in prostate size. They investigate the importance of these characteristics and the trade-offs men are willing to make between them. Preferences are elicited from a sample of 100 men attending an outpatient clinic in Ireland. The authors find all treatment characteristics are significant determinants of treatment choice. There is significant preference heterogeneity in the population for four treatment characteristics: time to symptom improvement, treatment reducing prostate size, risk of surgery, and sexual side effects. The importance of preference heterogeneity at the policy level within the context of shared decision making is discussed.

Effects of Categorizing Continuous Variables in Decision-Analytic Models

Purpose. When using continuous predictor variables in discrete-state Markov modeling, it is necessary to create categories of risk and assume homogeneous disease risk within categories, which may bias model outcomes. This analysis assessed the tradeoffs between model bias and complexity and/or data limitations when categorizing continuous risk factors in Markov models. Methods. The authors developed a generic Markov cohort model of disease, defining bias as the percentage change in life expectancy gain from a hypothetical intervention when using 2 to 15 risk factor categories as compared with modeling the risk factor as a continuous variable. They evaluated the magnitude and sign of bias as a function of disease incidence, disease-specific mortality, and relative difference in risk among categories. Results. Bias was positive in the base case, indicating that categorization overestimated life expectancy gains. The bias approached zero as the number of risk factor categories increased and did not exceed 4% for any parameter combinations or numbers of categories considered. For any given disease-specific mortality and disease incidence, bias increased with relative risk of disease. For any given relative risk, the relationship between bias and parameters such as disease-specific mortality or disease incidence was not always monotonic. Conclusions. Under the assumption of a normally distributed risk factor and reasonable assumption regarding disease risk and moderate values for the relative risk of disease given risk factor category, categorizing continuously valued risk factors in Markov models is associated with less than 4% absolute bias when at least 2 categories are used.

Do Intraindividual Variation in Disease Progression and the Ensuing Tight Window of Opportunity Affect Estimation of Screening Benefits?

Background . The effects of variation in disease progression between individuals on the effectiveness of screening have been assessed extensively in the literature. For several diseases, progression may also vary within individuals over time. The authors study the effects of intraindividual variation and the combined effects of inter- and intraindividual variation in disease progression on the effectiveness of screening. Methods . The authors investigated the risk reduction of aneurysmal subarachnoid hemorrhage (SAH) achieved by screening for intracranial aneurysms in a simulation study as a function of the inter- and intraindividual variation in the risk of aneurysm rupture. They also extended a previously constructed Markov model for the cost-effectiveness analysis of screening for new aneurysms in patients with clipped aneurysms after SAH. A time-varying risk of aneurysm rupture was introduced, and the influence of this variation on cost-effectiveness was assessed. Results . The risk reduction provided by screening decreased with increasing intraindividual variation in disease progression. The expected number of prevented instances of SAH was overestimated by 58% in this simulation study when high degrees of inter- and intraindividual variation were present. Interindividual variation alone resulted in up to 33% overestimation and intraindividual variation in up to 43% overestimation. In the extended Markov model, screening benefits were overestimated by 24% when a high degree of intraindividual variation was present but ignored. Conclusions . If intraindividual variation in disease progression is ignored in decision models, subsequent cost-effectiveness analyses of screening strategies will overestimate the benefits provided by screening. This bias is comparable to, but partially independent of, the bias caused by ignoring interindividual heterogeneity.

Optimal drug pricing, limited use conditions and stratified net benefits for Markov models of disease progression

Limited use conditions (LUCs) are a method of directing treatment with new drugs to those populations where they will be most cost effective. In this paper we investigate how a drug manufacturer could determine pricing and LUCs to maximize profits. We assume that the payer makes formulary decisions on the basis of net monetary benefits, that the disease can be modeled using a Markov model of disease progression, and that the drug reduces the probability of progression between states of the Markov model. LUCs are expressed as a range of probabilities of disease progression over which patients would have access to the new drug. We assume that the manufacturer determines the price and LUCs in order to maximize profits. We show that an explicit trade-off exists between the drug's price and the use conditions, that there is an upper bound on the drug price, that the proportion of the population targeted by the LUC does not depend on quality of life or costs in each health state or the payer's willingness to pay, and that high drug prices do not always correspond with high profits.

It's time to choose the study design!: net benefit analysis of alternative study designs to acquire information for evaluation of health technologies

Uncertainty in the decision-making process for reimbursement of health technologies could be reduced if additional information were available. Although methods to evaluate the monetary value of the uncertainty have been previously described, an economic evaluation of alternative methods to acquire additional information has not yet been thoroughly explored. Should resources be allocated to a retrospective study design or to a randomised controlled trial (RCT) when additional information is deemed justified? We propose an approach for cost-effectiveness analysis of designs of future studies that are required to evaluate health technologies for reimbursement. Biases inherent in study designs are the main factor that differentiates the ability of the studies to predict the technology's benefit. By quantifying this inherent-bias effect, the incremental effectiveness of future studies can be evaluated. Economic consequences of decisions regarding prioritization of the technologies, along with the expected costs incurred by the study's execution, account for the cost component of the equation. Deducting the result retrieved for the retrospective design from that of the RCT design gives the net information benefit.