1. Transforming the cost-effectiveness threshold into a ‘value threshold’ Initial findings from a simulation model Mike Paulden and Christopher McCabe

2. Problem The conventional cost-effectiveness (CE) threshold represents “an estimate of health forgone as other [services] are displaced to accommodate the additional costs of new technologies” (Claxton et al. 2013) Plotted as a straight line on the CE plane (Drummond et al. 2005) Numerous limitations and assumptions: Assumes constant marginal returns and divisibility of technologies No account for aspects of ‘value’ beyond those considered by the QALY Impact of imperfect information is not explicitly considered, nor the possibility that new interventions represent net disinvestments No account for multiple decision makers with conflicting objectives Recently, NICE has applied ‘modifiers’ to its baseline threshold to account for aspects of ‘value’ beyond the QALY (NICE 2009, 2014) Resulted in inconsistencies in NICE’s methodology (Paulden et al. 2014)

3. Objective Our objective is to transform the conventional CE threshold into a ‘value threshold’ of greater use to decision makers In doing so we aim to address the limitations previously described As a first step we have developed a simulation model in order to understand how a ‘value threshold’ may differ from a CE threshold Of key interest are the implications of: i.Relaxing conventional assumptions such as constant marginal returns to scale and perfect divisibility of technologies ii.Incorporating imperfect information and ‘value’ considerations within a complex health system with multiple decision makers iii.Extending the threshold so that it may be used for net disinvestments

4. Pool of initial technologies The cost and effectiveness of each technology is drawn from a distribution Each technology is randomly assigned a ‘value’ attribute and a specific health production function ‘shape’ (applies only if marginal returns are diminishing) Model schematic

5. Pool of initial technologies The cost and effectiveness of each technology is drawn from a distribution Each technology is randomly assigned a ‘value’ attribute and a specific health production function ‘shape’ (applies only if marginal returns are diminishing) Divisibility of technologies Technologies in the pool are either all divisible or all indivisible Marginal returns to scale Technologies in the pool either all have constant marginal returns to scale or all have diminishing marginal returns to scale Model schematic

6. Pool of initial technologies The cost and effectiveness of each technology is drawn from a distribution Each technology is randomly assigned a ‘value’ attribute and a specific health production function ‘shape’ (applies only if marginal returns are diminishing) Initial budget Upon the establishment of the health system, an initial budget is assigned for purchasing technologies from the pool Divisibility of technologies Technologies in the pool are either all divisible or all indivisible Marginal returns to scale Technologies in the pool either all have constant marginal returns to scale or all have diminishing marginal returns to scale Model schematic

7. Pool of initial technologies The cost and effectiveness of each technology is drawn from a distribution Each technology is randomly assigned a ‘value’ attribute and a specific health production function ‘shape’ (applies only if marginal returns are diminishing) Initial allocator Imperfect information Each decision maker has one of four levels of information regarding the effectiveness of technologies: none, poor, good, or perfect Other value considerations Each decision maker assigns one of four possible weights to ‘value’ considerations beyond the QALY: none, small, medium, or large Initial budget Upon the establishment of the health system, an initial budget is assigned for purchasing technologies from the pool 1. The initial allocator purchases technologies from the pool until the initial budget is exhausted Divisibility of technologies Technologies in the pool are either all divisible or all indivisible Marginal returns to scale Technologies in the pool either all have constant marginal returns to scale or all have diminishing marginal returns to scale Model schematic

8. Pool of initial technologies The cost and effectiveness of each technology is drawn from a distribution Each technology is randomly assigned a ‘value’ attribute and a specific health production function ‘shape’ (applies only if marginal returns are diminishing) New intervention Each new intervention represents either a net investment or net disinvestment Net investments impose costs on the health system, requiring that resources be released from other technologies Net disinvestments release resources, allowing these to be spend on other technologies from the pool Initial allocator Imperfect information Each decision maker has one of four levels of information regarding the effectiveness of technologies: none, poor, good, or perfect Other value considerations Each decision maker assigns one of four possible weights to ‘value’ considerations beyond the QALY: none, small, medium, or large Initial budget Upon the establishment of the health system, an initial budget is assigned for purchasing technologies from the pool 1. The initial allocator purchases technologies from the pool until the initial budget is exhausted Divisibility of technologies Technologies in the pool are either all divisible or all indivisible Marginal returns to scale Technologies in the pool either all have constant marginal returns to scale or all have diminishing marginal returns to scale Model schematic

9. Pool of initial technologies The cost and effectiveness of each technology is drawn from a distribution Each technology is randomly assigned a ‘value’ attribute and a specific health production function ‘shape’ (applies only if marginal returns are diminishing) Initial allocator Agent Imperfect information Each decision maker has one of four levels of information regarding the effectiveness of technologies: none, poor, good, or perfect Other value considerations Each decision maker assigns one of four possible weights to ‘value’ considerations beyond the QALY: none, small, medium, or large Initial budget Upon the establishment of the health system, an initial budget is assigned for purchasing technologies from the pool 1. The initial allocator purchases technologies from the pool until the initial budget is exhausted Value threshold Used by the agent to determine whether or not to recommend the new intervention 2. The agent recommends the new intervention if its expected value exceeds the agent’s value threshold Divisibility of technologies Technologies in the pool are either all divisible or all indivisible Marginal returns to scale Technologies in the pool either all have constant marginal returns to scale or all have diminishing marginal returns to scale Model schematic New intervention Each new intervention represents either a net investment or net disinvestment Net investments impose costs on the health system, requiring that resources be released from other technologies Net disinvestments release resources, allowing these to be spend on other technologies from the pool

10. Pool of initial technologies The cost and effectiveness of each technology is drawn from a distribution Each technology is randomly assigned a ‘value’ attribute and a specific health production function ‘shape’ (applies only if marginal returns are diminishing) Initial allocator ReallocatorAgent Imperfect information Each decision maker has one of four levels of information regarding the effectiveness of technologies: none, poor, good, or perfect Other value considerations Each decision maker assigns one of four possible weights to ‘value’ considerations beyond the QALY: none, small, medium, or large Initial budget Upon the establishment of the health system, an initial budget is assigned for purchasing technologies from the pool 1. The initial allocator purchases technologies from the pool until the initial budget is exhausted Value threshold Used by the agent to determine whether or not to recommend the new intervention 2. The agent recommends the new intervention if its expected value exceeds the agent’s value threshold Divisibility of technologies Technologies in the pool are either all divisible or all indivisible Marginal returns to scale Technologies in the pool either all have constant marginal returns to scale or all have diminishing marginal returns to scale Model schematic New intervention Each new intervention represents either a net investment or net disinvestment Net investments impose costs on the health system, requiring that resources be released from other technologies Net disinvestments release resources, allowing these to be spend on other technologies from the pool

11. Pool of initial technologies The cost and effectiveness of each technology is drawn from a distribution Each technology is randomly assigned a ‘value’ attribute and a specific health production function ‘shape’ (applies only if marginal returns are diminishing) Initial allocator ReallocatorAgent Imperfect information Each decision maker has one of four levels of information regarding the effectiveness of technologies: none, poor, good, or perfect Other value considerations Each decision maker assigns one of four possible weights to ‘value’ considerations beyond the QALY: none, small, medium, or large Initial budget Upon the establishment of the health system, an initial budget is assigned for purchasing technologies from the pool 1. The initial allocator purchases technologies from the pool until the initial budget is exhausted Value threshold Used by the agent to determine whether or not to recommend the new intervention 3. If the agent recommends a net investment, the reallocator must contract adopted NE/NW technologies and/or expand non-exhausted SE/SW technologies. Alternatively, if the agent recommends a net disinvestment, the reallocator may expand non-exhausted NE technologies and/or contract adopted SW technologies Divisibility of technologies Technologies in the pool are either all divisible or all indivisible Marginal returns to scale Technologies in the pool either all have constant marginal returns to scale or all have diminishing marginal returns to scale Model schematic 2. The agent recommends the new intervention if its expected value exceeds the agent’s value threshold New intervention Each new intervention represents either a net investment or net disinvestment Net investments impose costs on the health system, requiring that resources be released from other technologies Net disinvestments release resources, allowing these to be spend on other technologies from the pool

12. Pool of initial technologies The cost and effectiveness of each technology is drawn from a distribution Each technology is randomly assigned a ‘value’ attribute and a specific health production function ‘shape’ (applies only if marginal returns are diminishing) Initial allocator ReallocatorAgent Imperfect information Each decision maker has one of four levels of information regarding the effectiveness of technologies: none, poor, good, or perfect Other value considerations Each decision maker assigns one of four possible weights to ‘value’ considerations beyond the QALY: none, small, medium, or large Initial budget Upon the establishment of the health system, an initial budget is assigned for purchasing technologies from the pool 1. The initial allocator purchases technologies from the pool until the initial budget is exhausted Value threshold Used by the agent to determine whether or not to recommend the new intervention Divisibility of technologies Technologies in the pool are either all divisible or all indivisible Marginal returns to scale Technologies in the pool either all have constant marginal returns to scale or all have diminishing marginal returns to scale Agent’s authority Agent may have mandate to consider reallocation and/or an alternative to the intervention Model schematic 3. If the agent recommends a net investment, the reallocator must contract adopted NE/NW technologies and/or expand non-exhausted SE/SW technologies. Alternatively, if the agent recommends a net disinvestment, the reallocator may expand non-exhausted NE technologies and/or contract adopted SW technologies 2. The agent recommends the new intervention if its expected value exceeds the agent’s value threshold New intervention Each new intervention represents either a net investment or net disinvestment Net investments impose costs on the health system, requiring that resources be released from other technologies Net disinvestments release resources, allowing these to be spend on other technologies from the pool

13. Pool of initial technologies The cost and effectiveness of each technology is drawn from a distribution Each technology is randomly assigned a ‘value’ attribute and a specific health production function ‘shape’ (applies only if marginal returns are diminishing) Initial allocator ReallocatorAgent Imperfect information Each decision maker has one of four levels of information regarding the effectiveness of technologies: none, poor, good, or perfect Other value considerations Each decision maker assigns one of four possible weights to ‘value’ considerations beyond the QALY: none, small, medium, or large Initial budget Upon the establishment of the health system, an initial budget is assigned for purchasing technologies from the pool 1. The initial allocator purchases technologies from the pool until the initial budget is exhausted Value threshold Used by the agent to determine whether or not to recommend the new intervention 4. Prior to making its recommendation, the agent places its own valuations on both the new intervention and the reallocator’s preferred reallocation. If the agent has the authority to mandate a reallocation and/or propose an alternative to the new intervention then it also places a valuation upon this. The optimal value threshold is that which ensures that a new intervention is only recommended if doing so maximizes the expected value to the agent Divisibility of technologies Technologies in the pool are either all divisible or all indivisible Marginal returns to scale Technologies in the pool either all have constant marginal returns to scale or all have diminishing marginal returns to scale Agent’s authority Agent may have mandate to consider reallocation and/or an alternative to the intervention Model schematic 3. If the agent recommends a net investment, the reallocator must contract adopted NE/NW technologies and/or expand non-exhausted SE/SW technologies. Alternatively, if the agent recommends a net disinvestment, the reallocator may expand non-exhausted NE technologies and/or contract adopted SW technologies 2. The agent recommends the new intervention if its expected value exceeds the agent’s value threshold New intervention Each new intervention represents either a net investment or net disinvestment Net investments impose costs on the health system, requiring that resources be released from other technologies Net disinvestments release resources, allowing these to be spend on other technologies from the pool

14. Conventional Assumptions

15. Diminishing Returns to Scale

16. Indivisible Technologies

17. Imperfect Information and Other ‘Value’ Considerations

18. Agent Has Authority to Reallocate

19. Conclusions The conventional ‘CE threshold’ model is merely a special case among many approaches for determining a value threshold Departing from this special case allows for consideration of: Differences in the information available to, the values held by, and the objectives pursued by, multiple interacting decision makers The specific value characteristics of each technology This has potentially significant implications for the appropriate specification of value thresholds used for decision making Our findings provide insights for future theoretical work, as well as a rich source of potential hypotheses for researchers conducting empirical research in this area

20. Questions 1.Why should value considerations be accounted for within the threshold used for CE analysis? Isn’t it sufficient to simply apply weights to new technologies or to consider ‘values’ separately? 2.Why might differences in information, values and objectives across multiple interacting decision makers result in: a)Different thresholds for net investments and net disinvestments? b)Thresholds that cross into the SE and NW quadrants of the CE plane? 3.Why is the threshold dependent upon the agent’s authority? Are there any implications for the recommendations made by CADTH or for the decisions of Canadian policy makers who depend upon CADTH’s guidance?

21. References Claxton et al. (2013). Methods for the Estimation of the NICE Cost Effectiveness Threshold. CHE Research Paper 81. York: University of York. Drummond et al. (2005). Methods for the Economic Evaluation of Health Care Programmes. Third Edition. Oxford: Oxford University Press. Sendi et al. (2002). Opportunity costs and uncertainty in the economic evaluation of health care interventions. Health Economics, 11(1), 23–31. National Institute for Health and Care Excellence (2009). Appraising life- extending, end of life treatments. London: NICE. National Institute for Health and Care Excellence (2014). Consultation Paper: Value Based Assessment of Health Technologies. London: NICE. Paulden et al. (2014). Some Inconsistencies in NICE’s Consideration of Social Values. PharmacoEconomics. November 2014, 32(11), 1043-1053.