Clin Ther. 2013 Jul;35(7):904-14.

**A novel method to value real options in health care: the case of a multicohort human papillomavirus vaccination strategy.**

Favato G, Baio G, Capone A, Marcellusi A, Saverio Mennini F.

Institute of Leadership and Management in Health, Kingston University, London, United Kingdom. g.favato@kingston.ac.uk

**ABSTRACT:**

**Background:**

A large body of economic evaluations has already confirmed the cost-effectiveness of different human papillomavirus (HPV) vaccination strategies. Standard analyses might not capture the full economic value of novel vaccination programmes, since the relative simplicity of the cost-effectiveness fails to take account of the value of active management. Management decisions can be seen as a real options, a term used to refer to the application of option pricing theory to the valuation of investments in non-financial assets where much of the value is attributable to flexibility and learning over time. Real option valuation is treating the different types of managerial flexibility as options and valuing them with option pricing models.

**Objective**

This study was aimed to determine the real option value of four HPV vaccination strategies – targeting girls aged 12, 15, 18 and 25 – in comparison with the outcomes of a Bayesian cost-effectiveness analysis.

**Methods**

This paper applies the recently developed pay-off method which derives the real option value from the pay-off distribution of the project’s NPV, which is treated as a fuzzy set. The possibilistic rather than probabilistic distribution of outcomes and the recognition of the economic value of the active role of management differentiate the pay-off pricing method for real options from the cost-effectiveness paradigm.

**Results**

Costs per quality-adjusted life-year (QALY) gained appeared to be related to the number of cohorts targeted: a single cohort of girls aged 12 (€10,955; 95 CI: €1,021, €28,212) showed the lowest cost among the four alternative strategies evaluated. The real option valuation challenged the cost-effectiveness dominance of a single cohort of 12-year-old girls. The simultaneous vaccination of two cohorts of girls aged 12 and 15 yielded a real option value (€17,723) equivalent to that attributed to a single cohort of 12-year-old girls (€17,460).

**Conclusions**

A national vaccination programme targeting two cohorts should be the preferred method of implementation when the impact on access, coverage and, ultimately, time to prevention of HPV-induced diseases is taken into account. The use of both cost-effectiveness analysis and real option valuation could together improve the quality of policy-making under uncertain conditions, given the acknowledgement of the value of management in the implementation of healthcare programmes. Copyright © 2013 Elsevier HS Journals, Inc.

KEYWORDS: human papillomavirus, multicohort, real option, vaccination, valuation

PMID: 23806328

**SUPPLEMENT**

This paper presented a new method (pay-off method) to value real options in healthcare, which is intuitive to understand and less mathematically challenging than any previous real option pricing formula.

The main intuition behind the pay-off method is that management plays an active role in determining the economic value of the chosen project over its entire life. Like cost-effectiveness analysis, the pay-off method involves projecting future streams of costs and economic benefits, but its paradigm assumes that managers can influence the outcome by interventive actions that add value over time. By taking into account only the positive side of the distribution in the real option value, the pay-off method explicitly recognises the ability of managers to interrupt the intervention as soon as its net present value becomes negative, in order to avoid further losses. Moreover, management can decide to change the implementation choices made ex-ante, on the basis of information which only became available ex-post the investment decision. Management actions and decisions made during the life of an investment are valuable because they can push the pay-off of the initial investment closer to its upper possible threshold, rather than passively accept a probabilistic mean value.

The pay-off method utilizes fuzzy sets to determine the possibilistic, as opposed to the probabilistic, expected value of a given healthcare intervention. A fuzzy set is a class of elements with a continuum of grades of membership, characterized by a membership function which assigns to each element a grade of membership ranging between zero and one. In essence, the pay-off method replaces the probability distribution of a NPV outcome with a simpler triangular distribution, defined by a fuzzy set of three values:

a = corresponds to the base case mean NPV value

α= represents the distance between a and the minimum possible NPV value

β = is the distance between a and the maximum possible NPV value

The highest possibility (fully possible) is assigned to the base case and the lowest (near-zero) possibility to the minimum and maximum values of the distribution. The result is thus a triangular fuzzy distribution (A) that is equivalent to the fuzzy NPV of the project. The mean value of the positive values of the fuzzy NPV, E(A+), is the possibilistic mean value of the positive fuzzy NPV values, as shown graphically in Figure 1.

The possibilistic approach to uncertainty and the recognition of the economic value of the active role of management differentiate the pay-off pricing method for real options from the cost-effectiveness paradigm.

But would the pay-off method lead to different results compared to cost-effectiveness analysis?

To answer this question, we informed the pay-off model with cost-effectiveness data were derived from a full Bayesian study which evaluated the implementation and economic consequences of the HPV vaccination of 2, 3 and 4 cohorts of girls aged 12, 15, 18 and 25 years. Although the outcomes of the Bayesian model reported in the cost-effectiveness study could not be directly compared with any previous evaluation, the range of incremental cost per QALY gained for a single cohort of girls aged 12 years confirmed the cost-effectiveness dominance of immunising this cohort compared to the alternatives.

In contrast to the outcomes of a full Bayesian cost-effectiveness model, where the single cohort strategy is dominant, the pay-off method assigned the highest real option value to the two-cohort strategy, closely followed by the single cohort option. Figure 2 reports a summary of the pay-off valuation of the four immunization options.

The real option pricing of the four HPV vaccination strategies evaluated here offers new insights into the implementation of a national immunisation programme from the perspective of the National Health Service. The general acceptance of the use of cost-effectiveness analyses in the economic evaluation of healthcare can result in one of the most common errors in decision-making, commonly referred to as ‘frame blindness’, in which the wrong problem is addressed because a conceptual framework is created that results in a decision in which the best option is rejected.

The integration of cost-effectiveness analysis and real option valuation could improve the quality of policy decisions under conditions of uncertainty, due to the explicit recognition of the value of management in the implementation of healthcare programmes.

CONTACT INFORMATION

Prof. Giampiero Favato (Corresponding Author)

e-mail: favatog@gmail.com

**Figure 1. Triangular distribution of fuzzy set A. **The fuzzy set A is defined by three values: a (the best-case scenario NPV), α (the distance between the minimum and the best-case scenario NPV) and β (the distance between the maximum and the best-case scenario). The area between a-α represents the distribution of all possible negative NPV values while the opposite side, between 0 and a+β, shows the distribution of positive NPV values. The possibilistic mean value of the positive fuzzy NPV values E(A_+), is the fuzzy mean value of the NPV.

**Figure 2. Pay-off distribution of the four HPV vaccination strategies evaluated in the Real Options valuation. **The left-hand side of the distribution shows the distance (α) between the minimum NPV value and the base-case scenario NPV (a) for the four vaccination options evaluated, as identified in the data legend located in the lower right-hand corner of the graph. The right-hand side of the distribution reports the distance (β) between the maximum NPV value and the base-case scenario NPV (a).

The dotted lines in the centre of the distribution show the real options value for each option, which is the possibilistic mean value of the positive fuzzy NPV values multiplied by the positive area of the fuzzy NPV over the total area of the fuzzy NPV. The highest Real Options value (€17,723, red dotted line) was attributed to the two-cohort vaccination, followed by the single cohort (€17,461, blue dotted line) and, more distantly, by the three- (green dotted line) and four- (orange dotted line) cohort vaccination (€16,440 and €13,576 respectively).