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Early-Stage Valuation of Medical Devices: The Role of Developmental Uncertainty

Alan Girling, Terry Young, Celia Brown, Richard Lilford

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Appendix A1: Partial Valuation

Valuation is based on the post-market cash-flows (PMCF). Write, the expected value of PMCF given all the information available at G2. Since the project will be abandoned if Y < 0, the valuation at G2 is . The corresponding valuation at G1 is , where the expectation is taken at G1, over all quantities whose values will be resolved during the development phase. Write X for any quantity, or set of quantities, whose value will be resolved during development, and define .  The partial valuation allowing for X is defined as . The full early valuation, V₁, is just the partial valuation allowing for the complete set of developmental uncertainties, and is guaranteed to exceed any other partial valuation. I.e.  This is proved from Jensen’s inequality applied to the convex function, giving . The result follows on taking expectations over X in both sides of the inequality.

Partial valuations can be useful as a lower bound on early-stage value in situations where it is difficult to identify the extent to which uncertainty about some quantities will be resolved during the development cycle. The structure of the standard cash-flow model (section 2.3) with value-based pricing means that partial valuation can proceed by replacing some quantities by their expected values at G1. For example, suppose that we have viable priors for L, F and the price P,and that these quantities will be known by G2; but we are unable to grapple with the uncertainty surrounding N, the sales volume. Then, assuming N is independent of (L,F,P),

,

where denotes the expected number of sales, and the unit cost  is computed assuming that the fixed costs will be shared betweensales. The corresponding partial valuation is

.

The second factor on the right-hand side of this expression is the partial value per patient treated, assuming thatpatients are treated in total.

Appendix A2

Figures 4 and 5 have been constructed using Monte Carlo simulation of the distributions involved. For Figure 3 an explicit result was used: namely, if X is Normally distributed with mean  and standard deviation , then

where  and  are, respectively, the standard Normal distribution and density functions.

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