How to correctly calculate discounted healthcare costs and benefits
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How to correctly calculate discounted healthcare costs and bene®ts RD Baker University of Salford, Salford, UK A feature of a healthcare policy (such as screening) with interventions at speci®c ages is that when it is introduced, part of the population is too old to participate in the full programme. This fact changes the formulae to be used for cost and bene®t discounting in a non-intuitive way. General formulae are derived for the expected discounted costs and bene®ts of such health promotion policies, for a stationary population. Correct ways to calculate discounted costs and bene®ts via simulation are also described. The formulae have some surprising properties, for example the relative cost of two health policies does not depend on the discounting rate. They are also relevant to the ongoing debate over the correct discounting rate for bene®ts. It is shown that when health bene®ts follow quickly on treatments, varying the discounting rate for health bene®ts is merely equivalent to rescaling the cash value of a bene®t. It is only when bene®t follows long after treatment that the problem of choosing an appropriate discount rate for bene®ts cannot be simpli®ed. Keywords: cost discounting; medical screening; renewal process; stationary population; simulation
Introduction When evaluating alternative health care policies, it is customary to discount treatment costs (for a discussion of discounting, see for example, Reference 1). A treatment that costs £1 now under policy A is costlier than one that costs £1 in ten year's time under policy B, because if I invest 61 pence at 5% interest, it will swell to the necessary £1 in 10 years. Hence policy B only costs 61 pence in real terms, which is its discounted cost. The approximately continuous accrual of interest leads us to downweight a cost incurred time t ahead by a factor of exp
ÿgt. After n years with an annual interest rate of 100r%, we have that
1 rn exp
ng, so that the value of g is given by g log
1 r. In¯ation at a constant rate shrinks the buying power of saved money exponentially and so is easily accommodated within this framework, where it simply decreases the effective value of g. Discounting of health bene®ts as well as of treatment costs is more debatable, but the consensus is that both costs and bene®ts should be discounted at about 6% per year.2 Planners attempt to minimise the total net discounted cost C ÿ D over an in®nite time horizon, where C stands for expected total discounted treatment cost, and D for the money equivalent of expected total discounted bene®t from treatment. We naturally do not envisage that health policies such as screening will be in place for ever, but a happy
Correspondence: Dr RD Baker, Centre for OR and Applied Statistics. University of Salford, Salford M5 4WT, UK. E-mail [email protected]
advantage of discounting is that at 6%, costs of treatments 100 years in the future are only 0.25% of curren
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