34.7 Discounting Rewards

In addition to defining stage-dependent probabilities, tables can also describe stage-dependent rewards such as costs or utilities. However, if all you need to do is discount costs and utilities, a simple exponential formula may be used instead of a table. For example, the expression

can be used to discount the reward value at each stage. If the cycle length is not equal to the period of the discount rate (usually 1 year), then _stage should either be divided (for shorter cycle lengths) or multiplied (for long cycle lengths).

Discounting nearly always needs to be applied to an entire reward set, such as cost and/or effectiveness. TreeAge Pro has two options for discounting.

1. Apply a single discount rate to an entire reward set: Use the Tree Preferences to set a specified discount rate to be applied to any given reward set. We call this Global Discounting, and we recommend using this approach as it is the easiest to implement.

2. Adjust each reward manually: Use the Discount() function as described further below to manually change the value of each reward.

To apply a single discount rate to the entire reward set, enter the details in the Tree Preferences as described in the Payoff Preferences section. When the Global Discounting is applied to a reward set, the word "Discounted" appears after the reward name in the Markov View, as in the figure below.

The Healthcare tutorial example model Markov.Discounting.trex demonstrates global discounting in a Markov model along with use of the Discount functions for rewards. Note that analysis of the model using each discounting option yields the same results.

If you prefer to manually adjust each individual reward, rather than using TreeAge Pro's Global Discounting function, you can use TreeAge Pro’s built-in discounting function, Discount(). This Discount() function represents the exponential formula above and takes three parameters: value, rate and time. For example, the expression:

will yield the same result as the exponential formula shown above. The Discount() function is equally applicable to the discounting of costs and utilities.

TreeAge Pro’s built-in functions can be inserted into formulas either by typing them in yourself or by using the Formula Editor or auto-fill.