dynpv: Present values with dynamic pricing and dynamic uptake

In dynamicpv: Evaluates Present Values and Health Economic Models with Dynamic Pricing and Uptake

Present values with dynamic pricing and dynamic uptake

Description

Calculate present value for a payoff with dynamic (lifecycle) pricing and dynamic uptake (stacked cohorts).

Usage

dynpv(
  uptakes = 1,
  payoffs,
  horizon = length(payoffs),
  tzero = 0,
  prices = rep(1, length(payoffs) + tzero),
  discrate = 0
)

Arguments

uptakes	Vector of patient uptake over time
payoffs	Vector of payoffs of interest (numeric vector)
horizon	Time horizon for the calculation (length must be less than or equal to the length of payoffs)
tzero	Time at the date of calculation, to be used in lookup in prices vector
prices	Vector of price indices through the time horizon of interest
discrate	Discount rate per timestep, corresponding to price index

Details

Suppose payoffs in relation to patients receiving treatment (such as costs or health outcomes) occur over timesteps t=1, ..., T. Let us partition time as follows.

• Suppose j=1,...,T indexes the time at which the patient begins treatment.

• Suppose k=1,...,T indexes time since initiating treatment.

In general, t=j+k-1, and we are interested in the set of (j,k) such that 1 \leq t \leq T.

For example, t=3 comprises:

• patients who are in the third timestep of treatment that began in timestep 1: (j,k)=(1,3);

• patients who are in the second timestep of treatment that began in timestep 2, (j,k)=(2,2); and

• patients who are in the first timestep of treatment that began in timestep 3, (j,k)=(3,1)

The Present Value of a cashflow p_k for the u_j patients who began treatment at time j and who are in their kth timestep of treatment is as follows

PV(j,k,l) = u_j \cdot p_k \cdot R_{j+k+l-1} \cdot (1+i)^{2-j-k}

where i is the risk-free discount rate per timestep, p_k is the cashflow amount in today’s money, and p_k \cdot R_{j+k+l-1} is the nominal amount of the cashflow at the time it is incurred, allowing for an offset of l = tzero.

The total present value, TPV(l), is therefore the sum over all j and k within the time horizon T, namely:

TPV(l) = \sum_{j=1}^{T} \sum_{k=1}^{T-j+1} PV(j,k, l) \\ \; = \sum_{j=1}^{T} \sum_{k=1}^{T-j+1} u_j \cdot p_k \cdot R_{l+j+k-1} \cdot (1+i)^{2-j-k}

This function calculates PV(j,k,l) for all values of j, k and l, and returns this in a tibble.

Value

A tibble of class "dynpv" with the following columns:

• j: Time at which patients began treatment

• k: Time since patients began treatment

• l: Time offset for the price index (from tzero)

• t: Equals j+k-1

• uj: Uptake of patients beginning treatment at time j (from uptakes)

• pk: Cashflow amount in today's money in respect of patients at time k since starting treatment (from payoffs)

• R: Index of prices over time l+t (from prices)

• v: Discounting factors, (1+i)^{1-t}, where i is the discount rate per timestep

• pv: Present value, PV(j,k,l)

Examples

# Simple example
pv1 <- dynpv(
   uptakes = (1:10), # 1 patient uptakes in timestep 1, 2 patients in timestep 2, etc
   tzero = c(0,5), # Calculations are performed with prices at times 0 and 5
   payoffs = 90 + 10*(1:10), # Payoff vector of length 10 = (100, 110, ..., 190)
   prices = 1.02^((1:15)-1), # Prices increase at 2\% per timestep in future
   discrate = 0.05 # The nominal discount rate is 5\% per timestep;
                   # the real discount rate per timestep is 3\% (=5\% - 3\%)
)
pv1
summary(pv1)

# More complex example, using cashflow output from a heemod model

# Obtain dataset
democe <- get_dynfields(
   heemodel = oncpsm,
   payoffs = c("cost_daq_new", "cost_total", "qaly"),
   discount = "disc"
   )

# Obtain short payoff vector of interest
payoffs <- democe |>
   dplyr::filter(int=="new", model_time<11) |>
   dplyr::mutate(cost_oth = cost_total - cost_daq_new)

# Example calculation
pv2 <- dynpv(
   uptakes = rep(1, nrow(payoffs)),
   payoffs = payoffs$cost_oth,
   prices = 1.05^(0:(nrow(payoffs)-1)),
   discrate = 0.08
)
summary(pv2)

dynamicpv documentation built on Jan. 16, 2026, 1:07 a.m.