Calculate present value for a payoff in a single cohort with dynamic pricing across multiple timepoints

Present value of a series of payoffs for a single given cohort, entering at given future time, allowing for dynamic pricing. This function is a wrapper for dynpv() restricted to evaluation of a single cohort.

Usage

futurepv(tzero = 0, payoffs, prices, discrate)

Arguments

tzero

Time at the date of calculation, to be used in lookup in prices vector

payoffs

Vector of payoffs of interest (numeric vector)

prices

Vector of price indices through the time horizon of interest

discrate

Discount rate per timestep, corresponding to price index

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, \(PV(j,k,l)\)

See also

dynpv()

Examples

library(dplyr)
#> 
#> Attaching package: ‘dplyr’
#> The following objects are masked from ‘package:stats’:
#> 
#>     filter, lag
#> The following objects are masked from ‘package:base’:
#> 
#>     intersect, setdiff, setequal, union

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

# Obtain discount rate
discrate <- get_param_value(oncpsm, "disc")

# Obtain payoff vector of interest
payoffs <- democe |>
   filter(int=="new") |>
   mutate(cost_oth_rup = cost_total_rup - cost_daq_new_rup)
Nt <- nrow(payoffs)

# Run calculation for times 0-9
fpv <- futurepv(
  tzero = (0:9)*52,
  payoffs = payoffs$cost_oth_rup,
  prices = 1.001^(1:(2*Nt)-1), # Approx 5.3% every 52 steps
  discrate = 0.001 + discrate
)
fpv
#> # A tibble: 10,440 × 9
#>        j     k     l     t    uj    pk     R     v    pv
#>    <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#>  1     1     1     0     1     1  355.  1        1  355.
#>  2     1     1    52     1     1  355.  1.05     1  374.
#>  3     1     1   104     1     1  355.  1.11     1  394.
#>  4     1     1   156     1     1  355.  1.17     1  415.
#>  5     1     1   208     1     1  355.  1.23     1  437.
#>  6     1     1   260     1     1  355.  1.30     1  460.
#>  7     1     1   312     1     1  355.  1.37     1  485.
#>  8     1     1   364     1     1  355.  1.44     1  511.
#>  9     1     1   416     1     1  355.  1.52     1  538.
#> 10     1     1   468     1     1  355.  1.60     1  566.
#> # ℹ 10,430 more rows
summary(fpv)
#> Summary of Dynamic Pricing and Uptake
#>      Number of cohorts:             1044 
#>      Number of times:               10 
#>      Total uptake:                  1 
#> 
#>  Total and mean present values by timepoint: 
#> # A tibble: 10 × 3
#>    tzero  total   mean
#>    <dbl>  <dbl>  <dbl>
#>  1     0 52165. 52165.
#>  2    52 54948. 54948.
#>  3   104 57880. 57880.
#>  4   156 60967. 60967.
#>  5   208 64220. 64220.
#>  6   260 67646. 67646.
#>  7   312 71255. 71255.
#>  8   364 75056. 75056.
#>  9   416 79060. 79060.
#> 10   468 83278. 83278.