Budget Impact Applications

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

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Introduction

Our objective is to evaluate the budget impact of introducing a new intervention, assuming static or dynamic pricing. Uptake in budget impact models is already modeled in a dynamic fashion.

Methods and Assumptions

General assumptions

Budget impact models conventionally have no discounting and a shorter time horizon than cost-effectiveness models, so we will use a time horizon of 5 years here and a discount rate of 0\%. We will compute a budget impact model using current pricing (per convention) as well as by using dynamic pricing according to the assumptions previously set.

Dynamic pricing

To recap, we had the following assumptions concerning pricing, with a date of calculation of 2025-09-01.

• Costs are assumed to increases in line with general inflation (2.5% per year), except for effects on drug acquisition costs due to LoEs.
• The LoE for the SoC is assumed to occur first, at 2028-01-01, after which there is anticipated to be a 70% reduction in prices over one year.
• The new intervention has an LoE occuring three years later, at 2031-01-01, after which there would be a 50% reduction in prices over one year.

Dynamic uptake

We had the following assumptions concerning patient uptake.

• Only newly incident patients with the cancer being modeled would be eligible for the new treatment. Existing/prevalent patients with the condition would not be eligible.
• The disease incidence is 1 patient per week.
• Among these patients, were the new intervention to be made available, uptake of the new intervention would be expected to rise linearly from 0% to 100% after 2 years.

Implementation

Set-up

First we load the packages necessary for this vignette.

library(dplyr)
library(lubridate)
library(heemod)
library(dynamicpv)

# Time constants
days_in_year <- 365.25
days_in_week <- 7
cycle_years <- days_in_week / days_in_year # Duration of a one week cycle in years

# Time horizon (years) and number of cycles
thoz <- 20
Ncycles <- ceiling(thoz/cycle_years)

# Real discounting
disc_year <- 0.03 # Per year
disc_cycle <- (1+disc_year)^(cycle_years) - 1 # Per cycle

# Price inflation
infl_year <- 0.025 # Per year
infl_cycle <- (1+infl_year)^(cycle_years) - 1 # Per cycle

# Nominal discounting
nomdisc_year <- (1+disc_year)*(1+infl_year) - 1
nomdisc_cycle <- (1+nomdisc_year)^(cycle_years) - 1 # Per cycle

# State names
state_names = c(
  progression_free = "PF",
  progression = "PD",
  death = "Death"
  )

# PFS distribution for SoC with Exp() distribution and mean of 50 weeks
surv_pfs_soc <- heemod::define_surv_dist(
  distribution = "exp",
  rate = 1/50
)

# OS distribution for SoC with Lognorm() distribution, meanlog = 4.5, sdlog = 1
# This implies a mean of exp(4 + 0.5 * 1^2) = exp(4.5) = 90 weeks
surv_os_soc <- heemod::define_surv_dist(
  distribution = "lnorm",
  meanlog = 4,
  sdlog = 1
)

# PFS and OS distributions for new
surv_pfs_new <- heemod::apply_hr(surv_pfs_soc, hr=0.5)
surv_os_new <- heemod::apply_hr(surv_os_soc, hr=0.6)

# Define partitioned survival model, soc
psm_soc <- heemod::define_part_surv(
  pfs = surv_pfs_soc,
  os = surv_os_soc,
  terminal_state = FALSE,
  state_names = state_names
  )

# Define partitioned survival model, soc
psm_new <- heemod::define_part_surv(
  pfs = surv_pfs_new,
  os = surv_os_new,
  terminal_state = FALSE,
  state_names = state_names
  )

# Parameters
params <- heemod::define_parameters(
  # Discount rate
  disc = disc_cycle,
  # Disease management costs
  cman_pf = 80,
  cman_pd = 20,
  # Drug acquisition costs - the SoC regime only uses SoC drug, the New regime only uses New drug
  cdaq_soc = dispatch_strategy(
    soc = 400,
    new = 0
  ),
  cdaq_new = dispatch_strategy(
    soc = 0,
    new = 1500
  ),
  # Drug administration costs
  cadmin = dispatch_strategy(
    soc = 50,
    new = 75
  ),
  # Adverse event risks
  risk_ae = dispatch_strategy(
    soc = 0.08,
    new = 0.1
  ),
  # Adverse event average costs
  uc_ae = 2000,
  # Subsequent treatments
  csubs = dispatch_strategy(
    soc = 1200,
    new = 300
  ),
  # Health state utilities
  u_pf = 0.8,
  u_pd = 0.6,
)

# Define PF states
state_PF <- heemod::define_state(
  # Costs for the state
  cost_daq_soc = discount(cdaq_soc, disc_cycle),
  cost_daq_new = discount(cdaq_new, disc_cycle),
  cost_dadmin = discount(cadmin, disc_cycle),
  cost_dman = discount(cman_pf, disc_cycle),  
  cost_ae = risk_ae * uc_ae,
  cost_subs = 0,
  cost_total = cost_daq_soc + cost_daq_new + cost_dadmin + cost_dman + cost_ae + cost_subs,
  # Health utility, QALYs and life years
  pf_year = discount(cycle_years, disc_cycle),
  life_year = discount(cycle_years, disc_cycle),
  qaly = discount(cycle_years * u_pf, disc_cycle)
  )

# Define PD states
state_PD <- heemod::define_state(
  # Costs for the state
  cost_daq_soc = 0,
  cost_daq_new = 0,
  cost_dadmin = 0,
  cost_dman = discount(cman_pd, disc_cycle),  
  cost_ae = 0,
  cost_subs = discount(csubs, disc_cycle),
  cost_total = cost_daq_soc + cost_daq_new + cost_dadmin + cost_dman + cost_ae + cost_subs,
  # Health utility, QALYs and life years
  pf_year = 0,
  life_year = heemod::discount(cycle_years, disc_cycle),
  qaly = heemod::discount(cycle_years * u_pd, disc_cycle)
  )

# Define Death state
state_Death <- heemod::define_state(
  # Costs are zero
  cost_daq_soc = 0,
  cost_daq_new = 0,
  cost_dadmin = 0,
  cost_dman = 0,
  cost_ae = 0,
  cost_subs = 0,
  cost_total = cost_daq_soc + cost_daq_new + cost_dadmin + cost_dman + cost_ae + cost_subs,
  # Health outcomes are zero
  pf_year = 0,
  life_year = 0,
  qaly = 0,
)

# Define strategy for SoC
strat_soc <- heemod::define_strategy(
    transition = psm_soc,
    "PF" = state_PF,
    "PD" = state_PD,
    "Death" = state_Death
  )

# Define strategy for new
strat_new <- heemod::define_strategy(
  transition = psm_new,
  "PF" = state_PF,
  "PD" = state_PD,
  "Death" = state_Death
)

# Create heemod model
heemodel <- heemod::run_model(
  soc = strat_soc,
  new = strat_new,
  parameters = params,
  cycles = Ncycles,
  cost = cost_total,
  effect = qaly,
  init = c(1, 0, 0),
  method = "life-table"
)

# Dates
# Date of calculation = 1 September 2025
doc <- lubridate::ymd("20250901")
# Date of LOE for SoC = 1 January 2028
loe_soc_start <- lubridate::ymd("20280101")
# Maturation of SoC prices by LOE + 1 year, i.e. = 1 January 2029
loe_soc_end <- lubridate::ymd("20290101") 
# Date of LOE for new treatment = 1 January 2031
loe_new_start <- lubridate::ymd("20310101")
# Maturation of new treatment prices by LOE + 1 year, i.e. = 1 January 2032
loe_new_end <- lubridate::ymd("20320101") 

# Effect of LoEs on prices once mature
loe_effect_soc <- 0.7
loe_effect_new <- 0.5

# Calculation of weeks since DoC for LoEs and price maturities
wk_start_soc <- floor((loe_soc_start-doc) / lubridate::dweeks(1))
wk_end_soc <- floor((loe_soc_end-doc) / lubridate::dweeks(1))
wk_start_new <- floor((loe_new_start-doc) / lubridate::dweeks(1))
wk_end_new <- floor((loe_new_end-doc) / lubridate::dweeks(1))

# Price maturity times
wk_mature_soc <- wk_end_soc - wk_start_soc
wk_mature_new <- wk_end_new - wk_start_new

# Create a tibble of price indices of length 2T, then pull out columns as needed
# We only need of length T for now, but need of length 2T for future calculations later
pricetib <- dplyr::tibble(
  model_time = 1:(2*Ncycles),
  model_year = model_time * cycle_years,
  static = 1,
  geninfl = (1 + infl_cycle)^(model_time - 1),
  loef_soc = pmin(pmax(model_time - wk_start_soc, 0), wk_mature_soc) / wk_mature_soc,
  loef_new = pmin(pmax(model_time - wk_start_new, 0), wk_mature_new) / wk_mature_new,
  dyn_soc = geninfl * (1 - loe_effect_soc * loef_soc),
  dyn_new = geninfl * (1 - loe_effect_new * loef_new)
)

# Price indices required for calculations
prices_oth <- pricetib$geninfl
prices_static <- pricetib$static
prices_dyn_soc <- pricetib$dyn_soc
prices_dyn_new <- pricetib$dyn_new

# Time for uptake to occur
uptake_years <- 2

# Uptake vector for non-dynamic uptake
uptake_single <- c(1, rep(0, Ncycles-1))

# Uptake vector for dynamic uptake
uptake_weeks <- round(uptake_years / cycle_years)
share_multi <- c((1:uptake_weeks)/uptake_weeks, rep(1, Ncycles-uptake_weeks))
uptake_multi <- rep(1, Ncycles) * share_multi

# Pull out the payoffs of interest from oncpsm
payoffs <- get_dynfields(
    heemodel = heemodel,
    payoffs = c("cost_daq_new", "cost_daq_soc", "cost_total", "qaly", "life_year"),
    discount = "disc"
    ) |>
    dplyr::mutate(
      model_years = model_time * cycle_years,
      # Derive costs other than drug acquisition, as at time zero
      cost_nondaq = cost_total - cost_daq_new - cost_daq_soc,
      # ... and at the start of each timestep
      cost_nondaq_rup = cost_total_rup - cost_daq_new_rup - cost_daq_soc_rup
    )

# Create and view dataset for SoC
hemout_soc <- payoffs |> dplyr::filter(int=="soc")
head(hemout_soc)

# Create and view dataset for new intervention
hemout_new <- payoffs |> dplyr::filter(int=="new")
head(hemout_new)

The underlying health economic model is built as described in vignette("cost-effectiveness-applications"). We require additional coding for the budget impact evaluation.

# BIM settings
bi_horizon_yrs <- 5
bi_horizon_wks <- round(bi_horizon_yrs / cycle_years)
bi_discount <- 0

# Newly eligible patients
newly_eligible <- rep(1, Ncycles)

# Time for uptake to occur
uptake_years <- 2
uptake_weeks <- round(uptake_years / cycle_years)

# Market share of new intervention
share_multi <- c((1:uptake_weeks)/uptake_weeks, rep(1, Ncycles-uptake_weeks))

# Newly eligible patients receiving each intervention, "world with"
uptake_new <- newly_eligible * share_multi
uptake_soc <- newly_eligible - uptake_new

Results

Static prices

First we consider static prices, i.e. we assume the prices of existing resources remain unchanged from now in the horizon of the budget impact model. Let us use that function to calculate budgetary costs for the world without the new intervention.

# World without new intervention

# SoC, drug acquisition costs
wout1_soc_daqcost <- dynpv(
    uptakes = newly_eligible,
    payoffs = hemout_soc$cost_daq_soc_rup,
    horizon = bi_horizon_wks,
    prices = prices_static,
    discrate = bi_discount
    )

# SoC, other costs
wout1_soc_othcost <- dynpv(
    uptakes = newly_eligible,
    payoffs = hemout_soc$cost_nondaq_rup,
    horizon = bi_horizon_wks,
    prices = prices_static,
    discrate = bi_discount
    )

# Total budgetary costs
budget_wout1 <- budget_wout1_soc <- wout1_soc_daqcost + wout1_soc_othcost

The total budgetary costs in the world without are $r total(budget_wout1) in respect of r uptake(budget_wout1) patients.

Let us now calculate the budgetary costs in the world with the new intervention.

# World with

# SoC, drug acquisition costs
with1_soc_daqcost <- dynpv(
    uptakes = uptake_soc,
    payoffs = hemout_soc$cost_daq_soc_rup,
    horizon = bi_horizon_wks,
    prices = prices_static,
    discrate = bi_discount
    )

# SoC, other costs
with1_soc_othcost <- dynpv(
    uptakes = uptake_soc,
    payoffs = hemout_soc$cost_nondaq_rup,
    horizon = bi_horizon_wks,
    prices = prices_static,
    discrate = bi_discount
    )

# New intervention, drug acquisition costs
with1_new_daqcost <- dynpv(
    uptakes = uptake_new,
    payoffs = hemout_new$cost_daq_new_rup,
    horizon = bi_horizon_wks,
    prices = prices_static,
    discrate = bi_discount
    )

# New intervention, other costs
with1_new_othcost <- dynpv(
    uptakes = uptake_new,
    payoffs = hemout_new$cost_nondaq_rup,
    horizon = bi_horizon_wks,
    prices = prices_static,
    discrate = bi_discount
    )

# Total
budget_with1_soc <- with1_soc_daqcost + with1_soc_othcost
budget_with1_new <- with1_new_daqcost + with1_new_othcost
budget_with1 <- budget_with1_soc + budget_with1_new

Note the warning provided by dynamicpv. This is because the uptake vector for SoC, when trimmed of zeroes after uptake stops, has a different (shorter) length than the uptake vector for the new intervention. The calculation is still correct. However, the function is flagging for the user the different uptake vectors being used for different present value calculations.

# The uptake vector for the new intervention is long
length(trim_vec(uptake_new))

# The uptake vector for the SoC is short, once trimmed of excess zeros
length(trim_vec(uptake_soc))

The budgetary costs in the world with the new intervention are $r total(budget_with1), comprising $r total(budget_with1_soc) in respect of the costs of r uptake(budget_with1_soc) patients being treated with the SoC, and $r total(budget_with1_new) in respect of the costs of r uptake(budget_with1_new) patients being treated with the SoC.

# Budget impact
bi1_soc <- budget_with1_soc - budget_wout1_soc
bi1_new <- budget_with1_new
bi1 <- budget_with1 - budget_wout1

summary(bi1)

The total budget impact is $r total(bi1), representing an increase of r total(bi1)/total(budget_wout1) *100%.

Dynamic prices

Now let us recalculate the budget impact, assuming dynamic pricing in drug acquisition costs. This is simple with dynamicpv()::dynpv() because we just change the prices argument from prices_static to either prices_dyn_soc or prices_dyn_new for the drug acquisition costs. We will keep other costs unchanged.

# World without new intervention

# SoC, drug acquisition costs
wout2_soc_daqcost <- dynpv(
    uptakes = newly_eligible,
    payoffs = hemout_soc$cost_daq_soc_rup,
    horizon = bi_horizon_wks,
    prices = prices_dyn_soc,
    discrate = bi_discount
    )

# SoC, other costs - unchanged from static calculations
wout2_soc_othcost <- wout1_soc_othcost

# Total budgetary costs
budget_wout2 <- budget_wout2_soc <- wout2_soc_daqcost + wout2_soc_othcost

The total budgetary costs in the world without are $r total(budget_wout2) in respect of r uptake(budget_wout2) patients.

Let us now calculate the budgetary costs in the world with the new intervention.

# World with

# SoC, drug acquisition costs
with2_soc_daqcost <- dynpv(
    uptakes = uptake_soc,
    payoffs = hemout_soc$cost_daq_soc_rup,
    horizon = bi_horizon_wks,
    prices = prices_dyn_soc,
    discrate = bi_discount
    )

# SoC, other costs
with2_soc_othcost <- with1_soc_othcost

# New intervention, drug acquisition costs
with2_new_daqcost <- dynpv(
    uptakes = uptake_new,
    payoffs = hemout_new$cost_daq_new_rup,
    horizon = bi_horizon_wks,
    prices = prices_dyn_new,
    discrate = bi_discount
    )

# New intervention, other costs
with2_new_othcost <- with1_new_othcost

# Total
budget_with2_soc <- with2_soc_daqcost + with2_soc_othcost
budget_with2_new <- with2_new_daqcost + with2_new_othcost
budget_with2 <- budget_with2_soc + budget_with2_new

Notice that there is a similar warning as earlier. The budgetary costs in the world with the new intervention are $r total(budget_with2), comprising $r total(budget_with2_soc) in respect of the costs of r uptake(budget_with2_soc) patients being treated with the SoC, and $r total(budget_with2_new) in respect of the costs of r uptake(budget_with2_new) patients being treated with the new treatment.

# Budget impact
bi2_soc <- budget_with2_soc - budget_wout2_soc
bi2_new <- budget_with2_new
bi2 <- budget_with2 - budget_wout2

summary(bi2)

The total budget impact is $r total(bi2), representing an increase of r total(bi2)/total(budget_wout2) *100%.

Summary

| | | Static drug pricing | Dynamic drug pricing | |:---|:--|------------|------------| | World without new intervention || | | | | Standard of Care | r total(budget_wout1_soc) | r total(budget_wout2_soc) | | | New intervention | 0 | 0 | | | Total | r total(budget_wout1) | r total(budget_wout2) | | World with new intervention || | | | | Standard of Care | r total(budget_with1_soc) | r total(budget_with2_soc) | | | New intervention | r total(budget_with1_new) | r total(budget_with2_new) | | | Total | r total(budget_with1) | r total(budget_with2_new) | | Budget impact || | | | | Standard of Care | r total(bi1_soc) | r total(bi2_soc) | | | New intervention | r total(bi1_new) | r total(bi2_new) | | | Absolute impact | r total(bi1) | r total(bi2) | | | Relative impact (%) | r ((total(bi1))/(total(budget_wout1))*100)% | r ((total(bi2))/(total(budget_wout2))*100)% |

: Budget Impact model results with and without dynamic drug pricing

Discussion

• In both cases, the budget impact is large, with budgetary costs more than doubling with the introduction of the new intervention, over the time horizon of interest (r bi_horizon_yrs years).
• Dynamic pricing leads to greater anticipated costs of the new intervention and lower expected budgetary costs of the SoC, over the time horizon of interest. Accordingly, in this example, the budget impact is greater in the dynamic pricing scenario.
• Further stratification of the results, by intervention received, time period, cost component etc may reveal further insights. These are possible from the results calculated and presented by dynamicpv::dynpv() but not shown in this simple illustration.

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