Budget Impact Applications

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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)

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 $12,923,366 in respect of 522 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
#> Warning in addprod(e1, e2, mult = 1): Uptake vectors differ in length

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))
#> [1] 1044

# The uptake vector for the SoC is short, once trimmed of excess zeros
length(trim_vec(uptake_soc))
#> [1] 103

The budgetary costs in the world with the new intervention are $26,964,789, comprising $3,508,178 in respect of the costs of 103 patients being treated with the SoC, and $23,456,610 in respect of the costs of 419 patients being treated with the SoC.

# Budget impact
bi1_soc <- budget_with1_soc - budget_wout1_soc
#> Warning in addprod(e1, e2, mult = -1): Uptake vectors differ in length
bi1_new <- budget_with1_new
bi1 <- budget_with1 - budget_wout1

summary(bi1)
#> Summary of Dynamic Pricing and Uptake
#>      Number of cohorts:             261 
#>      Number of times:               1 
#>      Total uptake:                  0 
#>      Total present value:           14041423 
#>      Mean present value:            Inf

The total budget impact is $14,041,423, representing an increase of 109%.

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 $11,516,132 in respect of 522 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
#> Warning in addprod(e1, e2, mult = 1): Uptake vectors differ in length

Notice that there is a similar warning as earlier. The budgetary costs in the world with the new intervention are $28,535,724, comprising $3,460,107 in respect of the costs of 103 patients being treated with the SoC, and $25,075,617 in respect of the costs of 419 patients being treated with the new treatment.

# Budget impact
bi2_soc <- budget_with2_soc - budget_wout2_soc
#> Warning in addprod(e1, e2, mult = -1): Uptake vectors differ in length
bi2_new <- budget_with2_new
bi2 <- budget_with2 - budget_wout2

summary(bi2)
#> Summary of Dynamic Pricing and Uptake
#>      Number of cohorts:             261 
#>      Number of times:               1 
#>      Total uptake:                  0 
#>      Total present value:           17019592 
#>      Mean present value:            Inf

The total budget impact is $17,019,592, representing an increase of 148%.

Summary

Budget Impact model results with and without dynamic drug pricing
		Static drug pricing	Dynamic drug pricing
World without new intervention
	Standard of Care	12,923,366	11,516,132
	New intervention	0	0
	Total	12,923,366	11,516,132
World with new intervention
	Standard of Care	3,508,178	3,460,107
	New intervention	23,456,610	25,075,617
	Total	26,964,789	25,075,617
Budget impact
	Standard of Care	-9,415,187	-8,056,025
	New intervention	23,456,610	25,075,617
	Absolute impact	14,041,423	17,019,592
	Relative impact (%)	109%	148%

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 (5 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.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.