Title:	Evaluates Present Values and Health Economic Models with Dynamic Pricing and Uptake
Version:	0.4.1
Description:	The goal of 'dynamicpv' is to provide a simple way to calculate (net) present values and outputs from health economic models (especially cost-effectiveness and budget impact) in discrete time that reflect dynamic pricing and dynamic uptake. Dynamic pricing is also known as life cycle pricing; dynamic uptake is also known as multiple or stacked cohorts, or dynamic disease prevalence. Shafrin (2024) <doi:10.1515/fhep-2024-0014> provides an explanation of dynamic value elements, in the context of Generalized Cost Effectiveness Analysis, and Puls (2024) <doi:10.1016/j.jval.2024.03.006> reviews challenges of incorporating such dynamic value elements. This package aims to reduce those challenges.
License:	GPL (≥ 3)
URL:	https://MSDLLCpapers.github.io/dynamicpv/, https://github.com/MSDLLCpapers/dynamicpv
BugReports:	https://github.com/MSDLLCpapers/dynamicpv/issues
Encoding:	UTF-8
RoxygenNote:	7.3.3
Depends:	R (≥ 4.1.0)
Imports:	dplyr, readr, rlang, tidyr
Suggests:	flexsurv, ggplot2, heemod, knitr, lubridate, purrr, rmarkdown, scales, testthat (≥ 3.0.0), usethis
Config/testthat/edition:	3
LazyData:	true
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2026-01-10 23:19:25 UTC; dom
Author:	Dominic Muston [aut, cre], John Blischak [ctb], Merck & Co., Inc., Rahway, NJ, USA and its affiliates [cph, fnd]
Maintainer:	Dominic Muston <dominic.muston@msd.com>
Repository:	CRAN
Date/Publication:	2026-01-15 18:00:19 UTC

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

Description

The goal of 'dynamicpv' is to provide a simple way to calculate (net) present values and outputs from health economic models (especially cost-effectiveness and budget impact) in discrete time that reflect dynamic pricing and dynamic uptake. Dynamic pricing is also known as life cycle pricing; dynamic uptake is also known as multiple or stacked cohorts, or dynamic disease prevalence. Shafrin (2024) doi:10.1515/fhep-2024-0014 provides an explanation of dynamic value elements, in the context of Generalized Cost Effectiveness Analysis, and Puls (2024) doi:10.1016/j.jval.2024.03.006 reviews challenges of incorporating such dynamic value elements. This package aims to reduce those challenges.

Author(s)

Maintainer: Dominic Muston dominic.muston@msd.com (ORCID)

Other contributors:

• John Blischak (ORCID) [contributor]

• Merck & Co., Inc., Rahway, NJ, USA and its affiliates [copyright holder, funder]

See Also

Useful links:

• https://MSDLLCpapers.github.io/dynamicpv/

• https://github.com/MSDLLCpapers/dynamicpv

• Report bugs at https://github.com/MSDLLCpapers/dynamicpv/issues

Method to add two dynpv objects together

Description

Add together two objects each of class "dynpv"

Usage

## S3 method for class 'dynpv'
e1 + e2

Arguments

Value

S3 object of class "dynpv"

Method to subtract one dynpv object from another

Description

Subtract one object of S7 class "dynpv" from another

Usage

## S3 method for class 'dynpv'
e1 - e2

Arguments

Details

Present value of e1-e2 is the present values from e1 less that from e2. Total uptake of e1-e2 is the uptake from e1 less that from e2. Take care of this when using ⁠$mean⁠ of the summed object.

Value

S3 object of class "dynpv"

Method to add two dynpv objects together

Description

Add together two objects each of S3 class "dynpv": e1 + mult * e2

Usage

addprod(e1, e2, mult)

Arguments

Value

S3 object of class "dynpv"

See Also

dynpv(), futurepv()

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

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)

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

Description

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

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)

# 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
summary(fpv)

Helper function to get a tibble of the relevant fields from heemod output

Description

Helper function to get a tibble of the relevant fields from heemod output

Usage

get_dynfields(heemodel, payoffs, discount, fname = NA)

Arguments

Value

Tibble of payoffs taken from the heemod model, by intervention and model timestep (model_time).

The field vt is calculated as (1+i)^(1-model_time), where i is the discount rate per model timestep set in the heemod model through the parameter disc_cycle. This can be useful in 'rolling-up' payoff values to the timestep in which they were incurred.

An additional set of payoffs (identified with a "_rup" suffix) provides calculations of the payoffs as at the start of the timestep in which they were incurred, i.e. original payoff / vt.

See Also

heemod::heemod-package

Examples

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

Obtain parameter value(s) from a heemod output

Description

Obtain parameter value(s) from a heemod output

Usage

get_param_value(heemodel, param)

Arguments

Value

Value of the parameter from the heemod model

See Also

heemod::heemod-package

Examples

get_param_value(
   heemodel = oncpsm,
   param = "disc"
   )

Mean present value per uptaking patient

Description

Mean of the Present Value per uptaking patient, by time at which the calculation is performed (tzero input to dynpv()).

Usage

## S3 method for class 'dynpv'
mean(x, ...)

Arguments

Details

This is equal to total() divided by uptake().

Value

A number or tibble

See Also

dynpv(), futurepv()

Number of cohorts of uptaking patients

Description

Number of cohorts of uptaking patients, calculated as the length of the uptakes input to dynpv()

Usage

ncoh(df)

Arguments

Value

A number

See Also

dynpv(), futurepv()

Number of times at which present value calculations are performed

Description

Number of times at which present value calculations are performed, calculated as the length of the tzero input to dynpv()

Usage

ntimes(df)

Arguments

Value

A number

See Also

dynpv(), futurepv()

Heemod cost-effectiveness model example

Description

An example three state cost-effectiveness model in oncology built using heemod::heemod-package() according to the assumptions and specification in the accompanying paper.

Usage

oncpsm

Format

oncpsm

A heemod object

Source

Created based on assumptions.

Present value for each uptake cohort and calculation time

Description

Calculates the sum of the Present Value by uptake cohort (j) and time at which the calculation is performed (tzero input to dynpv())

Usage

sum_by_coh(df)

Arguments

Details

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.

This method returns \sum_{k=1}^{T-j+1} PV(j,k,l) for each value of j and l, where T is the time horizon of the calculation.

Value

A number or tibble

See Also

dynpv(), futurepv()

Summarize a dynpv object

Description

Summarize a dynpv object

Usage

## S3 method for class 'dynpv'
summary(object, ...)

Arguments

Value

A list of class "dynpv_summary" with the following elements:

• ncoh: Number of cohorts of uptaking patients, from ncoh()

• ntimes: Number of times at which present value calculations are performed, from ntimes()

• uptake: Total number of uptaking patients, from uptake()

• sum_by_coh: Present value for each uptake cohort and calculation time, from sum_by_coh()

• total: Total present value, from total()

• mean: Mean present value per uptaking patient, from mean(), equal to total/uptake.

See Also

dynpv(), futurepv()

Total present value

Description

Sum of the Present Value, by time at which the calculation is performed (tzero input to dynpv())

Usage

total(df)

Arguments

Details

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 by time at which the calculation is performed, TPV(l), is therefore the sum of PV(j,k,l) 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}

Value

A number or tibble

See Also

dynpv(), futurepv()

Trim the tailing zeroes from a long vector

Description

Trim the tailing zeroes from a long vector

Usage

trim_vec(vec)

Arguments

Value

A vector whose length is shorter than the original, if there were trailing zero elements

Examples

trim_vec(c(1:10, rep(0,3)))

Total number of uptaking patients

Description

Total number of uptaking patients, calculated as the sum of the uptake input to dynpv(), or \sum_{j=1}^T u_j

Usage

uptake(df)

Arguments

Value

A number or tibble

See Also

dynpv(), futurepv()