Package {EconEvalR}

Convert an EconBCR object to a data frame

Description

Convert an EconBCR object to a data frame

Usage

## S3 method for class 'EconBCR'
as.data.frame(x, ...)

Arguments

Value

A data frame with one row containing the benefit, cost, benefit-cost ratio, and decision.

Convert a Budget Impact Analysis Object to a Data Frame

Description

Converts an object of class "EconBIA" into a data frame suitable for exporting or further analysis.

Usage

## S3 method for class 'EconBIA'
as.data.frame(x, ...)

Arguments

Value

A data frame containing the annual budget impact results.

Examples

bia <- budget_impact_analysis(
  population = 10000,
  uptake = c(0.10, 0.20, 0.35, 0.45, 0.60),
  current_cost = 1200,
  new_cost = 1500,
  years = 5,
  discount = 0.03
)

df <- as.data.frame(bia)
head(df)

Convert a Cost-Effectiveness Acceptability Curve Object to a Data Frame

Description

Convert a Cost-Effectiveness Acceptability Curve Object to a Data Frame

Usage

## S3 method for class 'EconCEAC'
as.data.frame(x, ...)

Arguments

Value

A data frame containing the willingness-to-pay thresholds, probabilities of cost-effectiveness, and mean incremental net monetary benefit.

Convert a Cost-Effectiveness Acceptability Frontier Object to a Data Frame

Description

Converts an object of class "EconCEAF" into a data frame suitable for exporting or further analysis.

Usage

## S3 method for class 'EconCEAF'
as.data.frame(x, ...)

Arguments

Value

A data frame containing:

WTP

Willingness-to-pay threshold.

OptimalStrategy

Optimal strategy at each WTP.

Probability

Probability that the optimal strategy is cost-effective.

ExpectedNMB

Expected Net Monetary Benefit of the optimal strategy.

Examples

set.seed(123)

cost <- cbind(
  rnorm(100, 1000, 100),
  rnorm(100, 1200, 120),
  rnorm(100, 1400, 150)
)

effect <- cbind(
  rnorm(100, 0.70, 0.05),
  rnorm(100, 0.80, 0.05),
  rnorm(100, 0.90, 0.05)
)

ceaf <- cost_effectiveness_acceptability_frontier(
  cost = cost,
  effect = effect,
  wtp = c(0, 50000, 100000)
)

df <- as.data.frame(ceaf)
head(df)

Convert an Expected Value of Perfect Information Object to a Data Frame

Description

Converts an object of class "EconEVPI" into a data frame suitable for exporting or further analysis.

Usage

## S3 method for class 'EconEVPI'
as.data.frame(x, ...)

Arguments

Value

A data frame containing:

WTP

Willingness-to-pay threshold.

EVPI

Expected Value of Perfect Information.

ExpectedPerfectInformation

Expected value under perfect information, E[\max(NMB)].

ExpectedCurrentInformation

Expected value under current information, \max(E[NMB]).

Examples

set.seed(123)

cost <- cbind(
  rnorm(100, 1000, 100),
  rnorm(100, 1200, 120),
  rnorm(100, 1500, 140)
)

effect <- cbind(
  rnorm(100, 0.70, 0.05),
  rnorm(100, 0.82, 0.05),
  rnorm(100, 0.92, 0.05)
)

evpi <- expected_value_perfect_information(
  cost = cost,
  effect = effect,
  wtp = c(0, 50000, 100000)
)

df <- as.data.frame(evpi)
head(df)

Convert an Expected Value of Partial Perfect Information Object to a Data Frame

Description

Convert an Expected Value of Partial Perfect Information Object to a Data Frame

Usage

## S3 method for class 'EconEVPPI'
as.data.frame(x, ...)

Arguments

Value

A data frame.

Convert a Probabilistic Sensitivity Analysis Object to a Data Frame

Description

Convert a Probabilistic Sensitivity Analysis Object to a Data Frame

Usage

## S3 method for class 'EconPSA'
as.data.frame(x, ...)

Arguments

Value

A data frame containing every Monte Carlo simulation.

Convert a Tornado Diagram Object to a Data Frame

Description

Convert a Tornado Diagram Object to a Data Frame

Usage

## S3 method for class 'EconTornado'
as.data.frame(x, ...)

Arguments

Value

A data frame.

Convert a Decision Tree Analysis Object to a Data Frame

Description

Converts an object of class "EconTree" into a data frame suitable for exporting or further analysis.

Usage

## S3 method for class 'EconTree'
as.data.frame(x, ...)

Arguments

Value

A data frame containing the terminal node results.

Examples

strategy <- c(
  "Treatment A",
  "Treatment B",
  "Treatment C"
)

probability <- c(0.30, 0.45, 0.25)
cost <- c(1200, 1800, 2400)
effectiveness <- c(0.70, 0.82, 0.91)

tree <- decision_tree_analysis(
  strategy,
  probability,
  cost,
  effectiveness
)

df <- as.data.frame(tree)
head(df)

Benefit-Cost Ratio

Description

Computes the Benefit-Cost Ratio (BCR) for an investment, intervention, or project.

Usage

benefit_cost_ratio(benefit, cost)

Arguments

Details

The Benefit-Cost Ratio is calculated as

BCR = \frac{Benefit}{Cost}

Value

An object of class "EconBCR".

Examples

benefit_cost_ratio(
  benefit = 150000,
  cost = 100000
)

Budget Impact Analysis

Description

Performs a Budget Impact Analysis (BIA) by comparing the projected healthcare expenditure under current practice with a new intervention over multiple years.

Usage

budget_impact_analysis(
  population,
  uptake,
  current_cost,
  new_cost,
  years = length(uptake),
  discount = 0
)

Arguments

Details

The function calculates, for each year:

• Eligible population

• Number treated

• Current budget

• New budget

• Incremental budget impact

• Discounted budget impact

• Cumulative discounted impact

Value

An object of class "EconBIA".

Examples

bia <- budget_impact_analysis(
    population = 10000,
    uptake = c(0.10,0.20,0.35,0.45,0.60),
    current_cost = 1200,
    new_cost = 1500,
    years = 5,
    discount = 0.03
)

print(bia)
summary(bia)
plot(bia)
as.data.frame(bia)

Cost Effectiveness Analysis

Description

Performs a cost-effectiveness analysis (CEA) for two or more competing strategies by comparing their costs and effectiveness.

Usage

cost_effectiveness(strategy, cost, effectiveness)

Arguments

Details

Cost-effectiveness analysis (CEA) compares alternative interventions in terms of their costs and effectiveness. It provides the basis for identifying efficient interventions and supports subsequent analyses such as Incremental Cost-Effectiveness Ratio (ICER), dominance analysis, cost-effectiveness acceptability curves (CEAC), and expected value of information analyses.

This function summarizes the observed costs and effectiveness for each strategy to facilitate economic evaluation and decision making.

Value

An object of class "EconCEA".

References

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Briggs AH, Claxton K, Sculpher MJ (2006). Decision Modelling for Health Economic Evaluation. Oxford University Press.

Sanders GD, Neumann PJ, Basu A, Brock DW, Feeny D, Krahn M, Kuntz KM, Meltzer DO, Owens DK, Prosser LA, Salomon JA, Sculpher MJ, Trikalinos TA, Russell LB, Siegel JE, Ganiats TG (2016). Recommendations for Conduct, Methodological Practices, and Reporting of Cost-effectiveness Analyses. JAMA, 316(10), 1093–1103. doi:10.1001/jama.2016.12195

Examples

cea <- cost_effectiveness(
  strategy = c("Current", "Treatment A", "Treatment B"),
  cost = c(1000, 1300, 1700),
  effectiveness = c(0.60, 0.75, 0.90)
)

print(cea)
summary(cea)
plot(cea)
as.data.frame(cea)

Cost-Effectiveness Acceptability Curve

Description

Computes the Cost-Effectiveness Acceptability Curve (CEAC) using probabilistic sensitivity analysis (PSA) results across a range of willingness-to-pay (WTP) thresholds.

Usage

cost_effectiveness_acceptability_curve(
  incremental_cost,
  incremental_effect,
  wtp = seq(0, 1e+05, by = 1000)
)

Arguments

Details

The Cost-Effectiveness Acceptability Curve (CEAC) summarizes the probability that an intervention is cost-effective for different willingness-to-pay (WTP) thresholds.

The Incremental Net Monetary Benefit (INMB) is calculated as

INMB = \lambda \times \Delta E - \Delta C

where

• \lambda = Willingness-to-pay threshold.

• \Delta E = Incremental effectiveness.

• \Delta C = Incremental cost.

The CEAC is obtained by calculating the proportion of probabilistic sensitivity analysis simulations for which the Incremental Net Monetary Benefit is positive (INMB > 0) at each willingness-to-pay threshold.

CEACs provide a graphical summary of decision uncertainty and are widely used in health economic evaluation.

Value

An object of class "EconCEAC".

References

Fenwick E, Claxton K, Sculpher M (2001). Representing Uncertainty: The Role of Cost-Effectiveness Acceptability Curves. Health Economics, 10(8), 779–787. doi:10.1002/hec.635

Briggs AH, Claxton K, Sculpher MJ (2006). Decision Modelling for Health Economic Evaluation. Oxford University Press.

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Examples

set.seed(1)

cost <- rnorm(1000, 500, 100)

effect <- rnorm(1000, 0.35, 0.08)

ceac <- cost_effectiveness_acceptability_curve(
  incremental_cost = cost,
  incremental_effect = effect,
  wtp = seq(0, 5000, 100)
)

print(ceac)
summary(ceac)
plot(ceac)
as.data.frame(ceac)

Cost-Effectiveness Acceptability Frontier

Description

Computes the Cost-Effectiveness Acceptability Frontier (CEAF) for multiple competing strategies using probabilistic sensitivity analysis (PSA) results.

Usage

cost_effectiveness_acceptability_frontier(
  cost,
  effect,
  wtp = seq(0, 1e+05, by = 1000)
)

Arguments

Details

The Cost-Effectiveness Acceptability Frontier (CEAF) identifies the strategy with the highest expected Net Monetary Benefit (NMB) at each willingness-to-pay (WTP) threshold and estimates the probability that this strategy is cost-effective.

Net Monetary Benefit (NMB) is calculated as

NMB = \lambda \times Effect - Cost

where

• \lambda = Willingness-to-pay threshold.

For each willingness-to-pay threshold:

• Expected Net Monetary Benefit is calculated for each strategy.

• The strategy with the highest expected Net Monetary Benefit is identified.

• The probability that this optimal strategy is cost-effective is estimated.

Unlike the Cost-Effectiveness Acceptability Curve (CEAC), the CEAF focuses on the strategy with the highest expected Net Monetary Benefit and therefore identifies the optimal decision across willingness-to-pay thresholds.

Value

An object of class "EconCEAF".

References

Fenwick E, Claxton K, Sculpher M (2001). Representing Uncertainty: The Role of Cost-Effectiveness Acceptability Curves. Health Economics, 10(8), 779–787. doi:10.1002/hec.635

Fenwick E, Claxton K, Briggs A (2001). Cost-Effectiveness Acceptability Curves. Health Economics, 10(8), 779–787.

Briggs AH, Claxton K, Sculpher MJ (2006). Decision Modelling for Health Economic Evaluation. Oxford University Press.

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Examples

set.seed(123)

cost <- cbind(
  rnorm(1000, 1000, 100),
  rnorm(1000, 1200, 120),
  rnorm(1000, 1400, 150)
)

effect <- cbind(
  rnorm(1000, 0.70, 0.05),
  rnorm(1000, 0.80, 0.05),
  rnorm(1000, 0.90, 0.05)
)

ceaf <- cost_effectiveness_acceptability_frontier(
  cost = cost,
  effect = effect
)

print(ceaf)
summary(ceaf)
plot(ceaf)
as.data.frame(ceaf)

Decision Tree Analysis

Description

Performs a decision tree analysis by calculating the expected cost and expected effectiveness for terminal decision pathways based on their probabilities.

Usage

decision_tree_analysis(strategy, probability, cost, effectiveness)

Arguments

Details

Decision tree analysis is a standard decision-analytic technique used to evaluate alternative interventions under uncertainty by combining probabilities with associated costs and health outcomes.

Expected values are calculated as

Expected\ Cost = Probability \times Cost

and

Expected\ Effectiveness = Probability \times Effectiveness

The expected values for each terminal strategy can be compared to support evidence-based decision making and economic evaluation.

Value

An object of class "EconTree".

References

Briggs AH, Claxton K, Sculpher MJ (2006). Decision Modelling for Health Economic Evaluation. Oxford University Press.

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Sonnenberg FA, Beck JR (1993). Markov Models in Medical Decision Making: A Practical Guide. Medical Decision Making, 13(4), 322–338. doi:10.1177/0272989X9301300409

Examples

strategy <- c(
  "Treatment A",
  "Treatment B",
  "Treatment C"
)

probability <- c(
  0.30,
  0.45,
  0.25
)

cost <- c(
  1200,
  1800,
  2400
)

effectiveness <- c(
  0.70,
  0.82,
  0.91
)

tree <- decision_tree_analysis(
  strategy,
  probability,
  cost,
  effectiveness
)

print(tree)
summary(tree)
plot(tree)
as.data.frame(tree)

Discount Cash Flows

Description

Discounts one or more future cash flows to their present values using a specified discount rate.

Usage

discount_cashflow(cashflow, rate, period)

Arguments

Details

Discounted cash flow (DCF) analysis converts future cash flows into their present values by accounting for the time value of money.

The present value of each cash flow is calculated as

PV = \frac{CF_t}{(1+r)^t}

where

• CF_t = Cash flow at time period t.

• r = Discount rate.

• t = Time period.

Discounting is widely used in economic evaluation, investment appraisal, and cost-benefit analysis to compare costs and benefits occurring at different points in time.

Value

An object of class "EconDCF".

References

Boardman AE, Greenberg DH, Vining AR, Weimer DL (2018). Cost-Benefit Analysis: Concepts and Practice. 5th ed. Cambridge University Press.

Brealey RA, Myers SC, Allen F (2020). Principles of Corporate Finance. 13th ed. McGraw-Hill Education.

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Examples

discount_cashflow(
  cashflow = c(1000, 1200, 1500),
  rate = 0.10,
  period = 1:3
)

Discounted Payback Period

Description

Calculates the discounted payback period of an investment by accounting for the time value of money.

Usage

discounted_payback_period(cashflow, rate)

Arguments

Details

The discounted payback period is the time required for the cumulative discounted cash inflows to recover the initial investment. Each future cash flow is first converted to its present value using the specified discount rate.

The present value of each cash flow is calculated as

PV = \frac{CF_t}{(1+r)^t}

where

• CF_t = Cash flow at time period t.

• r = Discount rate.

• t = Time period.

When the investment is recovered during a period, linear interpolation is used to estimate the fractional discounted payback period.

Unlike the conventional payback period, the discounted payback period accounts for the time value of money, although it does not consider cash flows occurring after the investment has been recovered.

Value

An object of class "EconDiscountedPayback".

References

Boardman AE, Greenberg DH, Vining AR, Weimer DL (2018). Cost-Benefit Analysis: Concepts and Practice. 5th ed. Cambridge University Press.

Brealey RA, Myers SC, Allen F (2020). Principles of Corporate Finance. 13th ed. McGraw-Hill Education.

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Examples

dpb <- discounted_payback_period(
  cashflow = c(-50000, 12000, 15000, 18000, 20000),
  rate = 0.10
)

print(dpb)

Dominance Analysis

Description

Identifies strongly dominated strategies based on their costs and effectiveness.

Usage

dominance_analysis(strategy, cost, effectiveness)

Arguments

Details

Dominance analysis is used in cost-effectiveness analysis to identify strategies that are economically inefficient.

A strategy is considered strongly dominated if another strategy has both a lower cost and an equal or greater level of effectiveness.

Strongly dominated strategies are excluded from further economic evaluation because they are always less efficient than at least one competing strategy.

Value

An object of class "EconDominance".

References

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Briggs AH, Claxton K, Sculpher MJ (2006). Decision Modelling for Health Economic Evaluation. Oxford University Press.

Fenwick E, Claxton K, Sculpher M (2001). Representing uncertainty: the role of cost-effectiveness acceptability curves. Health Economics, 10(8), 779–787. doi:10.1002/hec.635

Examples

dominance_analysis(
  strategy = c("A", "B", "C"),
  cost = c(1000, 1200, 900),
  effectiveness = c(0.70, 0.75, 0.80)
)

Expected Value of Partial Perfect Information

Description

Computes the Expected Value of Partial Perfect Information (EVPPI) using a regression-based approximation.

Usage

expected_value_partial_perfect_information(
  cost,
  effect,
  parameter,
  wtp = seq(0, 1e+05, by = 1000),
  method = "gam"
)

Arguments

Details

The Expected Value of Partial Perfect Information (EVPPI) quantifies the expected value of eliminating uncertainty in a subset of model parameters while uncertainty in all remaining parameters is retained.

This implementation estimates EVPPI using a regression- based approximation in which Net Monetary Benefit (NMB) is regressed on the parameter of interest. The conditional expectation of NMB is estimated using Generalized Additive Models implemented in mgcv::gam().

Regression-based EVPPI methods provide an efficient approximation that avoids computationally intensive nested Monte Carlo simulation.

Value

An object of class "EconEVPPI".

References

Strong M, Oakley JE, Brennan A (2014). Estimating Multiparameter Partial Expected Value of Perfect Information from a Probabilistic Sensitivity Analysis Sample: A Nonparametric Regression Approach. Medical Decision Making, 34(3), 311–326. doi:10.1177/0272989X13505910

Briggs AH, Claxton K, Sculpher MJ (2006). Decision Modelling for Health Economic Evaluation. Oxford University Press.

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Examples

library(mgcv)

set.seed(123)

cost <- cbind(
  rnorm(1000,1000,100),
  rnorm(1000,1200,100)
)

effect <- cbind(
  rnorm(1000,0.70,0.05),
  rnorm(1000,0.82,0.05)
)

theta <- runif(1000)

evppi <- expected_value_partial_perfect_information(
    cost = cost,
    effect = effect,
    parameter = theta
)

Expected Value of Perfect Information

Description

Computes the Expected Value of Perfect Information (EVPI) across a range of willingness-to-pay (WTP) thresholds using probabilistic sensitivity analysis (PSA) results.

Usage

expected_value_perfect_information(
  cost,
  effect,
  wtp = seq(0, 1e+05, by = 1000)
)

Arguments

Details

The Expected Value of Perfect Information (EVPI) quantifies the expected value of eliminating all uncertainty in a decision problem. It represents the maximum amount a decision maker should be willing to pay for perfect information before selecting an intervention.

Net Monetary Benefit (NMB) is calculated as

NMB = \lambda \times Effect - Cost

where

• \lambda = Willingness-to-pay threshold.

EVPI is calculated as

EVPI = E[\max(NMB)] - \max(E[NMB])

where

• E[\max(NMB)] is the expected value under perfect information.

• \max(E[NMB]) is the maximum expected value under current information.

EVPI provides an upper bound on the value of acquiring additional information and is widely used to prioritize future research.

Value

An object of class "EconEVPI".

References

Claxton K (1999). The Irrelevance of Inference: A Decision-Making Approach to the Stochastic Evaluation of Health Care Technologies. Journal of Health Economics, 18(3), 341–364. doi:10.1016/S0167-6296(98)00039-3

Briggs AH, Claxton K, Sculpher MJ (2006). Decision Modelling for Health Economic Evaluation. Oxford University Press.

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Examples

set.seed(123)

cost <- cbind(
  rnorm(1000, 1000, 100),
  rnorm(1000, 1200, 120),
  rnorm(1000, 1500, 140)
)

effect <- cbind(
  rnorm(1000, 0.70, 0.05),
  rnorm(1000, 0.82, 0.05),
  rnorm(1000, 0.92, 0.05)
)

evpi <- expected_value_perfect_information(
  cost = cost,
  effect = effect
)

print(evpi)

Incremental Cost-Effectiveness Ratio

Description

Calculates the Incremental Cost-Effectiveness Ratio (ICER) between competing interventions based on differences in costs and effectiveness.

Usage

icer(cost, effectiveness)

Arguments

Details

The Incremental Cost-Effectiveness Ratio (ICER) is calculated as:

ICER = \frac{\Delta Cost}{\Delta Effectiveness}

where:

• Delta Cost = Difference in cost between interventions.

• Delta Effectiveness = Difference in effectiveness between interventions.

ICER represents the additional cost required to gain one additional unit of effectiveness when moving from one intervention to another.

Value

An object of class "EconICER".

References

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Briggs AH, Claxton K, Sculpher MJ (2006). Decision Modelling for Health Economic Evaluation. Oxford University Press.

Sanders GD, Neumann PJ, Basu A, Brock DW, Feeny D, Krahn M, Kuntz KM, Meltzer DO, Owens DK, Prosser LA, Salomon JA, Sculpher MJ, Trikalinos TA, Russell LB, Siegel JE, Ganiats TG (2016). Recommendations for Conduct, Methodological Practices, and Reporting of Cost-effectiveness Analyses. JAMA, 316(10), 1093–1103. doi:10.1001/jama.2016.12195

Examples

icer(
  cost = c(1000, 1300, 1700),
  effectiveness = c(0.60, 0.75, 0.90)
)

Internal Rate of Return

Description

Calculates the Internal Rate of Return (IRR) for a series of cash flows.

Usage

internal_rate_return(cashflow, interval = c(-0.99, 10), tol = 1e-08)

Arguments

Details

The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) of a series of cash flows equal to zero.

The IRR is obtained by solving

\sum_{t=0}^{n}\frac{CF_t}{(1+r)^t}=0

where:

• CF_t = Cash flow at time t.

• r = Internal Rate of Return.

• n = Number of time periods.

The solution is obtained numerically using stats::uniroot().

Value

An object of class "EconIRR".

References

Boardman AE, Greenberg DH, Vining AR, Weimer DL (2018). Cost-Benefit Analysis: Concepts and Practice. 5th ed. Cambridge University Press.

Brealey RA, Myers SC, Allen F (2020). Principles of Corporate Finance. 13th ed. McGraw-Hill Education.

Examples

internal_rate_return(
  cashflow = c(-10000, 3000, 3500, 4000, 4500)
)

Modified Internal Rate of Return

Description

Calculates the Modified Internal Rate of Return (MIRR) for a series of cash flows.

Usage

modified_internal_rate_return(cashflow, finance_rate, reinvest_rate)

Arguments

Details

The Modified Internal Rate of Return (MIRR) addresses limitations of the traditional Internal Rate of Return (IRR) by assuming that positive cash flows are reinvested at a specified reinvestment rate and negative cash flows are financed at a specified finance rate.

MIRR is calculated as

MIRR = \left( \frac{FV_{\mathrm{positive}}} {-PV_{\mathrm{negative}}} \right)^{1/n}-1

where

• FV_{\mathrm{positive}} = Future value of all positive cash flows compounded at the reinvestment rate.

• PV_{\mathrm{negative}} = Present value of all negative cash flows discounted at the finance rate.

• n = Number of compounding periods.

MIRR provides a unique rate of return and is generally preferred over the traditional IRR when multiple sign changes occur in the cash-flow stream.

Value

An object of class "EconMIRR".

References

Brealey RA, Myers SC, Allen F (2020). Principles of Corporate Finance. 13th ed. McGraw-Hill Education.

Boardman AE, Greenberg DH, Vining AR, Weimer DL (2018). Cost-Benefit Analysis: Concepts and Practice. 5th ed. Cambridge University Press.

Examples

mirr <- modified_internal_rate_return(
  cashflow = c(-50000, 12000, 15000, 18000, 20000),
  finance_rate = 0.08,
  reinvest_rate = 0.10
)

print(mirr)

Multi-Way Sensitivity Analysis

Description

Performs deterministic multi-way sensitivity analysis by simultaneously varying two or more model parameters and evaluating the resulting changes in the model outcome.

Usage

multi_way_sensitivity_analysis(parameters, model)

Arguments

Details

Multi-way sensitivity analysis is a deterministic sensitivity analysis in which two or more parameters are varied simultaneously to evaluate the robustness of model results to plausible changes in model inputs. It is commonly used to investigate interactions among uncertain parameters and to identify combinations of values that substantially influence decision outcomes.

Value

An object of class "EconMWSA".

References

Briggs AH, Claxton K, Sculpher MJ (2006). Decision Modelling for Health Economic Evaluation. Oxford University Press.

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Briggs AH, Weinstein MC, Fenwick EAL, Karnon J, Sculpher MJ, Paltiel AD (2012). Model parameter estimation and uncertainty: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force Working Group-6. Medical Decision Making, 32(5), 722–732. doi:10.1177/0272989X12458348

Examples

pars <- data.frame(
  Cost = c(1000, 1200, 1400),
  Effectiveness = c(0.70, 0.75, 0.82),
  Probability = c(0.90, 0.85, 0.80)
)

model <- function(x) {
  x$Effectiveness * 5000 -
    x$Cost * x$Probability
}

mw <- multi_way_sensitivity_analysis(
  parameters = pars,
  model = model
)

print(mw)

Net Health Benefit

Description

Calculates the Net Health Benefit (NHB) for one or more competing interventions using a specified willingness-to-pay threshold.

Usage

net_health_benefit(strategy, cost, effectiveness, willingness_to_pay)

Arguments

Details

Net Health Benefit (NHB) is calculated as

NHB = E - \frac{C}{\lambda}

where

• E = Effectiveness.

• C = Cost.

• \lambda = Willingness-to-pay threshold.

NHB expresses health outcomes in natural units after accounting for the opportunity cost of resources. A strategy with the highest NHB at a given willingness-to-pay threshold is considered the preferred option.

Value

An object of class "EconNHB".

References

Stinnett AA, Mullahy J (1998). Net Health Benefits: A New Framework for the Analysis of Uncertainty in Cost-Effectiveness Analysis. Medical Decision Making, 18(2 Suppl), S68–S80. doi:10.1177/0272989X98018002S09

Briggs AH, Claxton K, Sculpher MJ (2006). Decision Modelling for Health Economic Evaluation. Oxford University Press.

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Examples

nhb <- net_health_benefit(
  strategy = c("Current", "Treatment A", "Treatment B"),
  cost = c(1000, 1300, 1700),
  effectiveness = c(0.60, 0.75, 0.90),
  willingness_to_pay = 5000
)

print(nhb)

Net Monetary Benefit

Description

Calculates the Net Monetary Benefit (NMB) for one or more competing interventions using a specified willingness-to-pay threshold.

Usage

net_monetary_benefit(strategy, cost, effectiveness, willingness_to_pay)

Arguments

Details

Net Monetary Benefit (NMB) is calculated as

NMB = \lambda \times E - C

where

• \lambda = Willingness-to-pay threshold.

• E = Effectiveness.

• C = Cost.

Net Monetary Benefit converts health outcomes into monetary units using a specified willingness-to-pay threshold. Compared with the Incremental Cost-Effectiveness Ratio (ICER), the NMB framework facilitates statistical analysis and probabilistic sensitivity analysis. The strategy with the highest NMB at a given willingness-to-pay threshold is considered the preferred option.

Value

An object of class "EconNMB".

References

Stinnett AA, Mullahy J (1998). Net Health Benefits: A New Framework for the Analysis of Uncertainty in Cost-Effectiveness Analysis. Medical Decision Making, 18(Suppl. 2), S68–S80. doi:10.1177/0272989X98018002S09

Briggs AH, Claxton K, Sculpher MJ (2006). Decision Modelling for Health Economic Evaluation. Oxford University Press.

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Examples

nmb <- net_monetary_benefit(
  strategy = c("Current", "Treatment A", "Treatment B"),
  cost = c(1000, 1300, 1700),
  effectiveness = c(0.60, 0.75, 0.90),
  willingness_to_pay = 5000
)

print(nmb)

Net Present Value

Description

Calculates the Net Present Value (NPV) of a project.

Usage

net_present_value(cashflow, rate)

Arguments

Value

An object of class "EconNPV".

One-Way Sensitivity Analysis

Description

Performs deterministic one-way sensitivity analysis by varying a single model parameter while holding all other parameters constant.

Usage

one_way_sensitivity_analysis(base_case, low, high, model)

Arguments

Details

One-way sensitivity analysis is a deterministic sensitivity analysis in which one parameter is varied across a specified range while all other model inputs remain fixed at their base-case values. This approach is commonly used to evaluate the influence of individual parameters on model outcomes and to identify key drivers of decision uncertainty.

Value

An object of class "EconOWSA".

References

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Briggs AH, Claxton K, Sculpher MJ (2006). Decision Modelling for Health Economic Evaluation. Oxford University Press.

Briggs AH, Weinstein MC, Fenwick EAL, Karnon J, Sculpher MJ, Paltiel AD (2012). Model parameter estimation and uncertainty: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force Working Group-6. Medical Decision Making, 32(5), 722–732. doi:10.1177/0272989X12458348

Examples

model <- function(x) {
  5000 * x - 1000
}

ow <- one_way_sensitivity_analysis(
  base_case = 0.80,
  low = 0.60,
  high = 1.00,
  model = model
)

print(ow)

Partial Budget Analysis

Description

Performs a partial budget analysis to evaluate the economic consequences of a proposed change in management, production, or intervention.

Usage

partial_budget(added_returns, reduced_costs, added_costs, reduced_returns)

Arguments

Details

Partial budgeting evaluates the economic impact of a proposed change by considering only those costs and returns that differ between the current and proposed situations.

Net change is calculated as

(Added\ Returns + Reduced\ Costs) - (Added\ Costs + Reduced\ Returns)

A positive net change indicates that the proposed change is expected to improve profitability, whereas a negative value indicates an economic loss.

Value

An object of class "EconPB".

References

Kay RD, Edwards WM, Duffy PA (2016). Farm Management. 8th ed. McGraw-Hill Education.

Boardman AE, Greenberg DH, Vining AR, Weimer DL (2018). Cost-Benefit Analysis: Concepts and Practice. 5th ed. Cambridge University Press.

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Examples

partial_budget(
  added_returns = c(5000, 2500),
  reduced_costs = c(1500, 500),
  added_costs = c(2000, 1000),
  reduced_returns = c(500)
)

Payback Period

Description

Calculates the payback period of an investment based on a series of cash flows.

Usage

payback_period(cashflow)

Arguments

Details

The payback period is the time required for cumulative cash inflows to recover the initial investment. When the investment is recovered during a period, linear interpolation is used to estimate the fractional payback period.

The payback period is calculated as

Payback = t + \frac{Remaining\ Investment} {Cash\ Flow_{t+1}}

where

• t = Last period before full recovery.

• Remaining Investment = Unrecovered investment at the end of period t.

• Cash\ Flow_{t+1} = Cash inflow during the recovery period.

The payback period is widely used as a measure of investment liquidity but does not account for the time value of money or cash flows occurring after recovery.

Value

An object of class "EconPayback".

References

Boardman AE, Greenberg DH, Vining AR, Weimer DL (2018). Cost-Benefit Analysis: Concepts and Practice. 5th ed. Cambridge University Press.

Brealey RA, Myers SC, Allen F (2020). Principles of Corporate Finance. 13th ed. McGraw-Hill Education.

Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW (2015). Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Examples

pb <- payback_period(
  cashflow = c(-50000, 12000, 15000, 18000, 20000)
)

print(pb)

Plot Benefit-Cost Ratio Results

Description

Produces a bar chart comparing total benefits and total costs.

Usage

## S3 method for class 'EconBCR'
plot(x, ...)

Arguments

Value

Invisibly returns the midpoints of the bars.

Examples

x <- benefit_cost_ratio(
  benefit = 150000,
  cost = 100000
)

plot(x)

Plot Budget Impact Analysis

Description

Produces a visualization of the annual incremental budget impact and cumulative budget impact over time.

Usage

## S3 method for class 'EconBIA'
plot(x, type = c("annual", "cumulative"), ...)

Arguments

Value

Produces a budget impact plot.

Examples

bia <- budget_impact_analysis(
  population = 10000,
  uptake = c(0.10, 0.20, 0.35, 0.45, 0.60),
  current_cost = 1200,
  new_cost = 1500,
  years = 5,
  discount = 0.03
)

plot(bia)
plot(bia, type = "cumulative")

Plot Cost-Effectiveness Plane

Description

Plot Cost-Effectiveness Plane

Usage

## S3 method for class 'EconCEA'
plot(x, ...)

Arguments

Value

A Cost-Effectiveness Plane.

Plot Cost-Effectiveness Acceptability Curve

Description

Produces a Cost-Effectiveness Acceptability Curve (CEAC) showing the probability that an intervention is cost-effective over a range of willingness-to-pay (WTP) thresholds.

Usage

## S3 method for class 'EconCEAC'
plot(x, ...)

Arguments

Value

Produces a CEAC plot.

Plot Cost-Effectiveness Acceptability Frontier

Description

Produces a Cost-Effectiveness Acceptability Frontier (CEAF) showing the probability that the optimal strategy is cost-effective over a range of willingness-to-pay (WTP) thresholds.

Usage

## S3 method for class 'EconCEAF'
plot(x, ...)

Arguments

Value

Produces a CEAF plot.

Examples

set.seed(123)

cost <- cbind(
  rnorm(100, 1000, 100),
  rnorm(100, 1200, 120),
  rnorm(100, 1400, 150)
)

effect <- cbind(
  rnorm(100, 0.70, 0.05),
  rnorm(100, 0.80, 0.05),
  rnorm(100, 0.90, 0.05)
)

ceaf <- cost_effectiveness_acceptability_frontier(
  cost = cost,
  effect = effect,
  wtp = c(0, 50000, 100000)
)

plot(ceaf)

Plot Expected Value of Perfect Information

Description

Produces an Expected Value of Perfect Information (EVPI) curve across willingness-to-pay (WTP) thresholds.

Usage

## S3 method for class 'EconEVPI'
plot(x, ...)

Arguments

Value

Produces an EVPI plot.

Examples

set.seed(123)

cost <- cbind(
  rnorm(100, 1000, 100),
  rnorm(100, 1200, 120),
  rnorm(100, 1500, 140)
)

effect <- cbind(
  rnorm(100, 0.70, 0.05),
  rnorm(100, 0.82, 0.05),
  rnorm(100, 0.92, 0.05)
)

evpi <- expected_value_perfect_information(
  cost = cost,
  effect = effect,
  wtp = c(0, 50000, 100000)
)

plot(evpi)

Plot Expected Value of Partial Perfect Information

Description

Produces an Expected Value of Partial Perfect Information (EVPPI) curve across willingness-to-pay (WTP) thresholds.

Usage

## S3 method for class 'EconEVPPI'
plot(x, ...)

Arguments

Value

Produces an EVPPI plot.

Examples

evppi <- list(
  wtp = c(0, 50000, 100000),
  evppi = c(0, 125, 250)
)
class(evppi) <- "EconEVPPI"

plot(evppi)

Plot Multi-Way Sensitivity Analysis

Description

Plot Multi-Way Sensitivity Analysis

Usage

## S3 method for class 'EconMWSA'
plot(x, ...)

Arguments

Value

Produces a line plot of model outcomes.

Plot Probabilistic Sensitivity Analysis

Description

Displays the distribution of simulated outcomes.

Usage

## S3 method for class 'EconPSA'
plot(x, ...)

Arguments

Value

Produces a histogram with density curve.

Plot Threshold Analysis

Description

Plot Threshold Analysis

Usage

## S3 method for class 'EconThreshold'
plot(x, ...)

Arguments

Value

Produces a threshold analysis plot.

Plot Tornado Diagram

Description

Creates a tornado diagram for an object of class "EconTornado", showing the low and high outcome values for each parameter relative to the base-case value.

Usage

## S3 method for class 'EconTornado'
plot(x, ...)

Arguments

Value

Invisibly returns the supplied "EconTornado" object.

Plot Decision Tree Analysis Results

Description

Produces a bar plot of expected costs or expected effectiveness for each terminal strategy.

Usage

## S3 method for class 'EconTree'
plot(x, type = c("cost", "effectiveness"), ...)

Arguments

Value

Produces a bar plot.

Examples

strategy <- c(
  "Treatment A",
  "Treatment B",
  "Treatment C"
)

probability <- c(0.30, 0.45, 0.25)
cost <- c(1200, 1800, 2400)
effectiveness <- c(0.70, 0.82, 0.91)

tree <- decision_tree_analysis(
  strategy,
  probability,
  cost,
  effectiveness
)

plot(tree)
plot(tree, type = "effectiveness")

Present Value

Description

Calculates the present value of one or more future cash flows.

Usage

present_value(future_value, rate, period)

Arguments

Details

Present value is calculated as

PV=\frac{FV}{(1+r)^t}

where

• FV = Future Value

• r = Discount rate

• t = Time period

Value

An object of class "EconPV".

Examples

pv <- present_value(
    future_value = c(1000,1500,2000),
    rate = 0.10,
    period = 1:3
)

print(pv)

Print an EconBCR object

Description

Print an EconBCR object

Usage

## S3 method for class 'EconBCR'
print(x, ...)

Arguments

Value

Invisibly returns the object.

Print a Budget Impact Analysis Object

Description

Print a Budget Impact Analysis Object

Usage

## S3 method for class 'EconBIA'
print(x, ...)

Arguments

Value

The input object, invisibly.

Print a Cost-Effectiveness Acceptability Curve Object

Description

Print a Cost-Effectiveness Acceptability Curve Object

Usage

## S3 method for class 'EconCEAC'
print(x, ...)

Arguments

Value

The input object, invisibly.

Print a Cost-Effectiveness Acceptability Frontier Object

Description

Print a Cost-Effectiveness Acceptability Frontier Object

Usage

## S3 method for class 'EconCEAF'
print(x, ...)

Arguments

Value

The input object, invisibly.

Print an Expected Value of Perfect Information Object

Description

Print an Expected Value of Perfect Information Object

Usage

## S3 method for class 'EconEVPI'
print(x, ...)

Arguments

Value

The input object, invisibly.

Print an Expected Value of Partial Perfect Information Object

Description

Print an Expected Value of Partial Perfect Information Object

Usage

## S3 method for class 'EconEVPPI'
print(x, ...)

Arguments

Value

The input object, invisibly.

Print a Probabilistic Sensitivity Analysis Object

Description

Print a Probabilistic Sensitivity Analysis Object

Usage

## S3 method for class 'EconPSA'
print(x, ...)

Arguments

Value

The input object, invisibly.

Print a Tornado Diagram Object

Description

Print a Tornado Diagram Object

Usage

## S3 method for class 'EconTornado'
print(x, ...)

Arguments

Value

The input object, invisibly.

Print a Decision Tree Analysis Object

Description

Print a Decision Tree Analysis Object

Usage

## S3 method for class 'EconTree'
print(x, ...)

Arguments

Value

The input object, invisibly.

Probabilistic Sensitivity Analysis

Description

Performs Monte Carlo simulation for economic evaluation.

Usage

probabilistic_sensitivity_analysis(n = 1000, sampler, model, seed = NULL)

Arguments

Details

This function performs probabilistic sensitivity analysis (PSA) using Monte Carlo simulation. During each iteration, random parameters are generated by sampler() and passed to model(). The model must return one finite numeric outcome.

Value

An object of class "EconPSA".

Examples

sampler <- function() {

  list(
    cost = rnorm(1, 1000, 100),
    effectiveness = rbeta(1, 20, 5)
  )

}

model <- function(par) {

  par$effectiveness * 5000 -
    par$cost

}

psa <- probabilistic_sensitivity_analysis(
  n = 1000,
  sampler = sampler,
  model = model,
  seed = 123
)

Profitability Index

Description

Calculates the Profitability Index (PI).

Usage

profitability_index(cashflow, rate)

Arguments

Value

Object of class "EconPI".

Summarize an EconBCR object

Description

Summarize an EconBCR object

Usage

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

Arguments

Value

A data frame summarizing the benefit-cost analysis.

Summarize a Budget Impact Analysis Object

Description

Returns a summary of the annual and cumulative budget impact over the specified time horizon.

Usage

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

Arguments

Value

A data frame containing annual budget impact results.

Examples

bia <- budget_impact_analysis(
  population = 10000,
  uptake = c(0.10, 0.20, 0.35, 0.45, 0.60),
  current_cost = 1200,
  new_cost = 1500,
  years = 5,
  discount = 0.03
)

summary(bia)

Summarize a Cost-Effectiveness Analysis

Description

Summarize a Cost-Effectiveness Analysis

Usage

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

Arguments

Value

A data frame summarizing the cost-effectiveness analysis.

Summarize a Cost-Effectiveness Acceptability Curve Object

Description

Summarize a Cost-Effectiveness Acceptability Curve Object

Usage

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

Arguments

Value

A data frame summarizing the Cost-Effectiveness Acceptability Curve.

Summarize a Cost-Effectiveness Acceptability Frontier Object

Description

Returns a summary of the Cost-Effectiveness Acceptability Frontier (CEAF) results across all willingness-to-pay (WTP) thresholds.

Usage

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

Arguments

Value

A data frame containing:

WTP

Willingness-to-pay threshold.

OptimalStrategy

Optimal strategy at each WTP.

Probability

Probability that the optimal strategy is truly cost-effective.

ExpectedNMB

Expected Net Monetary Benefit.

Examples

set.seed(123)

cost <- cbind(
  rnorm(100, 1000, 100),
  rnorm(100, 1200, 120),
  rnorm(100, 1400, 150)
)

effect <- cbind(
  rnorm(100, 0.70, 0.05),
  rnorm(100, 0.80, 0.05),
  rnorm(100, 0.90, 0.05)
)

ceaf <- cost_effectiveness_acceptability_frontier(
  cost = cost,
  effect = effect,
  wtp = c(0, 50000, 100000)
)

summary(ceaf)

Summarize an Expected Value of Perfect Information Object

Description

Returns a summary of the Expected Value of Perfect Information (EVPI) across willingness-to-pay (WTP) thresholds.

Usage

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

Arguments

Value

A data frame containing:

WTP

Willingness-to-pay threshold.

EVPI

Expected Value of Perfect Information.

ExpectedPerfectInformation

Expected value under perfect information, E[\max(NMB)].

ExpectedCurrentInformation

Expected value under current information, \max(E[NMB]).

Examples

set.seed(123)

cost <- cbind(
  rnorm(100, 1000, 100),
  rnorm(100, 1200, 120),
  rnorm(100, 1500, 140)
)

effect <- cbind(
  rnorm(100, 0.70, 0.05),
  rnorm(100, 0.82, 0.05),
  rnorm(100, 0.92, 0.05)
)

evpi <- expected_value_perfect_information(
  cost = cost,
  effect = effect,
  wtp = c(0, 50000, 100000)
)

summary(evpi)

Summarize an Expected Value of Partial Perfect Information Object

Description

Returns a summary of the Expected Value of Partial Perfect Information (EVPPI) across willingness-to-pay (WTP) thresholds.

Usage

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

Arguments

Value

A data frame containing:

WTP

Willingness-to-pay threshold.

EVPPI

Expected Value of Partial Perfect Information.

Examples

evppi <- list(
  wtp = c(0, 50000, 100000),
  evppi = c(0, 125, 250)
)
class(evppi) <- "EconEVPPI"

summary(evppi)

Summarize a Probabilistic Sensitivity Analysis Object

Description

Summarize a Probabilistic Sensitivity Analysis Object

Usage

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

Arguments

Value

A data frame containing summary statistics.

Summarize a Tornado Diagram Object

Description

Summarize a Tornado Diagram Object

Usage

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

Arguments

Value

A data frame summarizing the tornado analysis.

Summarize a Decision Tree Analysis Object

Description

Returns a summary of the expected costs and expected effectiveness for each terminal node.

Usage

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

Arguments

Value

A data frame containing:

Strategy

Terminal strategy.

Probability

Terminal node probability.

Cost

Observed cost.

Effectiveness

Observed effectiveness.

ExpectedCost

Expected cost.

ExpectedEffectiveness

Expected effectiveness.

Examples

strategy <- c(
  "Treatment A",
  "Treatment B",
  "Treatment C"
)

probability <- c(0.30, 0.45, 0.25)
cost <- c(1200, 1800, 2400)
effectiveness <- c(0.70, 0.82, 0.91)

tree <- decision_tree_analysis(
  strategy,
  probability,
  cost,
  effectiveness
)

summary(tree)

Threshold Analysis

Description

Identifies the threshold value of a parameter at which a model outcome reaches a specified target.

Usage

threshold_analysis(lower, upper, target = 0, model, tol = 1e-08)

Arguments

Value

Object of class "EconThreshold".

Tornado Diagram

Description

Creates data for a tornado diagram.

Usage

tornado_diagram(parameter, low, high, base_case)

Arguments

Value

Object of class "EconTornado".

Two-Way Sensitivity Analysis

Description

Performs deterministic two-way sensitivity analysis by varying two model parameters simultaneously.

Usage

two_way_sensitivity_analysis(parameter1, parameter2, model)

Arguments

Value

An object of class "EconTWSA".