Background

Cost-effectiveness analysis (CEA) is one form of economic evaluation that compares the cost, effectiveness, and efficiency of a set of mutually exclusive strategies in generating desired benefits. The goal of cost-effectiveness is to identify the strategy that yields that greatest benefit at an acceptable level of efficiency. Effectiveness is often measured in terms of quality-adjusted life-years (QALYs); however, life-years, infections/cases averted, or other measures of benefit could be used, depending on the goals of the decision maker. Costs reflect the cost of implementing the strategy, as well as any relevant downstream costs. The determination of which costs to include depends on the perspective of the analysis. For a more in-depth explanation of cost-effectiveness analysis, see:

• Drummond et al., Methods for the Economic Evaluation of Health Care Programmes, 4th ed., 2015, Oxford University Press
• Neumann et al., Cost-Effectiveness in Health and Medicine, 2nd ed., 2016, Oxford University Press

Given a set of mutually exclusive strategies with associated costs and effectiveness, the first step in determining cost-effectiveness is to order strategies in order of increasing costs. As costs increase, effectiveness should also increase. Any strategy with lower effectiveness but higher costs than another strategy is said to be “strongly dominated”. A rational decision-maker would never implement a dominated strategy because greater effectiveness could be achieved at lower cost by implementing a different strategy (and the strategies are mutually exclusive). Therefore, dominated strategies are eliminated from further consideration.

Next, the incremental cost and incremental effectiveness of moving from one strategy to the next (in order of increasing costs) are calculated. The incremental cost-effectiveness ratio (ICER) for each strategy is then its incremental costs divided by its incremental effectiveness and represents the cost per unit benefit of “upgrading” to that strategy from the next least costly (and next least effective) strategy. At this point, “weakly dominated” strategies are identified. These are strategies for which there is a linear combination of two different strategies that dominates the strategy (lower costs and/or higher effectiveness). Weak dominance is also called “extended dominance”. Operationally, weakly dominated strategies can be identified by checking that ICERs increase with increasingly costly (and effective) strategies. If there is a “kink” in the trend, then weak/extended dominance exists. Once weakly dominated strategies are removed (and incremental quantities recalculated), the set of remaining strategies form the efficient frontier and associated ICERs can be interpreted for decision-making.

The dampack function calculate_icers() completes all of the calculations and checks described above. It takes as inputs the cost, effectiveness outcome (usually QALYs), and strategy name for each strategy, passed as separate vectors. It outputs a specialized data frame that presents the costs and effectiveness of each strategy and, for non-dominated strategies, the incremental costs, effectiveness, and ICER. Dominated strategies are included at the end of the table with the type of dominance indicated as either strong dominance (D) or extended/weak dominance (ED) in the Status column.

We present the application of calculate_icers() in the two examples below.

Example 1: CEA using average cost and effectiveness of HIV Screening strategies in the US

From: Paltiel AD, Walensky RP, Schackman BR, Seage GR, Mercincavage LM, Weinstein MC, Freedberg KA. Expanded HIV screening in the United States: effect on clinical outcomes, HIV transmission, and costs. Annals of Internal Medicine. 2006;145(11): 797-806. https://doi.org/10.7326/0003-4819-145-11-200612050-00004.

In this example, a model was used to assess the costs, benefits, and cost-effectiveness of different HIV screening frequencies in different populations with different HIV prevalence and incidence. To illustrate the CEA functionality of dampack, we will focus on the results evaluating HIV screening frequencies in a high-risk population (1.0% prevalence, 0.12% annual incidence) and accounting only for patient-level benefits (i.e., ignoring any reduction in secondary HIV transmission).

library(dampack)
#> Loading required package: ggplot2
v_hiv_strat_names <- c("status quo", "one time", "5yr", "3yr", "annual")

v_hiv_costs <- c(26000, 27000, 28020, 28440, 29440)

v_hiv_qalys <- c(277.25, 277.57, 277.78, 277.83, 277.76) / 12

icer_hiv <- calculate_icers(cost=v_hiv_costs, 
                            effect=v_hiv_qalys, 
                            strategies=v_hiv_strat_names)
icer_hiv
#>     Strategy  Cost   Effect Inc_Cost  Inc_Effect      ICER Status
#> 1 status quo 26000 23.10417       NA          NA        NA     ND
#> 2   one time 27000 23.13083     1000 0.026666667  37500.00     ND
#> 3        5yr 28020 23.14833     1020 0.017500000  58285.71     ND
#> 4        3yr 28440 23.15250      420 0.004166667 100800.00     ND
#> 5     annual 29440 23.14667       NA          NA        NA      D

library(kableExtra)
library(dplyr)
icer_hiv %>%
  kable() %>%
  kable_styling()

plot(icer_hiv)

plot(icer_hiv, 
     label="all")

plot(icer_hiv, 
     label="all") +
  theme_classic() +
  ggtitle("Cost-effectiveness of HIV screening strategies")

Example 2: CEA using a probabilistic sensitivity analysis of treatment strategies for Clostridioides difficile infection

From: Rajasingham R, Enns EA, Khoruts A, Vaughn BP. Cost-effectiveness of Treatment Regimens for Clostridioides difficile Infection: An Evaluation of the 2018 Infectious Diseases Society of America Guidelines. Clinical Infectious Diseases. 2020;70(5):754-762. https://doi.org/10.1093/cid/ciz318

In this example, we use a probabilistic sensitivity analysis (PSA) as the basis of our cost-effectiveness calculations, as is now recommended by the Second Panel on Cost-Effectiveness in Health and Medicine (Neumann et al. 2016). For more explanation about PSA and its generation process, please see our PSA vignette by typing vignette("psa_generation", package = "dampack") in the console after installing the dampack package. The PSA dataset in this example was conducted for a model of Clostridioides difficile (C. diff) infection that compared 48 possible treatment strategies, which varied in the treatment regimen used for initial versus recurrent CDI and for different infection severities. For didactic purposes, we have reduced the set of strategies down to the 11 most-relevant strategies; however, in a full CEA, all feasible strategies should be considered (as they are in Rajasingam et al. 2020).

Costs in this example include all treatment costs and lifetime downstream medical costs. Strategy effectiveness was measured in terms of quality-adjusted life-expectancy. Outcomes were evaluated for a 67-year-old patient, which is the median age of C. diff infection patients.

library(dampack)
data("psa_cdiff")

df_cdiff_ce <- summary(psa_cdiff)
head(df_cdiff_ce)
#>   Strategy meanCost meanEffect
#> 1       s3 57336.01   12.93996
#> 2      s27 57541.25   13.01406
#> 3      s33 57642.26   13.03891
#> 4      s31 57934.07   13.09663
#> 5      s43 58072.11   13.11286
#> 6      s44 58665.78   13.12833

icer_cdiff <- calculate_icers(cost = df_cdiff_ce$meanCost,
                              effect = df_cdiff_ce$meanEffect,
                              strategies = df_cdiff_ce$Strategy)
icer_cdiff %>%
  kable() %>%
  kable_styling()

icer_cdiff %>%
  filter(Status == "ND")%>%
  kable() %>%
  kable_styling()

plot(icer_cdiff)

plot(icer_cdiff, label = "all") # can lead to a 'busy' plot

plot(icer_cdiff, plot_frontier_only = TRUE) # completely removes dominated strategies from plot

plot(icer_cdiff, currency = "USD", effect_units = "quality-adjusted life-years") # customize axis labels