Chapter 4 Cost-effectiveness analysis

This Section presents the deterministic results, the one-way determinististic sensitivity analysis results, the scenario analyses results, the probabilistic sensitivity analysis results and the threshold analysis results that are obtained through the cost-effectiveness model. These results are obtained by applying the functions CEModel_det and CEModel_prob that are presented in Section 3. This Section is concluded with the value of information and risk analyses. In all these analyses, the wtp object, representing the willingness-to-pay threshold, has been set to €80,000 per QALY.

4.1 Deterministic discounted results

As explained in the previous Section, deterministic results are obtained by using the CEModel_det function and the params_det object as params argument of the function. The aggregated deterministic results are presented in Table 4.1.

Table 4.1: Discounted deterministic results
Totals eribulin Totals non-eribulin Incrementals ICER
QALY Costs QALY Costs QALY Costs
0.42 €45,578 0.36 €29,746 0.06 €15,832 €252,803

4.2 Disaggregated deterministic undiscounted results

The deterministic undiscounted results can also be obtained from the l.det.res list and are provided in as follows. Table 4.2 shows the undiscounted deterministic results.

Table 4.2: Undiscounted deterministic results
Eribulin Non-eribulin Incremental
Total life years - progression-free 0.368 0.382 -0.014
Total life years - progressed disease 0.325 0.192 0.133
Total QALY - progression-free 0.243 0.252 -0.009
Total QALY - progressed disease 0.179 0.106 0.073
Total QALY - disutility adverse event -0.001 0 0
Total costs - progression-free systemic treatment costs € 11,433 € 4,735 € 6,698
Total costs - administration € 3,325 € 1,873 € 1,453
Total costs - progression-free monitoring € 3,848 € 3,996 € -148
Total costs - progression-free surgery € 44 € 46 € -2
Total costs - progression-free radiotherapy € 153 € 159 € -6
Total costs - progression-free hospitalisation € 5,412 € 5,620 € -208
Total costs - adverse event € 895 € 384 € 512
Total costs - progressed disease systemic treatment costs € 10,741 € 6,342 € 4,399
Total costs - progressed disease monitoring € 2,736 € 1,615 € 1,120
Total costs - progressed disease surgery € 1 € 1 € 0
Total costs - progressed disease radiotherapy € 384 € 227 € 157
Total costs - progressed disease hospitalisation € 3,885 € 2,294 € 1,591
Total costs - unrealted health care € 2,967 € 2,451 € 516
Total costs - travel € 64 € 36 € 28
Total costs - last year of life € 96 € 89 € 7

4.3 Deterministic one-way sensitivity analyses

To generate the deterministic one-way sensitivity analyses (DOWSA) results, all parameters of the model were individually varied within their 95% confidence interval (CI), or by a 25% difference from their mean value when the 95%CI was not available. All calculations concerning these analyses are detailed in the generate_dowsa function (Rfolder). The results of these analyses are summarised in the tornado diagram below. The tornado diagram displays the 15 most influential parameters on the results. Interested readers can load the 03_dowsa_inputs.R (R folder) to inspect the inputs used for the DOWSA.

#Draw tornado diagram
##SOURCE tornado diagram: https://stackoverflow.com/questions/55751978/tornado-both-sided-horizontal-bar-plot-in-r-with-chart-axes-crosses-at-a-given
df <- generate_dowsa(params_det = params_det)

df <- as.data.frame(df)
df$UL_Difference <- as.numeric(as.character(df$UL_Difference))
df$Lower_Bound <- as.numeric(as.character(df$Lower_Bound))
df$Upper_Bound <- as.numeric(as.character(df$Upper_Bound))
df <- df[order(df$UL_Difference, decreasing = TRUE),] #order
df <- head(df, 15) # select 15 most influential parameters

# original value of output
base.value <- as.numeric(as.character(l.det.res[[1]][1,"Inc.QALY"])) * 
  wtp - as.numeric(as.character(l.det.res[[1]][1,"Inc.Costs"])) 

# get order of parameters according to size of intervals
# (I use this to define the ordering of the factors
# which I then use to define the positions in the plot)
order.parameters <- df %>% arrange(UL_Difference) %>%
  mutate(Parameter=factor(x=Parameter, levels=Parameter)) %>%
  select(Parameter) %>% unlist() %>% levels()

# width of columns in plot (value between 0 and 1)
width <- 0.95

# get data frame in shape for ggplot and geom_rect
df.2 <- df %>% 
  # gather columns Lower_Bound and Upper_Bound into a single column using gather
  gather(key='type', value='output.value', Lower_Bound:Upper_Bound) %>%
  # just reordering columns
  select(Parameter, type, output.value, UL_Difference) %>%
  # create the columns for geom_rect
  mutate(Parameter=factor(Parameter, levels=order.parameters),
         ymin=pmin(output.value, base.value),
         ymax=pmax(output.value, base.value),
         xmin=as.numeric(Parameter)-width/2,
         xmax=as.numeric(Parameter)+width/2)
ggplot() + 
  geom_rect(data = df.2, 
            aes(ymax=ymax, ymin=ymin, xmax=xmax, xmin=xmin, fill=type)) +
  theme_bw() + 
  labs(y = "Incremental Net Monetary Benefit") +
  scale_y_continuous(labels = dollar_format(prefix = "\u20ac ", suffix = "")) +
  theme(axis.title.y=element_text(colour = "black"), legend.position = 'bottom',
        legend.title = element_blank(),
        axis.title.x = element_text(size=8)) + 
  geom_hline(yintercept = base.value) +
  scale_x_continuous(breaks = c(1:length(order.parameters)), 
                     labels = order.parameters) +
  coord_flip()
Tornado diagram

Figure 4.1: Tornado diagram

4.4 Scenario analyses

The following scenarios were performed during the current cost-effectiveness analysis All the calculations underlying these analyses are provided in the 03_fun_scenarios.R file (R folder) and the scenario analyses results are summarised here.
- Hospital perspective: in this scenario, all costs which were not collected within SONABRE, expect administration and preparation costs, were set to 0.
- In the three following scenarios, we changed the distribution of OS, PFS, and TTD to Weibull, log-logistic, and lognormal respectively. This was done by modifying the params_det$s.mod.OS, params_det$s.mod.PFS, and params_det$s.mod.TTD objects to “Weibull”, “Loglogistic”, and “Lognormal” respectively.
- Vial sharing for eribulin: in this scenario, we used the mean administered dose of eribulin (1.93) to calculate the acquisition costs of eribulin. This assumed vial sharing. This analysis was done by setting the params_det$c.PFS.systhx.trt to 914, using the c.eri_mean object.
- Alternative utility values from previous publication: in this scenario, the health state utility value associated with PFS (params_det$u.PFS object) and PD (params_det$u.PD object) were 0.756 and 0.496, respectively. These utility values were obtained from the evidence review group (ERG) report concerning eribulin as third (or later) treatment line in the United Kingdom. The ERG used these utility values because they assumed that the utility values reported in Lopes et al.(Lopes et al. 2013) and used in the company submission were not correct. These corrected utility values were considered to be more approriate than the ones reported in Lopes et al (Lopes et al. 2013).
- No unrealted health care costs in the last year of life: in this scenario, the unrelated health care costs of the last year of life (obtained from PAID) were not accounted for. The inputs of the params_det$c.related object were set to 0.
- Use of hazard ratio from EMBRACE for OS and PFS: in this scenario, the hazard ratio’s reported in EMBRACE were applied on the non-eribulin survival curves to estimate PFS and OS of the eribulin group. The hazard ratios for OS and PFS were 0.81 and 0.87 respectively. This was performed by modifying the params_det$s.OS.trt and params_det$s.PFS.trt objects of the params_det list.

Table 4.3: Scenario analyses results
Total QALY eribulin Total costs eribulin Total QALY non-eribulin Total costs non-eribulin Incremental QALY Incremental Costs ICER
Deterministic base-case 0.419 45578 0.357 29746 0.0626263 15832 252803
Hospital perspective 0.419 42484 0.357 27181 0.0626263 15302 244346
Use of Weibull distribution to model OS 0.417 45304 0.352 29382 0.0641375 15921 248237
Use of Weibull distribution to model PFS 0.420 45322 0.357 29734 0.0626323 15588 248889
Use of lognormal distribution to model TTD 0.419 45801 0.357 29778 0.0626263 16023 255857
Vial sharing for eribulin 0.419 44306 0.357 29746 0.0626263 14560 232485
Alternative utility values from ERG 0.437 45578 0.383 29746 0.0542433 15832 291872
No last year of life treatment 0.419 45485 0.357 29658 0.0626263 15826 252713
Use of hazard ratio from EMBRACE for OS and PFS 0.411 41610 0.357 29746 0.0540690 11864 219424

4.5 Probabilistic results

Probabilistic results are obtained by running the CEModel_prob function. To execute this function, probabilistic parameters have first to be estimated. Probabilistic parameters are estimated outside the “for loop” that is used within the CEModel_prob function. Probabilistic parameters are estimated through the generate_psa_inputs function with the two arguments n.sim (number of iterations) and seed.num (random seed number). In the 01_model_inputs.R file, n.sim = 10,000 iterarions and seed.num = 500. The generate_psa_inputs function can be inspected in the 03_fun_psa_inputs.R file (R folder). This function estimates the probabilistic parameters and combines them in a list, in this case the l.params_prob list. Table 2 of the manuscript provides an overview of the input parameters, their standard errors and the distribution used to estimate their probabilistic values.

Once probabilistic parameters have been estimated, one can run the CEModel_prob function using the code below by specifying the params and n.sim arguments. For our base-case analysis, these are respectively l.params_prob and n.sim. The results obtained from this function is a matrix, that we called m.prob.res. Table 4.4 shows the mean probabilistic results. Finally, the probabilistic results can be visualised in the cost-effectiveness plane and the cost-effectiveness acceptability curve. The cost-effectiveness plane provides the incremental costs and QALY of each iteration while the cost-effectiveness acceptability curve provides the probability of eribulin being cost effective at different willingness-to-pay thresholds. In the cost-effectiveness plane, the dotted line represents the €80,000 per QALY willingness-to-pay threshold. The functions used in this part of the code have been adapted from the dampack package (???).

Table 4.4: Mean probabilistic results
Totals eribulin Totals non-eribulin Incrementals ICER
QALY Costs QALY Costs QALY Costs
0.434 €45,403 0.368 €29,622 0.066 €15,782 €239,338
Cost-effectiveness plane and cost-effectiveness acceptability curve

Figure 4.2: Cost-effectiveness plane and cost-effectiveness acceptability curve

Cost-effectiveness plane and cost-effectiveness acceptability curve

Figure 4.3: Cost-effectiveness plane and cost-effectiveness acceptability curve

4.5.1 Threshold analysis result

A threshold analysis was performed to determine at which price eribulin would become cost effective. This threshold analysis was performed based on the probabilistic results and is performed through the perform_threshold_analysis function (03.fun_threshold.R, R folder). The argument of this function dfprob should be a dataframe containing the probabilistic results. The scal.r.thr.disc object is the threshold at which eribulin would become cost effective (the discount at which the ICER would be below the €80,000 willingness-to-pay threshold).

Based on this analysis, a 95 % discount would be needed for eribulin to become cost effective.

4.6 Value of information and risk analyses

4.6.1 Per patient results

We calculated the expected value of perfect information (EVPI), also called Payer Uncertainty Burden (PUB), and the Payer Strategy Burden (PSB) associated with the reimbursement of eribulin (Grimm et al. 2017), which is referred to the monetary loss associated with reimbursing eribulin the manuscript. The EVPI (or PUB) can be added to the PSB, which forms the risk per patient associated with reimbursing eribulin. To calculated the EVPI, we have adapted the cal_evpi function (called evpi) from the dampack package to calculate the EVPI for a range of willingness-to-pay thresholds (???). This function is available in the 01_fun_analysis.R file. The EVPI per patient is plotted in Figure 4.4. The risk associated with reimbursing eribulin has been estimated by calculating the difference in expected net benefit between non-eribulin and eribulin (since eribulin is not cost effective). The calculations are provided below.

## function (v.wtp, m.e, m.c) 
## {
##     require(reshape2)
##     require(matrixStats)
##     n.sim <- nrow(m.e)
##     n.str <- ncol(m.e)
##     evpi <- as.data.frame(array(0, dim = c(length(v.wtp), 2)))
##     colnames(evpi) <- c("WTP", "EVPI")
##     evpi$WTP <- v.wtp
##     for (l in 1:length(v.wtp)) {
##         nmb <- m.e * v.wtp[l] - m.c
##         d.star <- which.max(colMeans(nmb))
##         m.loss <- nmb - nmb[, d.star]
##         evpi$EVPI[l] <- mean(rowMaxs(as.matrix(m.loss)))
##     }
##     return(evpi)
## }
Expected value of perfect information per patient

Figure 4.4: Expected value of perfect information per patient

In short, the EVPI (or PUB) per patient was €9 and the PSB was €10507. This resulted in a total risk of €10516 per patient. These figures correspond to 0, 0.13, and 0.13 forgone QALY per patients.

4.6.2 Population results

The above mentioned figures were scaled up to the Dutch population, assuming a technology lifetime of 10 years. The calculations for the 10-year population can be seen in the following code chunk.

#first calculation of number of eligible patients
scal.inci.pt   <- 14882     #number of incident patients in 2018: https://www.iknl.nl/nkr-cijfers?fs%7Cepidemiologie_id=7&fs%7Ctumor_id=369&fs%7Cregio_id=135&fs%7Cgedrag_id=12&fs%7Cperiode_id=86%2C87%2C88%2C89%2C90%2C91%2C92%2C93%2C94%2C95%2C96%2C97%2C98%2C99%2C100%2C101%2C102%2C103%2C104%2C105%2C106%2C107%2C108%2C109%2C110%2C111%2C112%2C113%2C114%2C115&fs%7Cgeslacht_id=16&fs%7Cleeftijdsgroep_id=76%2C40%2C41%2C42%2C43%2C44%2C45&fs%7Cjaren_na_diagnose_id=18&fs%7Ceenheid_id=2&cs%7Ctype=column&cs%7CxAxis=periode_id&cs%7Cseries=leeftijdsgroep_id&ts%7CrowDimensions=periode_id&ts%7CcolumnDimensions=leeftijdsgroep_id&lang%7Clanguage=nl

scal.pr.i.abc  <- 0.05    #proportion metastatic patients at diagnosis ("incident" advanced breast cancer (ABC)  patients): https://www.zorginstituutnederland.nl/publicaties/adviezen/2017/04/11/pakketadvies-palbociclib
scal.pr.d.abc <- 0.2    #proportion of patients who will develop ABC: https://www.zorginstituutnederland.nl/publicaties/adviezen/2017/04/11/pakketadvies-palbociclib

scal.num.pt <- ceiling(scal.inci.pt*scal.pr.i.abc + scal.inci.pt*(1-scal.pr.i.abc)*scal.pr.d.abc) # total number of ABC patients

scal.pr.eli.eri <- (45+74)/721 #proportion of eligible patients for eribulin in the entire population since the introduction of eribulin

scal.eri <- 15/32 # proportion of eligible patients who actually received eribulin after 01-01-2016 (15 is the number of patients who received eribulin, 32 is the number of eligible patients)

scal.eli.pop  <- scal.num.pt*scal.pr.eli.eri # proportion of eligible patients in the first year 
scal.EVPIpop  <- ceiling(sum(sapply(1:10, function (x) scal.eli.pop/(1+params_det$d.c)^(x-1)))) #calculate size of the patient population, discounting the size of the population each year by 4%

scal.pop.EVPI <- round(scal.EVPIpop * df_evpi[which(df_evpi$WTP == 80000), "EVPI"],0) #population EVPI at the 80000 euros per QALY threshold
pop.PSB <- round(scal.EVPIpop * PSB80000 * scal.eri,0) # population PSB at the 80000 euros per QALY threshold, assuming that not all patients received eribulin

pop.EVPI.1year <- round(scal.eli.pop * df_evpi[which(df_evpi$WTP == 80000), "EVPI"],0)# yearly EVPI

pop.PSB.1year <- round(scal.eli.pop * PSB80000 * scal.eri,0)# PSB over 1 year, assuming 47% of patients would receive eribulin

The population results were the following. The yearly population EVPI (or PUB) was €5,084 and the PSB was €2.9 million, which resulted in a risk of €2.9 million. These figures correspond to 0.06, 36.3, and 36.36 forgone QALY per year. The EVPI (or PUB) was €42,895 and the PSB was €24.5 million over a 10-year technology lifetime. This resulted in a 10-year risk of €24.5 million.

References

Grimm, Sabine Elisabeth, Mark Strong, Alan Brennan, and Allan J. Wailoo. 2017. “The Hta Risk Analysis Chart: Visualising the Need for and Potential Value of Managed Entry Agreements in Health Technology Assessment.” PharmacoEconomics 35 (12): 1287–96. https://doi.org/10.1007/s40273-017-0562-9.

Lopes, Gilberto, Stefan Glück, Kiran Avancha, and Alberto J. Montero. 2013. “A Cost Effectiveness Study of Eribulin Versus Standard Single-Agent Cytotoxic Chemotherapy for Women with Previously Treated Metastatic Breast Cancer.” Breast Cancer Research and Treatment 137 (1): 187–93. https://doi.org/10.1007/s10549-012-2326-8.