Economic evaluation

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Question

How to identify the most cost-effective pneumococcal conjugate vaccine to the national immunisation programme?

• The health benefit (effectiveness) of the pneumococcal infant immunisation programme is assessed by the expected gain in Quality-Adjusted Life Years (QALYs), corresponding to the expected reduction in the annual number of invasive pneumococcal disease in the whole Finnish population.
• The perspective of the analysis is that of the health care provider.
• The analysis is based on incremental cost effectiveness

Answer

A general approach to answer the question is based on the concept of incremental cost-effectiveness. For example, if there are only two vaccines to be compared, the more effective (and more expensive vaccine) is said to be more cost-effective if the incremental cost effectiveness ratio (ICER), comparing the vaccine to the less effective vaccine, exceeds the ICER of the less effective vaccine as compared to the alternative 'no vaccination'. The general principle is explained below (see 'Rationale').

The importance of alternative assumptions about protection against individual serotypes were assessed in a sensitivity analysis. Several 'modifications' for PCV10 and PCV13 were considered, regarding assumptions about the extent of indirect protection against serotypes 3, 6A, 6A, and 19A. A detailed account of the sensitivity analysis is on page Cost_effectiveness_sensitivity. These analyses included determining the difference in the QALYs gained under PCV10 and PCV13.

In summary, if PCV13 does not induce population-level (i.e. indirect) effects on serotype 3, the difference between PCV10 and PCV13 in quality adjusted life years (QALYs) gained and medical costs are relatively minor. Different assumptions about the roles of 6A protection by PCV10 and 6C protection by PCV13 lead to different preferences, with minor absolute differences in QALYs with respect to the overall effectiveness (QALYs gained) due to PCV vaccination.

Therefore, in view of the intrinsic uncertainties in the evaluation, PCV10 and PCV13 can be regarded as equally effective. This also means that incremental cost effectiveness ratios do not need to be calculated.

Evaluation tool

The following programme can be used to calculate the incremental cost effectiveness ratios (ICERs) for two alternative vaccination programmes. The input required is:

(a) the serotype compositions of the two vaccines to be compared (the defaults are PCV10 and PCV13), and

(b) the prices per dose for the two vaccine products.

The computation utilises the epidemiological model to predict the annual number of invasive pneumococcal disease (IPD) under both vaccination programmes and, for comparison, for the scenario 'no vaccination'. The summary table presents the ICERs. The vaccine programme with the lower ICER is identified as the more cost-effective of the two alternatives. Note, that some of the ouput is irrelevant if the vaccine programme is cost saving (i.e, if savings in medical costs exceed vaccine programme cost).

N.B. Some assumptions applied int the sensitivity analysis cannot be realised with the current version of the programme. In particular, there is currently no option to include direct protection only (i.e. vaccine efficacy for the vaccinated cohorts only) for individual serotypes. However, the sensitivity analyses show that the difference between 'direct protection only' and 'no protection at all' is usually not decisive for the overall effectiveness of conjugate vaccination. In other words, the most important assumptions concers indirect protection.

• Instructions for user: Choose the desired vaccine compositions and their prices and then press "Run code".

The results of the cost-effectiveness analysis will be displayed on a separate tab.

Scenarios Please choose the vaccines to be compared:: PCV-10 PCV-13 What is the price of a single PCV10 vaccination?: What is the price of a single PCV13 vaccination?: Do you want to adjust PCV-10 or PCV-13 vaccine composition?: No Yes User defined vaccine Choose the serotypes for the PCV-10 vaccine composition: 1 3 4 5 6A 6B 6C 7F 8 9N 9V 10 11 12 14 15 16 18C 19A 19F 20 22 23A 23F 33 35 38 Other Choose the serotypes for the PCV-13 vaccine composition: 1 3 4 5 6A 6B 6C 7F 8 9N 9V 10 11 12 14 15 16 18C 19A 19F 20 22 23A 23F 33 35 38 Other + Show code- Hide code #http://fi.opasnet.org/fi/Special:Opasnet_Base?id=op_fi4433.pneumokokki_vaestossa library(OpasnetUtils) library(ggplot2) openv.setN(100) if (length(vac) == 0) stop("Mitään skenaariota ei valittu") vac <- c("No_vaccination",vac) if(price10 == '') price10 <- 0 if(price13 == '') price13 <- 0 n_vac <- 1.8e5 vacprice <- data.frame( Vaccine = c("No_vaccination", "PCV10", "PCV13"), Result = c(0, price10, price13) ) vacprice <- EvalOutput(Ovariable("vacprice", data = vacprice[vacprice$Vaccine %in% vac , ])) * n_vac temp <- opbase.data("Op_en6353", subset = "serotypes_in_typical_pneumococcal_vaccines") temp$Obs <- NULL colnames(temp)[colnames(temp) == "Result"] <- "Serotype" serotypes <- temp[temp$Vaccine == "Existing serotypes" , "Serotype"] userserotypes <- temp[temp$Vaccine %in% vac , ] if(custom_vac) { userserotypes <- data.frame( Vaccine = c(rep("PCV10", length(vac_user10)), rep("PCV13", length(vac_user13))), Serotype = c(vac_user10, vac_user13) ) } # Näyttää monimutkaiselta tuo servacin määrittely. Eikö voisi tehdä helpomminkin? # -- Pointti on siis että kullekin käyttäjän valitsemalle rokotteelle tehdään merkintä # sen sisältämistä serotyypeistä 1 sisältyy 0 ei. Näin skenaariot saadaan tehtyä yksinkertaisella # kertolaskulla (ovariable). Alla oleva koodi on täysin vektorisoitu ja kiertää siten kaksi # lyhyttä for looppia (R:n puolella), mikä on kieltämättä aika pieni voitto tässä tapauksessa... servac <- merge( data.frame(userserotypes, Result = 1), # Serotypes, either default or user-defined merge(data.frame(Vaccine = vac), data.frame(Serotype = serotypes)), # All combinations of vaccines and serotypes all.y = TRUE ) servac$Result <- as.numeric(!is.na(servac$Result)) servac <- Ovariable( "servac", data = servac ) objects.latest("Op_en6358", code_name = "initiate") # [[:op_en:Economic evaluation]] ovariable ICER, function sumtable objects.latest("Op_en6353", code_name = "initiate") # [[:op_en:Epidemiological modelling]] ovariables VacCar, VacIPD objects.latest("Op_en6007", code_name = "answer") # [[OpasnetUtils/Drafts]] ## Read the annual IPD and carriage incidence data. ## The 0 entries in IPD and carriage data are replaced by small values. #IPD <- Ovariable("IPD", ddata = "Op_fi4305.pneumokokki_vaestossa") IPD <- Ovariable("IPD", ddata = "Op_fi4433.pneumokokki_vaestossa") # [[Markunkoesivu]] IPD@data <- IPD@data[IPD@data$Observation == "Incidence" , colnames(IPD@data) != "Observation"] #Car <- Ovariable("Car", ddata = "Op_fi4305.pneumokokki_vaestossa") Car <- Ovariable("Car", ddata = "Op_fi4433.pneumokokki_vaestossa") # [[Markunkoesivu]] Car@data <- Car@data[Car@data$Observation == "Carrier" , colnames(Car@data) != "Observation"] p_user <- q_user <- adultcarriers <- 1 p <- Ovariable("p", data = data.frame(Result = p_user)) q <- EvalOutput(Ovariable("q", data = data.frame(Result = q_user))) # EvalOutput must be used because q is mentioned twice in the code and there will otherwise be a merge mismatch. ## The true number of adult carriers may actually be larger than estimated. This adjusts for that. #Car <- Car * Ovariable("adjust", data = data.frame(Age = c("Under 5", "Over 5"), Result = c(1, adultcarriers))) #VacCar <- EvalOutput(VacCar) VacIPD <- EvalOutput(VacIPD) if (1==0) { cat("servac\n") oprint(summary(servac)) cat("Number of carriers\n") oprint(summary(VacCar)) cat("Incidence of invasive pneumococcal disease.\n") oprint(summary(VacIPD)) } #if("Iter" %in% colnames(VacCar@output)) N <- max(VacCar@output$Iter) else N <- 1 if("Iter" %in% colnames(VacIPD@output)) N <- max(VacIPD@output$Iter) else N <- 1 if (1==0) {ggplot(VacCar@output, aes(x = Serotype, weight = result(VacCar) / N, fill = Vaccine)) + geom_bar(position = "dodge") + theme_gray(base_size = 24) + labs(title = "Carriers", y = "Number of carriers in Finland") } ggplot(VacIPD@output, aes(x = Serotype, weight = result(VacIPD) / N, fill = Vaccine)) + geom_bar(position = "dodge") + theme_gray(base_size = 24) + labs(title = "Figure 1. Number of IPD cases per year, by serotype.", y = "Number of cases per year") VacIPD@output$Agegroup <- cut( as.numeric(levels(VacIPD@output$Age[VacIPD@output$Age])), breaks = c(0, 3, 5, 15, 65, 80, 101), include.lowest = TRUE ) VacIPD@marginal <- c(VacIPD@marginal, FALSE) ggplot(VacIPD@output, aes(x = Vaccine, weight = result(VacIPD) / N, fill = Agegroup)) + geom_bar(position = "stack") + theme_gray(base_size = 24) + labs(title = "Figure 2. Number of IPD cases per year, by age group.", y = "Number of cases per year") ###################### # Sum over Serotype VacIPD <- oapply(VacIPD, NULL, sum, c("Serotype"), na.rm = TRUE) Costs <- EvalOutput(Costs) # Healthcare costs Total_costs <- oapply(Costs, NULL, sum, c("Outcome", "Age")) Total_costs <- oapply(Total_costs, Total_costs@output[colnames(Total_costs@output) %in% c("Vaccine", "Iter")], mean) health_care_costs <- Total_costs Total_costs <- Total_costs + vacprice Total_costs@output <- Total_costs@output[c(colnames(Total_costs@output)[colnames(Total_costs@output) %in% c("Vaccine", "Iter")], "Result")] Total_costs@marginal <- colnames(Total_costs@output) %in% c("Vaccine", "Iter") QALYs <- EvalOutput(QALYs) #### Tässä voi tehdä tapauskohtaista säätöä valitsemalla sopivat indeksit. qalyind <- "Vaccine" if("Iter" %in% colnames(QALYs@output)) qalyind <- c(qalyind, "Iter") qalysum <- oapply(QALYs, INDEX = QALYs@output[qalyind], FUN = sum) qalysum@name <- "" colnames(qalysum@output)[colnames(qalysum@output) == "QALYsResult"] <- "Result" costsum <- Total_costs #### The actual model ICER <- EvalOutput(ICER) if (FALSE){#!is.null(debug_plot)) { temp <- QALYs temp <- oapply(temp, NULL, sum, "Outcome") temp@output$Age <- as.numeric(as.character(temp@output$Age)) plot1 <- ggplot( temp@output, aes(x = Age, y = QALYsResult, colour = Vaccine, group = Vaccine) ) + geom_line() + theme_gray(base_size = 24) + labs(title = "QALYs lost due to IPD", y = "QALYs lost per year") # + facet_wrap(~ Outcome) temp <- Costs temp <- oapply(temp, NULL, sum, "Outcome") temp@output$Age <- as.numeric(as.character(temp@output$Age)) plot2 <- ggplot( temp@output, aes(x = Age, y = CostsResult, colour = Vaccine, group = Vaccine) ) + geom_line() + theme_gray(base_size = 24) + labs(title = "IPD health care cost (excl. vaccination)", y = "") # + facet_wrap(~ Outcome) temp <- VacIPD temp@output$Age <- as.numeric(as.character(temp@output$Age)) plot3 <- ggplot( temp@output, aes(x = Age, y = VacIPDResult, colour = Vaccine, group = Vaccine) ) + geom_line() + theme_gray(base_size = 24) + labs(title = "IPD cases per year", y = "Cases per year") } #if (!is.null(debug_plot)) plot3 #if (!is.null(debug_plot)) plot2 #if (!is.null(debug_plot)) plot1 # Rigid implementation which doesnt allow uncertainty... qorder <- qalysum@output$Vaccine[order(result(qalysum), decreasing = TRUE)] QALYs_incremental <- c(0, -diff(result(qalysum)[match(qorder, qalysum@output$Vaccine)])) QALYs_gained <- cumsum(QALYs_incremental) Cost_total <- result(Total_costs)[match(qorder, Total_costs@output$Vaccine)] Cost_incremental <- c(0,diff( Cost_total)) ICER2 <- Cost_incremental / QALYs_incremental ICER2[1] <- 0 ipdtable <- oapply(VacIPD, VacIPD@output["Vaccine"], sum)@output colnames(ipdtable)[colnames(ipdtable) == "VacIPDResult"] <- "N_of_IPD_cases" oprint( ipdtable[order(match(ipdtable$Vaccine, qorder)),], sortable = FALSE, include.rownames = FALSE, caption = "Table 1. Number of cases of invasive pneumococcal disease (IPD) per year (see also Figures 1-2 below).", caption.placement = "top", digits = rep(0, ncol(ipdtable) + 1) ) ############################## ## print health care costs table sum_table1A <- data.frame( Vaccine = qorder, Medical_costs = result(health_care_costs)[match(qorder,health_care_costs@output$Vaccine)] * 1e-6, ## this row was corrected by Markku Nurhonen (mnud) 14 April 2015 ## old version listed prices sometimes in wrong order: Vaccine_programme_cost = result(vacprice) * 1e-6, Vaccine_programme_cost = result(vacprice)[match(qorder,vacprice@output$Vaccine)] * 1e-6, Health_care_costs = result(costsum)[match(qorder,costsum@output$Vaccine)] * 1e-6 ) oprint( sum_table1A, sortable = FALSE, include.rownames = FALSE, caption = "Table 2. Health care costs (in MEUR)", caption.placement = "top", digits = c(0,0,2,2,2) ) ############################## ## print summary table tekstia<-data.frame(Columns=c(" 1 Vaccine ", " 2 QALYs gained ", " 3 Incremental effect ", " 4 Health-case costs ", " 5 Incremental cost ", " 6 ICER ", " "), Content=c("vaccination programme", "QALYs gained in the Finnish population (*) as compared to 'no vaccination'", "difference in QALYs gained", "medical costs due to IPD in the Finnish population(*) plus the cost of vaccination (in MEUR, 180000 doses) ", "health-care cost difference (in MEUR)", "incremental cost-effectiveness ratio (in euros). The programme with the lower ICER is identified as the more cost-effective", "(*) QALYs and health-care costs refer to the Finnish population of 5.4 million individuals")) oprint( tekstia, include.rownames = FALSE, include.colnames = FALSE, caption = "Columns appearing in Table 3 (below)", caption.placement = "top" ) sum_table2 <- data.frame( Vaccine = qorder, QALYs_gained = QALYs_gained, Incremental_effect = QALYs_incremental, Health_care_costs = Cost_total * 1e-6, Incremental_cost = Cost_incremental * 1e-6, ICER = ICER2 ) oprint( sum_table2, sortable = FALSE, include.rownames = FALSE, caption = "Table 3. Cost-effectiveness analysis summary table ", caption.placement = "top", digits = c(0,0,0,0,2,2,2) )

Rationale

Vaccination programmes are ranked in ascending order according to their effectiveness. The effectiveness is measured as the expected reduction in invasive pneumococcal disease, as predicted by the epidemiological model. Alternatives for which there is at least one other alternative with lower cost and better effectiveness are first excluded. Each programme ('A') is then compared to the next more effective programme ('B') by the incremental cost-effectiveness ratio (ICER)R↻ :

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ICER = \frac{(C_B-S_B) - (C_A-S_A)}{E_B-E_A},}

where C is the price of the vaccination program, S is the savings in health care costs (as compared to strategy 'no vaccination') and E is the savings in QALYs (as compared to 'no vaccination'). Any programme that is followed by a (more effective) programme with a smaller ICER (i.e. one which produces an additional unit of effect with lower cost) is dropped off from further consideration. The ICERs are then re-calculated and the procedure repeated as many times as needed to eventually identify the most cost-effective alternative. For a tutorial on incremental cost effectiveness analysis, see Phillips (2009) .

Costs

Health care resource use in secondary health care, per IPD case and sequelae after meningitis, were estimated from the Hospital Discharge Register (2000-2006). For each meningitis and bacteremia case, an episode of care was constructed by linking the outpatient visits and inpatient hospitalizations, using the unique personal identity code. The case fatality ratio (CFR) for IPD was obtained from a Finnish study . The unit costs for hospitalizations and outpatient visits were estimated based on individual-level cost accounting data from one hospital district. Other unit cost estimates were mainly taken from a widely used national price list for the unit costs of health care in Finland. The costs were presented in 2012 prices and were evaluated from the health care provider perspective. Future costs and benefits were discounted at 3% per annum.

Data

Summary table of the data applied in the cost-effectiveness analysis. Note, that the cost-effectiveness analysis is based on age-year (0-100) specific data on IPD and life years lost.

1. QALY_menin = QALY losses due to meningitis incl. sequlae (in years, *)
2. QALY_bact = QALY losses due to bacteremia (in years, *)
3. CFR = Case fatality ratio for meningitis and bacteremia
4. Life_y_lost = Life years lost due to IPD (mengitis or bacteremia, *)
5. Cost_ menin = Medical costs attributed to meningitis incl. sequlae (in euros *)
6. Cost_ bact = Medical costs attributed to bacteremia  (in euros *)
7. Menin_proportion = Proportion of meningitis cases of all IPD cases
   (*) a discount rate of 3%/year was applied in all calculations

Estimated medical costs and years lost due to a single bacteremia or meningitis episode

Age class	QALY_men	QALY_bac	CFR	Life_y_lost	COST_men	COST_bac	Menin_proportion
<5 years	0.22	0.0079	0.014	31.1	22 070	1 986	0.037
5-64 years	0.16	0.0079	0.112	20.7	26 488	9 000	0.046
65+ years	0.08	0.0079	0.196	9.4	21 529	6 823	0.019

• Note: The above table lists averages within each age class. Cost-effectiveness analysis is based on age year -specific values.

Estimated medical costs and years lost in Finland without vaccination (per year)

Age group	QALY_meningitis	QALY_bacteremia	Life_years_lost	Cost_meningitis	Cost_bacteremia
0-4y	0.83	0.75	43.64	81 591	189 444
5-64y	2.89	2.90	895.01	470 949	3 308 515
65+y	0.51	2.34	555.60	125 916	2 020 437

Computation

Variable initiation (Only for developers)

+ Show code- Hide code library(OpasnetUtils) # Initiate model components primary_outcomes <- Ovariable("primary_outcomes", ddata = "Op_en6358.primary_outcomes") secondary_outcomes <- Ovariable("secondary_outcomes", ddata = "Op_en6358.secondary_outcomes") costs_per_outcomes <- Ovariable("costs_per_outcomes", ddata = "Op_en6358.costs_per_outcomes") QALYs_per_outcomes <- Ovariable("QALYs_per_outcomes", ddata = "Op_en6358.QALYs_per_outcomes") Outcomes <- Ovariable( "Outcomes", dependencies = data.frame( Name = c("primary_outcomes", "secondary_outcomes", "VacIPD"), Ident = c(rep("Op_en6358/initiate", 2), "Op_en6353/initiate") ), formula = function(...) { # Primaries out <- VacIPD * primary_outcomes # Secondaries temp <- out * secondary_outcomes # Combine outcomes under single index temp@output <- temp@output[!colnames(temp@output) %in% "Outcome"] colnames(temp@output)[colnames(temp@output) == "Outcome_new"] <- "Outcome" temp@output <- temp@output[colnames(temp@output) %in% colnames(out@output)] out <- orbind(out, temp) return(out) } ) # Healthcare costs Costs <- Ovariable( "Costs", dependencies = data.frame( Name = c("Outcomes", "costs_per_outcomes"), Ident = rep("Op_en6358/initiate", 2) ), formula = function(...) { out <- Outcomes * costs_per_outcomes return(out) } ) # QALYs lost QALYs <- Ovariable( "QALYs", dependencies = data.frame( Name = c("Outcomes", "QALYs_per_outcomes"), Ident = rep("Op_en6358/initiate", 2) ), formula = function(...) { out <- Outcomes * QALYs_per_outcomes return(out) } ) # Initiate analysis ovariable ICER and function sumtable ICER <- Ovariable("ICER", dependencies = data.frame(Name = c( "qalysum", "costsum", "QALYs" )), formula = function(...) { qalyorder <- oapply(QALYs, INDEX = QALYs@output["Vaccine"], FUN = sum) qalyorder <- as.character(qalyorder@output$Vaccine[order(result(qalyorder), decreasing = TRUE)]) qalysum2 <- qalysum costsum2 <- costsum # Take the Vaccine group from the previous group (based on reverse QALY order, i.e. worst first. levels(qalysum2@output$Vaccine) <- qalyorder[match(levels(qalysum2@output$Vaccine), qalyorder) + 1] levels(costsum2@output$Vaccine) <- qalyorder[match(levels(costsum2@output$Vaccine), qalyorder) + 1] # Remove NAs from the index or otherwise they will match anything. qalysum2@output <- qalysum2@output[!is.na(qalysum2@output$Vaccine) , ] costsum2@output <- costsum2@output[!is.na(costsum2@output$Vaccine) , ] out <- (costsum - costsum2) / (-1 * (qalysum - qalysum2)) # The formula calls for QALY _savings_, hence * -1 return(out) } ) sumtable <- function() { out <- merge( merge( merge( qalysum@output, costsum@output, by = "Vaccine" ), vacprice@output, all.x = TRUE ), ICER@output, all.x = TRUE ) out <- out[c("Vaccine", "Result.x", "Result.y", "vacpriceResult", "ICERResult")] colnames(out) <- c("Vaccine", "QALY", "Costs incl. price", "Vaccination price", "ICER") out <- out[ order(out$QALY, decreasing = TRUE) , ] return(out) } objects.store(primary_outcomes, secondary_outcomes, costs_per_outcomes, QALYs_per_outcomes, Outcomes, Costs, QALYs, ICER, sumtable) cat("Initiated ovariables primary_outcomes, secondary_outcomes, costs_per_outcomes, QALYs_per_outcomes, Outcomes, Costs, QALYs, ICER and function sumtable\n")

Cost calculation (Only for developers)

+ Show code- Hide code library(OpasnetUtils) cost_table <- opasnet.csv("/0/0e/Pneumococcus_cost_table.csv", wiki = "opasnet_en") #cost_table<-re#ad.table("Cost_Table.dat") ## 101*8 taulukko ## Title of cost_table: ## QALY losses and medical costs per case, separately for meningitis and bacteremia. ## (Note: QALY losses and costs for meningitis cases include sequlae.) ##Columns of cost_table : #1# Age (years) age<-cost_table[,1] #2# QALYs lost due to one meningitis case (incl. sequlae) QALY_men<-cost_table[,2] #3# QALYs lost due to one bacteremia case QALY_bac<-cost_table[,3] #4# case-fatality ratio for a meningitis or bacteremia case (ie for an IPD case) CFR<-cost_table[,4] #5# life years lost per one fatal IPD case LYL<-cost_table[,5] #6# Medical costs due to one meningitis case (including sequlae) COST_men<-cost_table[,6] #7# Medical costs due to one bacteremia case COST_bac<-cost_table[,7] #8# Proportion of meningitis cases among all IPD cases (rest are bacteremia) PROP_men<-cost_table[,8] ## Tässä koodissa "Cost_calculation.R" luetaan taulukko "Cost_Table.dat" ja muunnetaan ## se taukukoksi "Loss_per_IPDcase" vastaamaan yhtä IPD tapausta. ## ## Tällöin kust.vaik.-mallin antamat tulokset saadaan funktiossa ## "calc_qalys_and_med_costs" kun argumentiksi annetaan IPD tapausten määrät ## Suomessa ikävuosittain (101 kpl). Nämä IPD tapausten määrät vastaavat joko ## "ei rokoteta" tilannetta tai lasketaan epidemiologisen mallin avulla eri ## rokotevaihtiehdoille. (opasnetissä IPD-vektorit saadaan siis ovariablien kautta). ## ## Funktio "calc_3_ouput_tables" tuottaa 3 tulostaulukkoa. ## Nämä ovat kust.vaik.-mallin lopputulokset. ## Markku Nurhonen 15.8.2014 ###################################################################################### ## Adjust matrix "Loss_per_case" to correspond to one ipd case ## (instead of just meningitis or bacterremia case) onevec<-rep(1,101) adjustment<-cbind(onevec,PROP_men,(onevec-PROP_men),onevec,CFR,PROP_men,(onevec-PROP_men),onevec) Loss_per_case<-cbind(age,QALY_men,QALY_bac,CFR,LYL,COST_men,COST_bac,PROP_men) Loss_per_IPDcase<-Loss_per_case*adjustment ## Matriisia Loss_per_IPDcase käytetään päivitettäessä ## kustannuksia ja QALY-arvoja IPD insidenssien muuttuessa ## rokotteiden vaihtuessa calc_qalys_and_med_costs<-function(ipd_novacc,ipd,Loss_per_IPDcase) ## for two given 101-long IPD vectors ## ipd_novacc = ipd under NO vaccination ## ipd = ipd under vaccination ## this function gives a list of ## non-fatal,fatal and total QALYs gained: result[[1]]:(1,2,3) ## and medical costs under novacc and vacc: result[[2]]:(1,2) ## Loss_per_IPDcase is a 101*8 matrix { Loss_total_novacc<-matrix(ipd_novacc,101,8)*Loss_per_IPDcase Loss_total<-matrix(ipd,101,8)*Loss_per_IPDcase Gain<-apply(Loss_total_novacc-Loss_total,2,sum) ##koko populaatio ## Now columns 2+3 are nonfatal, 5 is fatal QALYs ## list Qalys gained: nonfatal, fatal and total QALYs<-c(Gain[2]+Gain[3], Gain[5], Gain[2]+Gain[3]+Gain[5]) ## Now columns 6+7 are medical costs ## list med cost under novacc and vacc medical_cost0<-cbind(Loss_total_novacc[,6]+Loss_total_novacc[,7],Loss_total[,6]+Loss_total[,7]) medical_cost<-apply(medical_cost0,2,sum) list(QALYs,medical_cost) } calc_3_output_tables<-function(ipd0,ipd1,ipd2,vaccine_cost1,vaccine_cost2,Loss_per_IPDcase) ## for 3 given 101-long IPD vectors ## ipd0 = ipd under NO vaccination ## ipd1= ipd under vaccination 1 ## ipd1= ipd under vaccination 2 ## and ## vaccine_cost1,vaccine_cost2= ## per dose costs of vaccines 1 and 2 ## Loss_per_IPDcase is a 101*8 matrix ## ## calculate a list of 3 output tables ## rows and columns as indicated below ## ## typical call of this function: ## calc_3_ouput_tables(IPD_noVac,IPD_pcv10,IPD_pcv13,20,40,Loss_per_IPDcase) { c1<-calc_qalys_and_med_costs(ipd0,ipd1,Loss_per_IPDcase) c2<-calc_qalys_and_med_costs(ipd0,ipd2,Loss_per_IPDcase) ## output table 1 ## columns(3): vaccination, non fatal, fatal and total qalys gained ## rows: no_vacc, vacc1, vacc2 table1<-rbind(rep(0,3),c1[[1]],c2[[1]]) qalys_gained<-table1[,3] ## output table 2 ## columns(3): medical costs, vaccination programme costs, health care costs ##rows: no_vacc, vacc1, vacc2 vaccine_cost_tot<-180000*c(0,vaccine_cost1,vaccine_cost2) med_cost<-c(c1[[2]],c2[[2]][2]) healthcare_cost<-med_cost+vaccine_cost_tot table2<-cbind(med_cost,vaccine_cost_tot,healthcare_cost) ## ouput table3 ## columns(5): 1.QALYs gained compared to no_vacc ## 2.incremental effects (=incremental QALYS gained) ## 3.Health care costs 4.incremental costs ## 5.ICER=column4/column2 ##rows: no_vacc, vacc1, vacc2 incr_qalys<-(c(qalys_gained,0)-c(0,qalys_gained))[seq(3)] incr_costs<-(c(healthcare_cost,0)-c(0,healthcare_cost))[seq(3)] table3<-cbind(qalys_gained,incr_qalys,healthcare_cost,incr_costs,c(0,incr_costs[-1]/incr_qalys[-1])) list(table1,table2,table3) } objects.store(age, QALY_men, QALY_bac, CFR, LYL, COST_men, COST_bac, PROP_men, onevec, adjustment, Loss_per_case, Loss_per_IPDcase, calc_qalys_and_med_costs, calc_3_output_tables ) cat("Objects age, QALY_men, QALY_bac, CFR, LYL, COST_men, COST_bac, PROP_men, onevec, adjustment, Loss_per_case, Loss_per_IPDcase, calc_qalys_and_med_costs, calc_3_output_tables successfully stored.\n" )

Sensitivity

The effects of alternative vaccine compositions on the outcomes of the cost-effectiveness analysis were assessed. Several modifications for PCV10 and PCV13 were considered. Conclusion: The assumption about serotype 3 in PCV13 is crucial. In addition, assumptions about the role of 6A in PCV10 is important. For results, see Cost_effectiveness_sensitivity.

If serotype 3 is not included as a vaccine type in PCV13, then the differences between PCV10 and PCV13 in quality adjusted life years (QALYs) gained and medical costs are relatively minor. Therefore, in view of the intrinsic uncertainties in the model, PCV10 and PCV13 can be regarded as equally effective.

See also

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