Cost-effectiveness and budget effect of pre-exposure prophylaxis for HIV-1 prevention in Germany from 2018 to 2058

Background Pre-exposure prophylaxis (PrEP) is a highly effective HIV prevention strategy for men-who-have-sex-with-men (MSM). The high cost of PrEP has until recently been a primary barrier to its use. In 2017, generic PrEP became available, reducing the costs by 90%. Aim Our objective was to assess cost-effectiveness and costs of introducing PrEP in Germany. Methods We calibrated a deterministic mathematical model to the human immunodeficiency virus (HIV) epidemic among MSM in Germany. PrEP was targeted to 30% of high-risk MSM. It was assumed that PrEP reduces the risk of HIV infection by 85%. Costs were calculated from a healthcare payer perspective using a 40-year time horizon starting in 2018. Results PrEP can avert 21,000 infections (interquartile range (IQR): 16,000–27,000) in the short run (after 2 years scale-up and 10 years full implementation). HIV care is predicted to cost EUR 36.2 billion (IQR: 32.4–40.4 billion) over the coming 40 years. PrEP can increase costs by at most EUR 150 million within the first decade after introduction. Ten years after introduction, PrEP can become cost-saving, accumulating to savings of HIV-related costs of EUR 5.1 billion (IQR: 3.5–6.9 billion) after 40 years. In a sensitivity analysis, PrEP remained cost-saving even at a 70% price reduction of antiretroviral drug treatment and a lower effectiveness of PrEP. Conclusion Introduction of PrEP in Germany is predicted to result in substantial health benefits because of reductions in HIV infections. Short-term financial investments in providing PrEP will result in substantial cost-savings in the long term.


Introduction
This document provides additional information on the mathematical model, calibration and multivariate sensitivity analysis of study on the cost-effectiveness and budget effect of preexposure prophylaxis (PrEP) in Germany.

Mathematical transmission model
This study includes a compartmental deterministic mathematical transmission model that was developed for the HIV epidemic among men-who-have-sex-with-men (MSM) in the Netherlands [1,2] and that was adapted to the HIV epidemic among MSM in Germany. The schematic representation of the model is presented in figure S1. Figure S1 -Schematic representation of the compartmental deterministic model (the mathematical equations can be found on pages 3-4 of the supplement). The state variables used in the equations are shown between brackets. The parameters used in the equations are added next to the arrows that indicate the rate of change between the different compartments of the model. We assume that individuals can only start using PrEP when they are not infected with HIV. Individuals can become infected with HIV despite the use of PrEP.The arrows for infected (but not using PrEP) go through the boxes of individuals using PrEP that have an unrecognized HIV infection to the boxes of individuals that have been diagnosed but who do not use treatment (yet).

Equations of the transmission model
The model consists of 15 ordinary differential equations, including two equations that describe individuals that are not infected with HIV that use PrEP or do not use PrEP, ten equations that describe disease progression, two equations that describe the force of infection (or the rate by which individuals become infected) [3] and one equation that describes mixing between individuals of different risk groups [3,4]. The equations are summarized below.
Ordinary differential equations for people not infected with HIV Individuals not infected with HIV are sub-divided into individuals that are not on PrEP, denoted as S (susceptible individuals modelled using equation 1) and individuals using PrEP denoted as SP (suspeptible individuals using PrEP, modelled using equation 2). The sexual activity classes are defined in the equations in four groups a ranging from the group with the highest sexual activity (a = 1) to the group with the lowest sexual activity (a = 4

Equations for HIV infected undiagnosed individuals using PrEP
The equations used to model individuals that become infected with HIV despite the use of PrEP (denoted as HP in equations 6 through 8), are comparable to the equations used to model HIVinfected individuals that do not use PrEP (equations 3, 4 and 5). Individuals using PrEP are assumed to be tested for HIV every six months at a rate (denoted as δ P ).
People treated with antiretroviral drug treatment are assumed to have the same mortality as the general population [7].
Equations for the force of infection PrEP, βσ P for individuals using PrEP and βRx for individuals using antiretroviral drug treatment.
Mixing matrix Ma,j is a mixing matrix in which the elements a,j are the probability that an individual in sexual activity class a forms a sexual partnership with an individuals with sexual activity j. The mixing matrix includes a factor ε which denotes the degree of assortative mixing, and δa,j denotes Kronecker delta which is equal to zero if individuals are in the same sexual activity class or equal to one if the individuals are in different sexual activity classes [4].

Model calibration
The model has been calibrated to the historic HIV epidemic based on: the estimated German MSM population size [5], number of MSM diagnosed with HIV, percentage diagnosed with a CD4 greater than 500 cells per μl and percentage diagnosed with a CD4 cell count less than 200 cells per μl, estimated number of MSM living with HIV in Germany and the estimated number of new infections [8] (Table S1).

Costs
The costs are considered from the perspective of the health care payer (statutory health insurance).

Costs of PrEP
In our analysis we assumed that PrEP will be reimbursed by the German health care payer. As such we included the costs of PrEP into our analysis. The cost for PrEP comprise regular physician visits and laboratory testing during PrEP according to the German practice guidelines [11]. Unit costs for each service are derived from the Uniform Value Scale (UVS; Einheitlicher Bewertungsmaßstab) [12] for the SHI (statutory health insurance) perspective (Table S2). The annual costs for providing PrEP, including monitoring and costs of the drugs, are € 823.91.

Cost of HIV Treatment
We previously reported that expenditure on HIV is mainly driven by the costs of antiretroviral drugs [13] The costs of antiretroviral drugs are reimbursed by the health care payer.
The cost of antiretroviral drug treatment was based on the price of the recommended antiretroviral drug regimens for treatment of HIV in Germany [11]. The German treatment guidelines recommend to always include a backbone of two nucleoside reverse transcriptase inhibitors (NRTI) in combination with a third drug which is either a protease inhibitor (PI), a non-nucleoside reverse transcriptase inhibitor (NNRTI) or an integrase inhibitor (INI) [14]. For these ART components the mean cost per DDD (defined daily dose) was calculated based on the price of the largest package size given in the Lauer-Taxe® pharmacy price formulation [15]. In the cost calculation single-tablet preparations are distinguished from multi-tablet regimes.
To reflect current clinical practice the proportion of HIV-infected MSM receiving a given antiretroviral drug regimen is used to calculate a weighted mean ART cost. The Seroconvert-Study run by the Robert Koch-Institute (RKI) includes HIV-infected patients with a confirmed seroconversion within the three years prior to study participation [16]. Information on the antiretroviral drug regimen among MSM in this study who initiated ART in 2015 or 2016 was provided by the RKI (table S3). The annual cost per ART-regime and the weighted mean cost of ART are given in table S3. Based on these data the costs of treating a HIV-infected individual in Germany is at average € 15,010.78 per year. The main paper includes a sensitivity analysis which showed that the impact of reducing the price of antiretroviral drugs by up 90% (Table 2 and Table 3). We also considered costs, other than antiretroviral drugs, of treating HIV that are paid by the health care payer. These other costs physician visits, hospitalization, rehabilitation, home care, domestic help, travel cost and productivity loss that is covered by health care payer (partial or full inability to work, and sick leave after six weeks. The first six weeks of sick leave were not considered as these are paid by the employer). We based these costs on the values reported in the K3A study [13], which performed a detailed micro-costing on treatment of HIV-positive patients in 2008 in German clinical practice [13]. The values reported for 362 MSM participating in the K3A study [13] have been adjusted to reflect 2016 values using the harmonized German general consumer price index [17]. The total annual costs of treating HIV-infected MSM in Germany is € 17,015.93, which includes € 2,005 for non-antiretroviral drug related costs and € 15,010.78 for antiretroviral drugs (Table S4).

Utility weights
The utility weights of the quality adjusted life years (QALYs) are based on estimates from Tengs and colleagues [18]. For individuals using PrEP, we assumed a utility weight of 1 [1] (Table S5).

Multivariate sensitivity analysis using recursive partitioning
Recursive partitioning using the rpart library in R version 3.5.0 was used for multivariate analysis [19]. The primary endpoint in this analysis is the median budget effect for PrEP at 85% effectiveness and 30% coverage. All 32 model parameters that were varied by simulation were entered in this analysis. The N of the recursive partitioning tree represents the number of simulations that fulfill all of the given criteria for a branch in the tree. The percentage represents the proportion of simulations which are lower than the median budget effect of PrEP at current generic price with 80% effectiveness (a median saving of €5.1 billion over 40 years). The percentages highlighted in red represent branches of the tree in which 50% or more of the simulations resulted in a higher-than-median budget effect. The percentages highlighted in green represent branches of the tree in which 50% or less of the simulations resulted in a lower-than-median budget effect. Observations for which less than 90 simulations (equal to less than 10% of all simulations) were found were not included. In our model, the proportion of MSM in in the second-highest sexual activity group (>24.8%) was the strongest predictor for lower-than-median cost savings ( Figure S2).   Minimum of years to reach break-even point in which the cumulative undiscounted costs of HIV infections averted exceed the costs of a PrEP programme. The analysis are stratified by the effectiveness of PrEP in reducing the risk of HIV infection and the future costs of antiretroviral drug treatment compared to the current costs. PrEP is assumed to be initiated in 2018. The break-even point for the discounted costs (at an annual rate of 3%) are presented in Table 3 of the main paper.