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In the process of price determination, sofosbuvir and PCSK9 inhibitors have posed an unprecedented question to regulatory agencies and to decision-makers in general. On the one hand, the value-based price for these agents has been estimated with an acceptable degree of approximation (EUR 3,500 yearly for PCSK9 inhibitors [1]; around 35,000 EUR [2] per patient for sofosbuvir; 1US$ = 0.8933 EUR); price negotiations can therefore be aimed at these price values. On the other hand, even if the price of these agents is reduced from their current level (EUR 12,500 for PCSK9 inhibitors [1]; EUR 48,000 [2] for sofosbuvir) to the above-mentioned value-based estimates, the economic impact of these drugs on national health systems remains clearly unsustainable [3,4].

A number of preliminary analyses have however shown that, if the prices of these high-impact drugs are adapted to the number of potential patients according to price-volume models, the average treatment cost across all treated patients can be reduced to a great extent thus leading to a sustainable situation. Experiences of this type have been conducted in Italy. For example, the price-volume agreement made by our national drug agency with Gilead (treatment cost for “initial patients” = 37,000 EUR per patient; treatment cost for the “last” patients included in the agreement = EUR 4,000 per patient; average = EUR 18,000 per patient) has allowed us to treat Italian patients with hepatitis C at an acceptable average price, which is compatible with current sustainability constraints (yearly overall expenditure for sofosbuvir: less than EUR 500 million). Of course, a crucial point in this context is that Gilead has accepted such an agreement.

A recent report [5] has further investigated the rationale underlying these price-volume agreements by examining in particular the agreements made in Italy for sofosbuvir and ranibizumab. The main result of this investigation was represented by the following price-volume model (which is based on an exponential relationship):
.
PRICE = f (Npt) = fPRICE e –(0.693/PHP) x Npt [Equation 1]

where:

-Npt is the cumulative number of treated patients;

-PRICE (in euro/patient) is the cost of the treatment (expressed as a function of Npt) that is assumed to undergo an exponential decay as Npt increases;

-fPRICE (in euro) is the “initial” price on the y axis attributed to the treatment (i.e. the full price with no discount);

-PHP (expressed as number of patients) is defined as the “price-halving population” and, in the framework of this exponential model, represents the number of patients at which the drug price is iteratively halved.

To parameterise this model, the value of PHP was set at 18,500 patients for sofosbuvir and at 42,000 patients for ranibizumab. The model in fact requires that an “appropriate” value of PHP is separately determined for each of the different high-impact agents managed through this approach. In addition, according to a still unpublished report focused on PCSK9 inhibitors (Messori et al., 2015; unpublished observations), the value of PHP suggested for these agents was set at no more than 25,000 patients.

More recently, a slightly modified version of the above exponential model (Messori et al., 2015; unpublished observations) has been proposed for handling the price of orphan drugs. In this case, the exponential relationship (designed for a nationwide population of less than 1,000 patients) acts in the opposite directions because, in comparison with value-based prices, the treatment cost of an orphan drug shows an inverse relation with the number of patients: hence, the treatment cost of the orphan drug increases as the nationwide number of potential patients decreases.

The exponential equation for orphan drugs is the following:
.
PRICE = f (Npt) = fPRICE x e (0.693/PDP) x (1000 – Npt) [Equation 2]
where:

-Npt is the expected number of treated patients;

-PRICE (in euro/patient) is the cost of the orphan drug treatment (expressed as a function of Npt) which is assumed to undergo an exponential increase as Npt decreases;

-fPRICE (in euro) is the “baseline” price on the y axis attributed to the treatment (i.e. the full price with no discount) under the assumption that 1,000 patients are treated; for sake of simplicity, fPRICE has been set to 10,000 EUR in all examples described in this paper;

-PDP (expressed as number of patients) is defined as the “price-doubling population” and, in the framework of this exponential model, represents the decrease in the number of patients that iteratively determines a doubling of drug price.

To parameterise the orphan drug model, it is necessary to choose an “appropriate” value of PDP, which should be common (i.e. the same) across all orphan agents included in the model. Some attempts to identify this “appropriate” value of PDP have been described in the above mentioned report; according to these preliminary experiences, the optimal PDP seems to be comprised in the range from 100 to 400 patients.

Figure 1 shows, in the left panel, the exponential model for orphan drugs and, in the right panel, the exponential model for price-volume agreements (with the data of sofosbuvir and ranibizumab). Although the orphan drug model shows three different values of PDP, it should be recalled that the “final” application of the model requires the identification of a single “appropriate” value of PDP (to be used across all orphan drugs under examination). By contrast, in the price-volume model, the values of PHP are intended to be separately estimated for each of the high-impact drugs.

One advantage of this two-fold exponential approach is that orphan drugs and high-impact drugs can be managed according to a common conceptual framework: in fact, the modelling process for price determination essentially focuses on the identification of a single parameter: PHP or PDP.

Andrea Messori
HTA Unit
ESTAR Toscana
Regional Health System
50100 Firenze
ITALY

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References

1. McCarthy M. New cholesterol drugs are overpriced, independent analysis finds. BMJ 2015;351:h4864

2. Messori A, Maratea D, Fadda V, Gatto R, Trippoli S. An Italian perspective: studying the cost-effectiveness of sofosbuvir before completion of national price negotiations. Eur J Gastroenterol Hepatol. 2014 Jul;26(7):813-4.

3. Etzion O, Ghany MG. A cure for the high cost of hepatitis C virus treatment. Ann Intern Med. 2015 May 5;162(9):660-1.

4. Messori A. Newest Treatments for Hepatitis C: How Can We Manage Sustainability? Clin Infect Dis. 2015 Aug 10. pii: civ667. [Epub ahead of print]

5. Messori A. Criteria for drug pricing: preliminary experiences with modeling the price-volume relationship. Sci Pharm 2015, in press, preprint available at http:/www.osservatorioinnovazione.net/papers/scipharm2015.pdf
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Fig.1. Left panel: Price-vs-patients relationship for orphan drugs. The graph shows three different exponential models that assume PDP = 150 patients (dotted line in red), 200 patients (solid line in blue), and 300 patients (dashed line in green), respectively. Other assumptions: fPRICE = 10,000 EUR (for number of patients = 1,000). Right panel: Price-volume relationship for two high-impact drugs: ranibizumab (lower curve; PHP=42,000 patients) and sofosbuvir (upper curve; PHP=18,500 patients)