Devin Incerti, Elmar Alizadeh, Ali Ruderian, Jeff Sullivan, Darius Lakdawalla
Introduction
Generalized cost-effectiveness analysis (GCEA) has grown in popularity over the last several years due to increased awareness of the restrictive assumptions underpinning traditional cost-effectiveness restrictive assumptions underpinning traditional cost-effectiveness analysis (CEA). In this post, we review two key components of GCEA—(1) dynamic pricing and (2) stacked cohorts—and show how both components can be implemented with EntityRisk’s PROVEN™ platform. The term “stacked cohorts” is used to refer to multi-cohort models in which both existing and new cohorts of patients utilize a drug over its life cycle. Stacked cohorts are most impactful when combined with dynamic pricing models, which allow drug prices to change over time according to market dynamics such as genericization, competitor entry, Inflation Reduction Act (IRA) price-negotiation, and the like.
Dynamic Pricing
Although CEAs often assume that drug prices remain constant over time, real-world prices do not remain constant. “Dynamic pricing” relaxes this assumption by allowing real (i.e., inflation-adjusted) net drug prices to change over the drug life cycle. For instance, prices typically drop dramatically after patent expiration when generics, biosimilars, or branded competitors enter the market.
It may seem obvious that dynamic pricing is more realistic, but critics argue that forecasting future price growth introduces too much uncertainty about the timing of generic entry and competitor entry, and about the timing and magnitude of the resulting net price declines. In reality, however, every modeling approach is already making assumptions in the face of this uncertainty. For instance, models with static prices implicitly assume away price growth, and all of its causes, for all time. Few assumptions are perfect, but in this case, the scientific literature provides evidence that supports more credible assumptions than zero price growth.
Modeling price changes over time requires knowledge of price growth both before and after loss of exclusivity (LOE). Net drug prices have been flat for the last 10 years, even in nominal terms. We therefore believe that it is conservative to assume that real net prices remain constant (i.e., grow by 0%) until LOE.
Similarly, several recent studies can be used to estimate the extent to which prices decline after LOE. Helland and Seabury used data from 1998 to 2008 to show that prices drop by an average of 74% after generic entry, and a study by the IMS Institute for Healthcare Informatics in 2016 found that average prices declined by 51% in the first year following LOE, with the decline increasing to 57% by the second year, and to 67% at year five. Price drops found in the IMS study were even larger for oral medications as average prices declined by 66%, 74%, and 80% at one, two, and five years post LOE, respectively.
Stacked Cohorts
Traditional CEAs almost always simulate outcomes for a single cohort of patients, but real-world contexts feature continual entry of new patients initiating use of the drugnew patient cohorts initiating use of the drug. Thus, even if traditional CEAs are augmented to model price dynamics, they will still ignore treatment utilization dynamics. The number of patients using a drug at any point in time depends on both the incidence of disease and treatment utilization amongst the prevalent population. For chronic medical conditions, novel drugs entering the market treat both those who already have the disease and those who are diagnosed after product entry. Although price dynamics can be modeled for a single cohort, we recommend using stacked cohorts to ensure that price and treatment utilization dynamics are both accounted for; analyses that are limited to one cohort will underestimate the impact of price dynamics by undercounting the number of patients using a drug at later time periods, including after LOE.
A Simple Example
Analyses with stacked cohorts extend traditional CEAs by modeling the following:
- Changes in prices over time
- The size of each cohort
Consider an illustrative example. Suppose that:
- The model has 6-month cycles;
- Each cohort is simulated for 5 cycles (2.5 years);
- The annual discount rate is 3%;
- The (net) price remains constant until year 2, at which time it experiences a one-time 70% decline, followed by annual declines of $5,000 in each subsequent period;
- New cohorts enter the model every model cycle;
- There are 3 total cohorts;
- Each cohort is of equal size;
- The fraction of patients taking the drug declines over time, and each cohort has the same utilization trend.
Costs across all cohorts in each period are shown in the rightmost column: they are equal to the sum of utilization across the cohorts multiplied by the net drug price in that period. Total discounted costs across all periods are computed by multiplying the discount factor in each period by the per period cost and then summing the result. Note that the number of periods in a stacked cohort application (7 in this example) is greater than the number of model cycles (5 in this example) for which each cohort is simulated, because cohorts do not perfectly overlap. For instance, suppose we modeled two cohorts for five model cycles each. If the second cohort starts one period later than the first, it follows that we will end up with six periods.
Implementation with PROVEN™
Although stacked cohorts are intuitive, implementation is not straightforward. In real applications it is necessary to:
- Model many cohorts–for instance, our default in PROVEN™-is to assume that a new cohort enters the model every cycle (e.g., a model with monthly cycles and an 80-year time horizon would have 960 cohorts);
- Consider cases in which cohort sizes (typically) change over time;
- Integrate forecasts of treatment utilization for each cohort;
- Sum effects (e.g., quality-adjusted life-years) across cohorts in addition to costs;
- Possibly account for changes in treatment effectiveness over time;
- Normalize results using cohort sizes to allow for comparison to single-cohort models;
- Account for uncertainty with probabilistic sensitivity analysis (PSA);
- Compute value-based prices (VBPs)[1].
EntityRisk has simplified these tasks by fully automating the process of “stacking” costs and effects from a single-cohort simulation. This means that PROVEN™ can ingest (or generate via its disease-modeling engine) a traditional CEA and quickly convert it to a GCEA that incorporates dynamic prices and stacked cohorts. Users start by modeling the real net price trajectory by entering (1) the initial net price, (2) price growth pre-LOE, and (3) price growth post-LOE. PROVEN™ then projects utilization by (1) automatically inferring utilization by period for the initial cohort given information on the price of the drug and the drug acquisition costs used in the ingested CEA, and optionally (2) incorporating user-defined utilization time trends. Finally, users enter information on the cohorts: (1) the number of cohorts, (2) the size of each cohort, and (3) the time interval on which successive cohorts enter.
This functionality works seamlessly with the Monte Carlo simulation techniques used to incorporate parameter uncertainty in PSA. The code is highly efficient (i.e., vectorized) because it produces results for all treatment strategies, parameter simulations, and subgroups at once, and it utilizes analytical tricks in certain special cases (e.g., when equally sized cohorts enter every model cycle) so that results can be generated almost instantly. PROVEN™ even makes the complex calculation of VBPs with stacked cohorts easy: we have developed specialized formulas so that VBPs can still be computed without resorting to slow and potentially inaccurate optimization algorithms.
Conclusion
Traditional cost-effectiveness models, which do not incorporate dynamic pricing or stacked cohorts, sacrifice accuracy for the sake of simplicity. Advances in computing power and statistical methods render this sacrifice obsolete, allowing for more realistic models. Greater realism in turn enables more accurate incorporation of social value to patients, families, and other stakeholders.
Stay tuned for future posts that will examine the impact of GCEA in real-world applications.
[1] A VBP is the maximum net price that can be charged for a drug to still be cost-effective at a given willingness to pay. Put differently, it is the net price in which the total discounted incremental monetary benefits of treatment are equal to the total discounted incremental costs.
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