1 INTRODUCTION

Advancing medical knowledge and technologies are increasing understanding of patient heterogeneity. Patients previously thought to have the same disease and treated homogeneously can be discovered instead to have subtle differences and respond differently to different treatments (Bieber, 2013; Padmanabhan, 2014). An effective treatment for one patient may not be as effective for others. To provide equal and optimal care for all, it is important to identify differences within disease groups and develop therapies to provide effective care for all patients. Heterogeneity may be identified through discovery of biomarkers including genetic testing, blood testing or medical imaging. Stratified therapies can be developed to specifically target biomarker positive patients (Beckman et al., 2011).

Stratified therapies may come at a higher cost to pharmaceutical manufacturers, with both the initial discovery of disease biomarkers and their routine detection incurring additional costs (ABPI, 2014). This may not be fully acknowledged in decision-making processes of healthcare providers. The National Institute of Health and Care Excellence (NICE) in England and Wales, currently gives no additional consideration to stratified treatments over conventional unstratified (full population) therapies and the economic evaluation of stratified medicines can bring additional challenges (Coyle et al., 2020; Hawkins & Scott, 2011; Shabaruddin et al., 2015). Pharmaceutical manufacturers may therefore be cautious to invest additional costs required to develop a stratified therapy without any additional expected reimbursement. Consequently, current practice may be stifling development of stratified therapies, with patients and healthcare providers losing out.

Financially, a pharmaceutical manufacturer may prefer to develop drugs for heterogeneous populations. Existing motivations for developing a stratified therapy may be that a biomarker subgroup is already established, or a therapy has failed to gain approval in a broader patient population. For example, CRYSTAL study data showed that combination therapy was only cost-effective for specific subgroups of patients in the original trial (Harty et al., 2018). However, a healthcare provider may need to provide greater incentive for continued and focused development of stratified therapy by pharmaceutical manufacturers, such as flexible pricing (Anonymous, 2013).

A number of authors have suggested modeling of the decision-making processes for stratified therapies. Sahlin and Hemerén present a decision theoretic model based on the idea of personalized medicine and discuss potential moral issues that may arise (Sahlin & Hermerén, 2012). Bardey and De Donder model the effect on genetic screening to identify patients for prevention methods, considering the perspective of the insurer (Bardey & De Donder, 2013).

Antoñanzas et al. model the decision of the health authority when faced with the decision whether to use a test to match patients to a treatment (Antoñanzas et al., 2015). They consider two treatments where each is most effective for a different subgroup of patients and conclude personalized medicine may impact drug development and reimbursement decisions. Zaric (2016) explores the impact to the payer of implementing precision medicine via a companion diagnostic test across four scenarios where a drug and biomarker test have already been developed.

In this paper we develop a model for the decision-making process for stratified therapies. This enables us to establish when a pharmaceutical manufacturer and a national decision-maker prefer either a stratified or unstratified therapy. Our model is distinct from the existing literature in that it focuses on the decision of NICE but also considers the view of the pharmaceutical manufacturer in the development of stratified therapies. In this work we show that as a consequence of the current processes of health technology assessment, preferences of the healthcare provider and pharmaceutical manufacturer for stratification for a particular therapy can be misaligned, and consider the conditions under which this misalignment occurs. We then explore solutions that reduce/remove this misalignment, increasing the motivation for developing stratified therapies and improving health care.

2 UTILITY MODELS

To consider the impact of different methods of incentivization, we model the pharmaceutical manufacturer decision making process, and the preferences of the healthcare provider. Using decision theoretic methods (DeGroot, 2005; Minton et al., 1962; Oliehoek & Visser, 2010), we incorporate utility functions capturing the main factors considered by either a pharmaceutical manufacturer or healthcare provider in deciding to develop or reimburse a therapy.

The healthcare provider is motivated to provide the best healthcare or obtain the most quality adjusted life-years (QALYs) subject to its budget. However, when appraising a single therapy, NICE does not consider the cost implications on a micro-economic scale and does not undertake a cost minimization exercise. Instead, the selection of the most cost-effective therapies is indirectly achieved using willingness-to-pay thresholds, with decisions to fund a particular therapy being made on a case-by-case basis as new therapies become available. Meanwhile pharmaceutical manufacturers bear the upfront costs of developing a therapy, plus the potential cost of developing a biomarker test for a stratified therapy. Reimbursement for any drug developed must therefore cover the pharmaceutical manufacturer's initial investment, through a combination of large effect size leading to high price and/or large patient population.

Considering these two perspectives led us to develop the utility model described in the next two subsections. Model parameters are given in Table 1.

TABLE 1. Definitions and values of parameters used in this study Definition Notation Value used Source Population parameters Population size 1000 See text Biomarker prevalence in population 0 to 1 Actual effect in biomarker positive (subgroup) 0.85 (QALYs) Taken from NICE TA519 Actual effect in biomarker negative (complement) −1 to 1 (QALYs) Production costs Therapy production cost (per patient) 100 (£) Estimate Biomarker test production cost (per patient) 10 (£) Estimate Therapy development cost (total) 5,000,000 (£) Estimate Biomarker test development cost (total) 500,000 (£) Estimate Additional costs associated with treatment Incremental difference for one-off costs (per patient, e.g. administration, AE management) −711 (£) Taken from NICE TA519 Incremental costs per additional QALY gained (per patient, e.g. disease monitoring) 11,450.6 (£/QALY) Taken from NICE TA519 Healthcare provider willingness to pay Threshold healthcare provider is willing to pay for stratified treatment, per QALY gained 48,000 (£/QALY) Taken from NICE TA519 Threshold healthcare provider is willing to pay for a non-stratified treatment, per QALY gained 48,000 (£/QALY) Taken from NICE TA519 True value of QALY to healthcare provider 60,000 (£) Estimate Abbreviations: AE: adverse event, NICE, National Institute of Health and Care Excellence; QALY: quality adjusted life-year. 2.1 Healthcare provider utility functions

The utility to the healthcare provider captures the value of the benefit to the population associated with the availability of the new drug less the cost that the healthcare provider must pay for the drug, both relative to existing care. Our theoretical “healthcare provider” represents both NICE, who are the decision maker in England and Wales, and the NHS, who deliver healthcare.

Let denote the number of patients expected to receive the therapy across the lifetime of the treatment if approved for the full population. We define to be the prevalence of a subgroup, with the prevalence of its complement, where the treatment effect may vary across the subgroup and complement. We assume all patients fall into one of these two groups.

Let and denote the true average benefit (in QALYs) per patient in the subgroup and complement respectively. We assume this benefit is known, following estimation in a successful clinical trial assessing the efficacy of the treatment. For a stratified treatment, that is, one developed for treatment of the subgroup alone, the total health benefit (in QALYs) will then be . For a non-stratified treatment, that is one developed in the full population, the total health benefit will be where . If the true monetary value of a QALY is equal to , with units £/QALY, then the value of the new stratified or non-stratified drug is respectively or . Treatment related inputs could be based on absolute value or relative to existing care.

Assume that the healthcare provider is willing to pay a total of per QALY for an unstratified drug and its associated costs, and similarly for a stratified drug. For our base scenario, we assume these to have the same value, however we model these separately to allow exploration of varying their values independently. To estimate the utility to the healthcare provider, we subtract these costs from the value of the benefit received by the healthcare provider for the therapy based on their willingness to pay threshold. This gives the following total utility for the full population: (1) The utility function for the healthcare provider for a stratified therapy has a form similar to the utility for the full population, but contains subgroup-specific terms, and is given by (2)

It would not make sense for since it is illogical for the healthcare provider to be willing to pay more than it values the health gain. A healthcare provider has a limited budget meaning it cannot afford to pay for every treatment as it must ensure it can consider future treatments. Furthermore, if the healthcare provider has no preference whether new treatments are developed or reimbursed, nor any incentive to consider new therapies, since it receives the same value for money regardless. Hence so that the healthcare provider has an incentive to adopt new and better therapies. Similarly .

2.2 Pharmaceutical manufacturer utility functions

For the pharmaceutical manufacturer, we assume a utility function equal to the total profit from treating the full population or identified subgroup with the drug. This is equal to the average price paid by the healthcare provider to the pharmaceutical manufacturer for the therapy minus manufacturing cost (), multiplied by the number of patients, , less the development costs, .

Let and denote the prices of stratified and conventional therapies respectively accounting for the total that the healthcare provider is willing to pay for the overall benefit with denoting the average additional cost incurred per patient for each incremental QALY, and the average additional cost incurred, independent of QALY benefit. We assume the pharmaceutical manufacturer negotiates the maximum price the healthcare provider is willing to pay. Thus and are given by (3) (4)

We assume that the diagnostic and drug are developed and sold by the same pharmaceutical manufacturer. This means that we do not need to assume the healthcare provider pays separately for the diagnostic test.

For a non-stratified medicine developed for the whole patient population, the utility to the pharmaceutical manufacturer is thus (5) The utility for a stratified therapy is similar, but includes the costs of developing () and producing () the biomarker test: (6) 3 RESULTING PREFERENCES FOR PHARMACEUTICAL MANUFACTURER (PM) AND HEALTHCARE PROVIDER (HP) 3.1 PM preference general form The pharmaceutical manufacturer will prefer to develop a stratified therapy whenever (7) From Equations (5) and (6), that is whenever (8) If , this simplifies to (9)

In order for the pharmaceutical manufacturer to be motivated to develop the therapy, at least one of and must be .

3.2 HP preference general form Similarly, assuming , the healthcare provider will prefer to have a stratified therapy whenever (10)

If this simplifies to .

3.3 Alignment of pharmaceutical manufacturer and healthcare provider preferences From Equations (8) and (10) the preferences of the healthcare provider and pharmaceutical manufacturer will align when (11) Setting means the left side of the equation reduces to zero, and the right simplifies so that (12)

This would be true when the costs of treating a patient in the complement, , are equal to the cost per patient in the full population of developing and producing the biomarker test, .

As the decision to develop the therapy either for a biomarker positive population or for a wider population lies with the pharmaceutical manufacturer, the healthcare provider may be left with a suboptimal outcome. This is explored in detail in the example below.

3.4 Retrospective example: pembrolizumab for advanced urothelial carcinoma

To assess the characteristics of our model with realistic values, as our base scenario, we retrospectively use the setting and parameter values of the publicly available information from the NICE single technology appraisal of pembrolizumab for treating locally advanced or metastatic urothelial carcinoma after platinum containing chemotherapy (Anonymous, 2017; Bellmunt et al., 2017; Gallacher et al., 2019). These are shown in Table 1, alongside details explaining their source. Later, these parameters are varied in sensitivity analyses.

In this appraisal there was no restriction of pembrolizumab to specific subgroups of patients. However, the same therapy is restricted to patients with a specific biomarker (PD-L1 status) in other indications. PD-L1 status is assessed as the combined positive score (CPS), measuring the number of PD-L1 positive cells relative to the total number of tumor cells. Clinical outcomes from the KEYNOTE-045 trial of pembrolizumab (Bellmunt et al., 2017) for the PD-L1 subgroups were presented for patient groups with ≥1% CPS and ≥10% CPS, with respective prevalence () of approximately 40% and 30% from the whole patient population. However, QALY estimates from TA519 were only available for the full trial population.

The mechanism of action of the therapy is consistent with these subgroups, and the KEYNOTE-045 trial of pembrolizumab protocol specified that it would explore these subgroups. The hazard ratio for overall survival did show a trend with PD-L1 (Bellmunt et al., 2017). However, the researchers did not find a statistically significant interaction effect between PD-L1 status and pembrolizumab in KEYNOTE-045, and chose to seek approval for the wider population, ignoring PD-L1 status (Anonymous, 2017).

This case study was selected because of the availability of the parameter values necessary for our model. We use this case study to illustrate the impact of a range of different sizes of effect in the PD-L1 negative subgroup, varying the value of , including when there is equal efficacy to the subgroup, generalizing beyond the pembrolizumab example. Negative efficacy represents the potential negative effects of pembrolizumab (low absolute efficacy and adverse events) relative to existing care. We do not mean to suggest that pembrolizumab should have been approved as a stratified therapy for this indication.

The population size, , is the number of patients likely to receive the therapy across the lifetime of the therapy. The company predicted approximately 500 patients would be eligible for therapy annually. Given the existence of approved similar therapies and evolving treatment pathway, we set as 1000.

We used the value of 48,000 as the threshold () as this matches the incremental cost-effectiveness ratio (ICER) from the company base case analysis in their initial submission, and assumes the pharmaceutical manufacturer will allow for some uncertainty in their modeling, rather than hitting the £50,000 per incremental QALY threshold for end of life therapies.

For we added the incremental costs that all patients would incur regardless of the level of benefit received (terminal care cost, post-discontinuation cost, adverse event cost). For we combined the incremental costs that were affected by QALY benefit (disease management cost, drug administration cost), and divided by the total number of incremental QALYs. For other applications of our model, it may make sense to make administration cost independent of benefit.

We set as £60,000 initially, implying the healthcare provider makes meaningful gains of approximately 20% per QALY compared to the default willingness-to-pay threshold, and consider alternative values in sensitivity analyses reported below.

3.5 Results of example

Figure 1 shows the range of values of and where there is preference for stratification for each of the healthcare provider and pharmaceutical manufacturer. The healthcare provider boundary of preference is shown by the purple line, horizontal at the line of no effect in the complement group (). When there is a positive treatment effect in the complement, the healthcare provider would prefer to give these patients access to the treatment, that is for the drug to be developed for the full population, and when there is a negative effect, the healthcare provider would prefer stratification.

Contour plot of healthcare provider (HP) and pharmaceutical manufacturer (PM) preferences, and healthcare provider losses if pharmaceutical manufacturer and healthcare provider preferences do not align

The boundary of preference for the pharmaceutical manufacturer is shown by the pink curve. Above the curve, the company prefers not to stratify, whilst below it prefers to stratify. The region indicated with white lines portrays the values of and where it is not in the pharmaceutical manufacturer's interest to develop a therapy (either stratified or for the full population) as they are unable to recoup development costs and so may not develop a drug at all.

Details underlying Figure 1 are given in Supporting Information.

The disagreement between the pharmaceutical manufacturer and healthcare provider is shown by the region between the purple and pink curves in Figure 1. The different colors in this region indicate the magnitude of the loss to the healthcare provider when the pharmaceutical manufacturer chooses to develop the therapy in line with their own preferences. The region is characterized by a weak negative effect in the complement population. The region expands to include much stronger values of negative effect when the prevalence of the biomarker negative population is much smaller relative to the biomarker positive population.

Figure 2 shows the sensitivity of the pharmaceutical manufacturer initial preference to the parameter with higher positive values leading the pharmaceutical manufacturer to prefer stratification even when there is a small benefit of the treatment in the complement population.

Demonstrating preferences for the pharmaceutical manufacturer for different values of

Additional sensitivity analyses to both the base case preferences are shown in the appendix.

4 METHODS FOR ALIGNING PREFERENCES OF HEALTHCARE PROVIDER AND PHARMACEUTICAL MANUFACTURER

We considered three approaches to aligning the preferences of the healthcare provider and pharmaceutical manufacturer.

4.1 Increasing the price of stratified therapies

Our first approach is to increase the amount the healthcare provider is willing to pay for a stratified therapy ().

Rearranging Equation (8), the healthcare provider's and pharmaceutical manufacturer's preferences align if (13)

Returning to our pembrolizumab example, Figure 3 shows the changes to preferences of both the healthcare provider and pharmaceutical manufacturer when is given by Equation (13) for a range of values of . Resulting values of are given in Table 2. The preferences now align, with the points at which they change shown by the solid pink line. This alignment has come at a cost to the healthcare provider who has had to compromise on their initial preference. The region indicated by the white line, where the pharmaceutical manufacturer would prefer not to develop the drug, has slightly reduced.

Alignment of solutions 1 and 2. HP, healthcare provider; PM, pharmaceutical manufacturer

TABLE 2. Resulting values for solutions 1 and 2 to align preferences for varying prevalence across the base case 0.05 0.1 0.2 0.3 0.4 0.5 Solution 1 parameter values (£/QALY) 48,000 48,000 48,000 48,000 48,000 48,000 54,342 (+13.2) 51,082 (+6.4%) 49,452 (+3.0%) 48,909 (+1.9%) 48,637 (+1.3%) 48,474 (+1.0%) Solution 2 parameter values (£) 500,000 500,000 500,000 500,000 500,000 500,000 269,528 (54%) 261,976 (52%) 246,874 (49%) 231,772 (46%) 216,670 (43%) 201,568 (40%) 230,472 (46%) 238,024 (48%) 253,126 (51%) 268,228 (54%) 283,329 (57%) 298,432 (60%) Abbreviation: QALY: quality adjusted life-year. 4.2 Contributing to biomarker development costs

Our second approach is for the healthcare provider to make an upfront contribution toward biomarker test development costs. Let and denote contributions to the biomarker test development costs made by the healthcare provide and pharmaceutical manufacturer respectively, with . We later discuss how this is different to the earlier solution.

Adapting Equation (11) to incorporate these contributions, the preferences will align when