Drugs: price, cost and willingness to pay

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[vc_row type=”in_container” full_screen_row_position=”middle” scene_position=”center” text_color=”dark” text_align=”left” top_padding=”30″ overlay_strength=”0.3″ shape_divider_position=”bottom”][vc_column column_padding=”no-extra-padding” column_padding_position=”all” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_shadow=”none” column_border_radius=”none” width=”1/1″ tablet_text_alignment=”default” phone_text_alignment=”default” column_border_width=”none” column_border_style=”solid”][vc_column_text][nectar_dropcap color=”#3452ff”]T [/nectar_dropcap]here have been numerous articles recently in popular media about the price of drugs, the cost of bringing a drug to market, and the stakeholders and countries involved. Many of them go into detailed statistics about the differences in prices, their rationale, and where they should be. In this weeknote, I’ll attempt to give our view on why systems-based solutions to any issue being talked about today are essential, otherwise we might end up making things worse.[/vc_column_text][/vc_column][/vc_row][vc_row type=”in_container” full_screen_row_position=”middle” scene_position=”center” text_color=”dark” text_align=”left” top_padding=”30″ overlay_strength=”0.3″ shape_divider_position=”bottom”][vc_column column_padding=”no-extra-padding” column_padding_position=”all” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_shadow=”none” column_border_radius=”none” width=”1/1″ tablet_text_alignment=”default” phone_text_alignment=”default” column_border_width=”none” column_border_style=”solid”][vc_column_text]First, it is essential we distinguish between three concepts: the cost of production for a producer, the willingness to pay for a consumer, and the price of a product. In simple economic terms, the cost of production has to be less than the willingness to pay, otherwise there will be nothing sold. Somewhere in between those two dollar amounts is the negotiated price. The difference between the price and the cost of production is called profit, and the difference between price and the willingness to pay is consumer surplus. Profits are self explanatory, and often vilified. Consumer surplus is the dollar amount of happiness when you feel you got a great deal.[/vc_column_text][/vc_column][/vc_row][vc_row type=”in_container” full_screen_row_position=”middle” scene_position=”center” text_color=”dark” text_align=”left” top_padding=”30″ overlay_strength=”0.3″ shape_divider_position=”bottom”][vc_column column_padding=”no-extra-padding” column_padding_position=”all” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_shadow=”none” column_border_radius=”none” el_class=”text-center” width=”1/1″ tablet_text_alignment=”default” phone_text_alignment=”default” column_border_width=”none” column_border_style=”solid”][image_with_animation image_url=”7154″ alignment=”” animation=”Fade In” img_link_large=”yes” border_radius=”none” box_shadow=”none” max_width=”100%”][/vc_column][/vc_row][vc_row type=”in_container” full_screen_row_position=”middle” scene_position=”center” text_color=”dark” text_align=”left” top_padding=”30″ overlay_strength=”0.3″ shape_divider_position=”bottom”][vc_column column_padding=”no-extra-padding” column_padding_position=”all” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_shadow=”none” column_border_radius=”none” width=”1/1″ tablet_text_alignment=”default” phone_text_alignment=”default” column_border_width=”none” column_border_style=”solid”][vc_column_text]This is essential to realize: price is not just determined by the cost of production, but also by how much someone is willing to pay for the product. We are all different, so when negotiating a price, some people are willing to pay more and others less for the same product. Similarly, certain companies can produce the same product for lower cost while others need more resources.[/vc_column_text][/vc_column][/vc_row][vc_row type=”in_container” full_screen_row_position=”middle” scene_position=”center” text_color=”dark” text_align=”left” top_padding=”30″ overlay_strength=”0.3″ shape_divider_position=”bottom”][vc_column column_padding=”no-extra-padding” column_padding_position=”all” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_shadow=”none” column_border_radius=”none” width=”1/1″ tablet_text_alignment=”default” phone_text_alignment=”default” column_border_width=”none” column_border_style=”solid”][vc_column_text]So what has happened to the clinical trial system? First, for many patients, a willingness to pay is replaced by the ability to pay. This is especially true for most life-threatening diseases. So right away, our right-hand limit becomes very high. Second, the cost of producing a drug includes, among other things, the cost of going through the clinical trial system. As we know, not all drugs make it through the system, so this also includes the cost of uncertainty. Combining these two moves our cost of producing our drug very high as well.[/vc_column_text][/vc_column][/vc_row][vc_row type=”in_container” full_screen_row_position=”middle” scene_position=”center” text_color=”dark” text_align=”left” top_padding=”30″ overlay_strength=”0.3″ shape_divider_position=”bottom”][vc_column column_padding=”no-extra-padding” column_padding_position=”all” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_shadow=”none” column_border_radius=”none” el_class=”text-center” width=”1/1″ tablet_text_alignment=”default” phone_text_alignment=”default” column_border_width=”none” column_border_style=”solid”][image_with_animation image_url=”7156″ alignment=”” animation=”Fade In” img_link_large=”yes” border_radius=”none” box_shadow=”none” max_width=”100%”][/vc_column][/vc_row][vc_row type=”in_container” full_screen_row_position=”middle” scene_position=”center” text_color=”dark” text_align=”left” top_padding=”30″ overlay_strength=”0.3″ shape_divider_position=”bottom”][vc_column column_padding=”no-extra-padding” column_padding_position=”all” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_shadow=”none” column_border_radius=”none” width=”1/1″ tablet_text_alignment=”default” phone_text_alignment=”default” column_border_width=”none” column_border_style=”solid”][vc_column_text]Suddenly, we are in a different world. In this world, people are asked to place a dollar amount on their life and companies are asked to declare a cost they aren’t sure about. This leads to both sides looking to the other for a good price point; drug companies try and charge as much as they can and society has developed mechanisms to try and make drugs available for everyone. Drug companies charge higher than the cost of producing a drug and patients, with the help of reimbursements, are able to pay more than they might be willing to. The result is that we have a price that is very likely higher than it should be, but we can never be certain.[/vc_column_text][/vc_column][/vc_row][vc_row type=”in_container” full_screen_row_position=”middle” scene_position=”center” text_color=”dark” text_align=”left” top_padding=”30″ overlay_strength=”0.3″ shape_divider_position=”bottom”][vc_column column_padding=”no-extra-padding” column_padding_position=”all” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_shadow=”none” column_border_radius=”none” width=”1/1″ tablet_text_alignment=”default” phone_text_alignment=”default” column_border_width=”none” column_border_style=”solid”][vc_column_text]From the supply side, high costs are caused by uncertainty in the clinical trial system, the danger of lawsuits, and the fact that developing new drugs that stop death is very difficult. From the demand side, the fact that Medicare is not allowed to negotiate drug prices (though the Veterans Administration is) is one of the reasons we see higher prices. In many economic systems, this is fine, after all, you don’t negotiate the price of salt when you buy it at the store. However, the United States also does not allow imports of drugs, resulting in the same drug being sold in different countries for vastly different prices. A closed system that disallows competition and no negotiating power means that we can see drugs being priced as high as our systems can sustain them. Finally, from the demand side, there is uncertainty on how much we should be spending on healthcare in general, with the last year of life responsible for one-third of medicare expenditures.[/vc_column_text][/vc_column][/vc_row][vc_row type=”in_container” full_screen_row_position=”middle” scene_position=”center” text_color=”dark” text_align=”left” top_padding=”30″ overlay_strength=”0.3″ shape_divider_position=”bottom”][vc_column column_padding=”no-extra-padding” column_padding_position=”all” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_shadow=”none” column_border_radius=”none” width=”1/1″ tablet_text_alignment=”default” phone_text_alignment=”default” column_border_width=”none” column_border_style=”solid”][vc_column_text]This is exemplified with the recent example of Gilead. Recently, a senate committee reviewed how the drug maker priced Sovaldi and Harvoni, both Hepatitis C Drugs.  According to Sen. Ron Wyden, Gilead was “fully aware that as the prices kicked up, the number of Americans treated and cured would go down.” This, when viewed from the supply side, makes perfect sense. If there is uncertainty around future profits, a company will aim to charge as much as it can, and lower than the “ability to pay” amount.[/vc_column_text][/vc_column][/vc_row][vc_row type=”in_container” full_screen_row_position=”middle” scene_position=”center” text_color=”dark” text_align=”left” top_padding=”30″ overlay_strength=”0.3″ shape_divider_position=”bottom”][vc_column column_padding=”no-extra-padding” column_padding_position=”all” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_shadow=”none” column_border_radius=”none” width=”1/1″ tablet_text_alignment=”default” phone_text_alignment=”default” column_border_width=”none” column_border_style=”solid”][vc_column_text]Harvoni’s price is about $94,500 per patient and Sovaldi about $84,000 per patient in the US, but in Egypt, Sovaldi is available for $900; Germany, around $67,000; Canada about $55,000. This shows the advantage of operating in a closed economic system. Were imports and reimports allowed from other countries, the discrepancy in price could not be maintained. Further, patent laws restrict similar molecules from being produced.[/vc_column_text][/vc_column][/vc_row][vc_row type=”in_container” full_screen_row_position=”middle” scene_position=”center” text_color=”dark” text_align=”left” top_padding=”30″ overlay_strength=”0.3″ shape_divider_position=”bottom”][vc_column column_padding=”no-extra-padding” column_padding_position=”all” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_shadow=”none” column_border_radius=”none” width=”1/1″ tablet_text_alignment=”default” phone_text_alignment=”default” column_border_width=”none” column_border_style=”solid”][vc_column_text]Gilead spent tens of millions of dollars to complete Sovaldi’s clinical trials. The average drug developed by a major pharmaceutical company costs at least $4 billion. Yet, Sovaldi costs about $130 to manufacture. The next version is expected to be even more expensive.  If you visualize the uncertainty range from $130 to $4 billion, you understand why pricing in drug markets is not solely based on the cost of production. Together, Sovaldi and Harvoni generated $14.2 billion in global sales for the first nine months of 2015. That’s a large profit, but Gilead claims it is also a large consumer surplus due to downstream health savings and the quality of the drugs that have saved lives, which of course would have a higher value else we wouldn’t have bought the drugs.[/vc_column_text][/vc_column][/vc_row][vc_row type=”in_container” full_screen_row_position=”middle” scene_position=”center” text_color=”dark” text_align=”left” top_padding=”30″ overlay_strength=”0.3″ shape_divider_position=”bottom”][vc_column column_padding=”no-extra-padding” column_padding_position=”all” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_shadow=”none” column_border_radius=”none” width=”1/1″ tablet_text_alignment=”default” phone_text_alignment=”default” column_border_width=”none” column_border_style=”solid”][vc_column_text]So what is the answer? Simplifying the clinical trials process, protecting pharmaceuticals against lawsuits, and providing more funding for drug development? No, that will only solve one side of the pricing puzzle. It will decrease the cost of drug production, but the price point will still be very high because of the high ability to pay of our current system. Is the answer negotiating drug prices, allowing imports, and better end-of-life counseling? No again, because this only affects the consumer side of the puzzle, and could potentially lead to us not developing cures, and still having high drug prices[/vc_column_text][/vc_column][/vc_row][vc_row type=”in_container” full_screen_row_position=”middle” scene_position=”center” text_color=”dark” text_align=”left” top_padding=”30″ overlay_strength=”0.3″ shape_divider_position=”bottom”][vc_column column_padding=”no-extra-padding” column_padding_position=”all” background_color_opacity=”1″ background_hover_color_opacity=”1″ column_shadow=”none” column_border_radius=”none” width=”1/1″ tablet_text_alignment=”default” phone_text_alignment=”default” column_border_width=”none” column_border_style=”solid”][vc_column_text]Can you do both simultaneously? Potentially, that will require stakeholder alignment, and an overhaul of the system. How would one even start such a process? One answer is here, with many more to come on this website. Our team is currently exploring methods to leverage technology, make information transparent, and provide recommendations to truly take advantage of the strong feeling that the clinical trials system needs to change. We are living in times where the political climate, the changing healthcare system, and a focus on individualization can be used to finally solve this puzzle.[/vc_column_text][/vc_column][/vc_row]

Inverse optimization is an area of study where the purpose is to infer the unknown parameters of an optimization problem when a set of observations is available on the previous decisions made in the settings of the problem. We develop a framework to effectively and efficiently infer the cost vector of a linear optimization problem based on multiple observations on the decisions made previously. 

We then test our models in the setting of a diet problem on a data-set obtained from NHANES; The data-set is accessible via the link bellow:

https://github.com/CSSEHealthcare/Dietary-Behavior-Dataset

A set of female individuals with the above criteria were considered. Further demographic and diet considerations (in order to select similar patients) led to selecting 11 different individuals’ one day of intake as the initial dataset for the model. In another setting, we only considered people that have consumed a reasonable amount of sodium and water. We consider these two nutrients as the main constraints in the DASH diet. 



In order to compare different potential data and their performance with the model, we used different data groups from the NHANES database. A group of middle-aged women with certain similar characteristics and a group of people with certain attributes in their diets. In the first group, we did not consider how the individual’s daily diet is reflecting on the constraints that the forward problem had and we relied on their own personal answer to questions regarding hypertension and also how prone they thought they were to type-2 diabetes. The result was a sparse set of variables and an inconclusive optimal solution in regards to the preferences. In the second group, we tried to obtain sub-optimal data. We prioritized the maximum sodium intake constraint and the water intake constraints as our main and most important constraints. 

We introduce a new approach that combines inverse optimization with conventional data analytics to recover the utility function of a human operator. In this approach, a set of final decisions of the operator is observed. For instance, the final treatment plans that a clinician chose for a patient or the dietary choices that a patient made to control their disease while also considering her own personal preferences. Based on these observations, we develop a new framework that uses inverse optimization to infer how the operator prioritized different trade-offs to arrive at her decision. 

We develop a new inverse optimization framework to infer the constraint parameters of a linear (forward) optimization based on multiple observations of the system. The goal is to find a feasible region for the forward problem such that all given observations become feasible and the preferred observations become optimal. We explore the theoretical properties of the model and develop computationally efficient equivalent models. We consider an array of functions to capture various desirable properties of the inferred feasible region. We apply our method to radiation therapy treatment planning—a complex optimization problem in itself—to understand the clinical guidelines that in practice are used by oncologists. These guidelines (constraints) will standardize the practice, increase planning efficiency and automation, and make high-quality personalized treatment plans for cancer patients possible.

Assume that a decision-maker’s uncertain behavior is observed. We develop a an inverse optimization framework to impute an objective function that is robust against misspecifications of the behavior. In our model, instead of considering multiple data points, we consider an uncertainty set that encapsulates all possible realizations of the input data. We adopt this idea from robust optimization, which has been widely used for solving optimization problems with uncertain parameters. By bringing robust and inverse optimization together, we propose a robust inverse linear optimization model for uncertain input observations. We aim to find a cost vector for the underlying forward problem such that the associated error is minimized for the worst-case realization of the uncertainty in the observed solutions. That is, such a cost vector is robust in the sense that it protects against the worst misspecification of a decision-maker’s behavior. 

As an example, we consider a diet recommendation problem. Suppose we want to learn the diet patterns and preferences of a specific person and make personalized recommendations in the future. The person’s choice, even if restricted by nutritional and budgetary constraints, may be inconsistent and vary over time. Assuming the person’s behavior can be represented by an uncertainty set, it is important to find a cost vector that renders the worst-case behavior within the uncertainty set as close to optimal as possible. Note that the cost vector can have a general meaning and may be interpreted differently depending on the application (e.g., monetary cost, utility function, or preferences). Under such a cost vector, any non-worst-case diet will thus have a smaller deviation from optimality.  

Radiation therapy is frequently used in diagnosing patients with cancer. Currently, the planning of such treatments is typically done manually which is time-consuming and prone to human error. The new advancements in computational powers and treating units now allow for designing treatment plans automatically.

To design a high-quality treatment, we select the beams sizes, positions, and shapes using optimization models and approximation algorithms. The optimization models are designed to deliver an appropriate amount of dose to the tumor volume while simultaneously avoiding sensitive healthy tissues. In this project, we work on finding the best beam positions for the radiation focal points for Gamma Knife® Perfexion™, using quadratic programming and algorithms such as grassfire and sphere-packing.

In radiation therapy with continuous dose delivery for Gamma Knife® Perfexion™, the dose is delivered while the radiation machine is in movement, as oppose to the conventional step-and-shoot approach which requires the unit to stop before any radiation is delivered. Continuous delivery can increase dose homogeneity and decrease treatment time. To design inverse plans, we first find a path inside the tumor volume, along which the radiation is delivered, and then find the beam durations and shapes using a mixed-integer programming optimization (MIP) model. The MIP model considers various machine-constraints as well as clinical guidelines and constraints.

Perioperative services are one of the vital components of hospitals and any disruption in their operations can leave a downstream effect in the rest of the hospital. A large body of evidence links inefficiencies in perioperative throughput with adverse clinical outcomes. A regular delay in the operating room (OR), may lead to overcrowding in post-surgical units, and consequently, more overnight patients in the hospital. Conversely, an underutilization of OR is not only a waste of an expensive and high-demand resource, but it also means that other services who have a demand are not able to utilize OR. This mismatch in demand and utilization may, in turn, lead to hold-ups in the OR and cause further downstream utilization. We investigate the utilization of operating rooms by each service. The null hypothesis of this work is that the predicted utilization of the OR, i.e., the current block schedule, matches completely with the actual utilization of the service. We test this hypothesis for different utilization definitions, including physical and operational utilization and reject the null hypothesis. We further analyze why a mismatch may exist and how to optimize the schedule to improve patient flow in the hospital.

Primary care is an important piece in the healthcare system that affects the downstream medical care of patients heavily. There are specific challenges in primary care as healthcare shifts from fee-for-service to population health management and medical home, focuses on cost savings and integrates quality measures. We consider the primary care unit at a large academic center that is facing similar challenges. In this work we focus on the imbalance in workload, which is a growing regulatory burden and directly concerns any staff in primary care. It can result in missed opportunities to deliver better patient care or providing a good work-environment for the physicians and the staff. We consider the primary care unit at the large academic center and focus on their challenge in balancing staff time with quality of care through a redesign of their system. We employ optimization models to reschedule providers’ sessions to improve the patient flow, and through that, a more balanced work-level for the support staff. 

This work was performed with the MIT/MGH Collaboration.

In many healthcare services, care is provided continuously, however, the care providers, e.g., doctors and nurses, work in shifts that are discrete. Hence, hand-offs between care providers is inevitable. Hand-offs are generally thought to effect patient care, although it is often hard to quantify the effects due to reverse causal effects between patients’ duration of stay and the number of hand-off events. We use a natural randomized control experiment, induced by physicians’ schedules, in teaching general medicine teams. We employ statistical tools to show that between the two randomly assigned groups of patients, a subset who experiences hand-off experience a different length of stay compared to the other group.

This work was performed with the MIT/MGH Collaboration.

Many outpatient facilities with expensive resources, such as infusion and imaging centers, experience surge in their patient arrival at times and are under-utilization at other times. This pattern results in patient safety concerns, patient and staff dissatisfaction, and limitation in growth, among others. Scheduling practices is found to be one of the main contributors to this problem.

We developed a real-time scheduling framework to address the problem, specifically for infusion clinics. The algorithm assumes no knowledge of future appointments and does not change past appointments. Operational constraints are taken into account, and the algorithm can offer multiple choices to patients.

We generalize this framework to a new scheduling model and analyze its performance through competitive ratio. The resource utilization of the real-time algorithm is compared with an optimal algorithm, which knows the entire future. It can be proved that the competitive ratio of the scheduling algorithm is between 3/2 and 5/3 of an optimal algorithm.

This work was performed with the MIT/MGH Collaboration.

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