Kenneth Arrow on healthcare economics: a 21st century appreciation

Nobel laureate Kenneth Arrow passed away on February 21, 2017. In a classic, fifty-year-old paper entitled Uncertainty and the Welfare Economics of Medical Care, Arrow discussed how:

“the operation of the medical-care industry and the efficacy with which it satisfies the needs of society differs from… a competitive model… If a competitive equilibrium exists at all, and if all commodities relevant to costs or utilities are in fact priced in the market, then the equilibrium is necessarily [Pareto] optimal” (emphasis added)

Note the implicit assumption that price reflects value, to which I’ll return. As Arrow elegantly explained, there are vast differences between the actual healthcare market and the competitive model, and, moreover, these differences arise from important features of the actual healthcare market.

Identifying the lack of realism of the competitive model in health care may lead to deeper understanding of the actual system. In essence this is what Arrow does. Although both medical care and our expectations have changed greatly, Arrow ’63 is still valid and worth reading today.

Here is Arrow’s summary of the differences between the healthcare market and typical competitive markets.

The nature of demand

Demand for medical services is irregular and unpredictable:

“Medical services, apart from preventive services, afford satisfaction only in the event of illness, a departure from the normal state of affairs… Illness is, thus, not only risky but a costly risk in itself, apart from the cost of medical care.”

Expected behavior of the physician

“It is at least claimed that treatment is dictated by objective needs of the case and not limited by financial considerations… Charity treatment in one form or another does exist because of this tradition about human rights to adequate medical care.”

Product uncertainty

“Recovery from disease is as unpredictable as its incidence…  Because medical knowledge is so complicated, the information possessed by the physician as to the consequences and possibilities of treatment is necessarily very much greater than that of the patient, or at least so it is believed by both parties.”

Supply conditions

Barriers to entry include licensing and other controls on quality (accreditation) and costs.

“One striking consequence of the control of quality is the restriction on the range offered… The declining ratio of physicians to total employees in the medical-care industry shows that substitution of less trained personnel, technicians and the like, is not prevented completely, but the central role of the highly trained physician is not affected at all.”

Pricing practices

There are no fixed prices:

“extensive price discrimination by income (with an extreme of zero prices for sufficiently indigent patients)… the apparent rigidity of so-called administered prices considerably understates the actual flexibility.”

Avik Roy observes in a critical National Review article that “Because patients don’t see the bill until after the non-refundable service has been consumed, and because patients are given little information about price and cost, patients and payors are rarely able to shop around for a medical service based on price and value.”

Medicine has seen major changes since Arrow’s 1963 paper. For example, the treatment of blocked coronary arteries has evolved from coronary bypass to angioplasty to early stents and finally drug-eluting stents. We have seen the advent of minimally invasive surgery, robotic surgery and catheter-based cardiac valve repair and replacement. We have seen drugs to treat hepatitis C and biologicals to treat arthritis and cancer. Many conditions have been transformed from acute to chronic but (at least temporarily) manageable. There are also divergent trends, such as increases in both natural childbirth and Caesarean sections.

In the last 50 years, medicine has become more powerful, but also significantly more complex and overall, more expensive. Intensive care units are a good example, both valuable therapeutically, but expensive to provide. At the same time, many treatments are both better (more valuable to the patient) and less expensive to provide; these range from root canal (frequently two visits to the dentist instead of four) to the significantly less invasive treatments for many cardiac rhythm abnormalities (radio-frequency ablation) and stents for coronary artery disease. The advent of epinephrine auto-injectors has been a lifesaver, but the cost of the Epi-Pen has increased significantly.

Can a competitive economic system appropriately and reasonably price such treatments and devices? Arrow argues that, if not, non-market social institutions will arise and address these challenges. Here is a deeper look.

Arrow’s first two points are still virtually axiomatic today: demand for medical services has become even more unpredictable with the continued growth of advanced, effective interventions and corresponding, appropriately increasing (in my opinion), patient expectations. Similarly, as medical care advances, we increasingly see medical care as a human right and in many cases, a societal obligation. We have come to expect treatment dictated by objective needs and not limited by financial considerations, not only from physicians but from a growing number of key players including pharmaceutical companies. To their credit, in many cases (AIDS comes to mind) pharmaceutical companies have responded by sharply reducing prices in the developing world.

Powerful chemotherapeutic and biologic drugs may have increased the uncertainty and asymmetry of information observed by Arrow, both in their effectiveness and in their side effects. In many cases one needs the language and mathematics of probability and statistics to evaluate, assess and describe their efficacy and utility. One needs an understanding of probability to determine when and how to use common preventive techniques, such as mammograms and PSA screening. Here is an example, paraphrased from Gigerenzer and Edwards (see also Strogatz). Women 40 to 50 years old, with no family history of breast cancer, are a low-risk population; the overall probability of breast cancer in this population is 0.8%. Assume that mammography has a sensitivity of 90% and a false positive rate of 7%.  A woman has a positive mammogram. What is the probability that she has breast cancer? Among 25 German doctors surveyed, 36% said 90% or more, 32% said 50-80%, and 32% said 10% or less. Most (95%) of United States doctors thought the probability was approximately 75%.  (See the links above for the answer, or see my next blog on the challenge of communicating probability).

Arrow’s information asymmetry remains, despite the growing availability of accessible medical information on the web, perhaps for good reasons such as the ability to effectively address the needs of sicker patients.

I would amend Arrow’s discussion of supply conditions to include a wide variety of cost barriers ranging from large fixed costs of ICUs to the costs of medical research. The high cost of basic medical services relative to per capita GDP in the the developing world represents a barrier as high as any faced in the developed world.  As Arrow notes, society has addressed this challenge through a variety of pricing mechanisms outside traditional competitive models. This may not, and in general will not achieve a Pareto optimum, but their wide endorsement by society does indeed suggest that these approaches achieve a more general optimum.

“I propose here the view that, when the market fails to achieve an optimal state, society will, to some extent at least, recognize the gap, and nonmarket social institutions will arise attempting to bridge it… But it is contended here that the special structural characteristics of the medical-care market are largely attempts to overcome the lack of optimality due to the nonmarketability of the bearing of suitable risks and the imperfect marketability of information. These compensatory institutional changes, with some reinforcement from usual profit motives, largely explain the observed noncompetitive behavior of the medical-care market, behavior which, in itself, interferes with optimality. The social adjustment towards optimality thus puts obstacles in its own path.”

It is this view which I find too limiting. I would suggest that society has at least implicitly concluded that price alone does not define value, and thus formed a broader definition of optimality, not simply Pareto optimality in a competitive market. Society is finding and supporting ways to overcome obstacles toward this broader sense of optimality.

The Bill & Melinda Gates Foundation vaccination project aims to reduce the number of children that die each year from preventable disease (currently around 1.5 million). The lifebox project, founded by Dr Atul Gawande, provides affordable, high quality pulse oximeters to the developing world and now seeks to address basic surgical safety in the developing world. Important advances also arise in the developing world; most recently, an easy to deliver, more effective oral cholera vaccine developed in Vietnam.

Arrow himself recognizes the limits of a traditional economic description of the medical care market in his concluding Postscript, arguing that “The logic and limitations of ideal competitive behavior under uncertainty force us to recognize the incomplete description of reality supplied by the impersonal price system.” I conclude more generally that prices not only do not necessarily represent value in medical care (as Arrow observed), but that the combination of uncertainty, externalities, high costs, divergent economies, and technological advance means that price alone cannot describe value in medical care. A broader more general theory of healthcare economics with a foundation standing on the shoulders of giants such as Kenneth Arrow, with perhaps a more general multi-dimensional Pareto optimum, might help us all better understand where we are and where we might go.

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Brent Gibbons’s journal round-up for 30th January 2017

Every Monday our authors provide a round-up of some of the most recently published peer reviewed articles from the field. We don’t cover everything, or even what’s most important – just a few papers that have interested the author. Visit our Resources page for links to more journals or follow the HealthEconBot. If you’d like to write one of our weekly journal round-ups, get in touch.

For this week’s round-up, I selected three papers from December’s issue of Health Services Research. I didn’t intend to to limit my selections to one issue of one journal but as I narrowed down my selections from several journals, these three papers stood out.

Treatment effect estimation using nonlinear two-stage instrumental variable estimators: another cautionary note. Health Services Research [PubMed] Published December 2016

This paper by Chapman and Brooks evaluates the properties of a non-linear instrumental variables (IV) estimator called two-stage residual inclusion or 2SRI. 2SRI has been more recently suggested as a consistent estimator of treatment effects under conditions of selection bias and where the dependent variable of the 2nd-stage equation is either binary or otherwise non-linear in its distribution. Terza, Bradford, and Dismuke (2007) and Terza, Basu, and Rathouz (2008) furthermore claimed that 2SRI estimates can produce unbiased estimates not just of local average treatment effects (LATE) but of average treatment effects (ATE). However, Chapman and Brooks question why 2SRI, which is analogous to two-stage least squares (2SLS) when both the first and second stage equations are linear, should not require similar assumptions as in 2SLS when generalizing beyond LATE to ATE. Backing up a step, when estimating treatment effects using observational data, one worry when trying to establish a causal effect is bias due to treatment choice. Where patient characteristics related to treatment choice are unobservable and one or more instruments is available, linear IV estimation (i.e. 2SLS) produces unbiased and consistent estimates of treatment effects for “marginal patients” or compliers. These are the patients whose treatment effects were influenced by the instrument and their treatment effects are termed LATE. But if there is heterogeneity in treatment effects, a case needs to be made that treatment effect heterogeneity is not related to treatment choice in order to generalize to ATE.  Moving to non-linear IV estimation, Chapman and Brooks are skeptical that this case for generalizing LATE to ATE no longer needs to be made with 2SRI. 2SRI, for those not familiar, uses the residual from stage 1 of a two-stage estimator as a variable in the 2nd-stage equation that uses a non-linear estimator for a binary outcome (e.g. probit) or another non-linear estimator (e.g. poisson). The authors produce a simulation that tests the 2SRI properties over varying conditions of uniqueness of the marginal patient population and the strength of the instrument. The uniqueness of the marginal population is defined as the extent of the difference in treatment effects for the marginal population as compared to the general population. For each scenario tested, the bias between the estimated LATE and the true LATE and ATE is calculated. The findings support the authors’ suspicions that 2SRI is subject to biased results when uniqueness is high. In fact, the 2SRI results were only practically unbiased when uniqueness was low, but were biased for both ATE and LATE when uniqueness was high. Having very strong instruments did help reduce bias. In contrast, 2SLS was always practically unbiased for LATE for different scenarios and the authors use these results to caution researchers on using “new” estimation methods without thoroughly understanding their properties. In this case, old 2SLS still outperformed 2SRI even when dependent variables were non-linear in nature.

Testing the replicability of a successful care management program: results from a randomized trial and likely explanations for why impacts did not replicate. Health Services Research [PubMed] Published December 2016

As is widely known, how to rein in U.S. healthcare costs has been a source of much hand-wringing. One promising strategy has been to promote better management of care in particular for persons with chronic illnesses. This includes coordinating care between multiple providers, encouraging patient adherence to care recommendations, and promoting preventative care. The hope was that by managing care for patients with more complex needs, higher cost services such as emergency visits and hospitalizations could be avoided. CMS, the Centers for Medicare and Medicaid Services, funded a demonstration of a number of care management programs to study what models might be successful in improving quality and reducing costs. One program implemented by Health Quality Partners (HQP) for Medicare Fee-For-Service patients was successful in reducing hospitalizations (by 34 percent) and expenditures (by 22 percent) for a select group of patients who were identified as high-risk. The demonstration occurred from 2002 – 2010 and this paper reports results for a second phase of the demonstration where HQP was given additional funding to continue treating only high-risk patients in the years 2010 – 2014. High-risk patients were identified as having a diagnosis of congestive heart failure (CHF), chronic obstructive pulmonary disease (COPD), coronary artery disease (CAD), or diabetes and had a hospitalization in the year prior to enrollment. In essence, phase II of the demonstration for HQP served as a replication of the original demonstration. The HQP care management program was delivered by nurse coordinators who regularly talked with patients and provided coordinated care between primary care physicians and specialists, as well as other services such as medication guidance. All positive results from phase I vanished in phase II and the authors test several hypotheses for why results did not replicate. They find that treatment group patients had similar hospitalization rates between phase I and II, but that control group patients had substantially lower phase II hospitalization rates. Outcome differences between phase I and phase II were risk-adjusted as phase II had an older population with higher severity of illness. The authors also used propensity score re-weighting to further control for differences in phase I and phase II populations. The affordable care act did promote similar care management services through patient-centered medical homes and accountable care organizations that likely contributed to the usual care of control group patients improving. The authors also note that the effectiveness of care management may be sensitive to the complexity of the target population needs. For example, the phase II population was more homebound and was therefore unable to participate in group classes. The big lesson in this paper though is that demonstration results may not replicate for different populations or even different time periods.

A machine learning framework for plan payment risk adjustment. Health Services Research [PubMed] Published December 2016

Since my company has been subsumed under IBM Watson Health, I have been trying to wrap my head around this big data revolution and the potential of technological advances such as artificial intelligence or machine learning. While machine learning has infiltrated other disciplines, it is really just starting to influence health economics, so watch out! This paper by Sherri Rose is a nice introduction into a range of machine learning techniques that she applies to the formulation of plan payment risk adjustments. In insurance systems where patients can choose from a range of insurance plans, there is the problem of adverse selection where some plans may attract an abundance of high risk patients. To control for this, plans (e.g. in the affordable care act marketplaces) with high percentages of high risk consumers get compensated based on a formula that predicts spending based on population characteristics, including diagnoses. Rose says that these formulas are still based on a 1970s framework of linear regression and may benefit from machine learning algorithms. Given that plan payment risk adjustments are essentially predictions, this does seem like a good application. In addition to testing goodness of fit of machine learning algorithms, Rose is interested in whether such techniques can reduce the number of variable inputs. Without going into any detail, insurers have found ways to “game” the system and fewer variable inputs would restrict this activity. Rose introduces a number of concepts in the paper (at least they were new to me) such as ensemble machine learningdiscrete learning frameworks and super learning frameworks. She uses a large private insurance claims dataset and breaks the dataset into what she calls 10 “folds” which allows her to run 5 prediction models, each with its own cross-validation dataset. Aside from one parametric regression model, she uses several penalized regression models, neural net, single-tree, and random forest models. She describes machine learning as aiming to smooth over data in a similar manner to parametric regression but with fewer assumptions and allowing for more flexibility. To reduce the number of variables in models, she applies techniques that limit variables to, for example, just the 10 most influential. She concludes that applying machine learning to plan payment risk adjustment models can increase efficiencies and her results suggest that it is possible to get similar results even with a limited number of variables. It is curious that the parametric model performed as well as or better than many of the different machine learning algorithms. I’ll take that to mean we can continue using our trusted regression methods for at least a few more years.

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Chris Sampson’s journal round-up for 16th January 2017

Every Monday our authors provide a round-up of some of the most recently published peer reviewed articles from the field. We don’t cover everything, or even what’s most important – just a few papers that have interested the author. Visit our Resources page for links to more journals or follow the HealthEconBot. If you’d like to write one of our weekly journal round-ups, get in touch.

Competition and quality indicators in the health care sector: empirical evidence from the Dutch hospital sector. The European Journal of Health Economics [PubMed] Published 3rd January 2017

In case you weren’t already convinced, this paper presents more evidence to support the notion that (non-price) competition between health care providers is good for quality. The Dutch system is based on compulsory insurance and information on quality of hospital care is made public. One feature of the Dutch health system is that – for many elective hospital services – prices are set following a negotiation between insurers and hospitals. This makes the setting of the study a bit different to some of the European evidence considered to date, because there is scope for competition on price. The study looks at claims data for 3 diagnosis groups – cataract, adenoid/tonsils and bladder tumor – between 2008 and 2011. The authors’ approach to measuring competition is a bit more sophisticated than some other studies’ and is based on actual market share. A variety of quality indicators are used for the 3 diagnosis groups relating mainly to the process of care (rather than health outcomes). Fixed and random effects linear regression models are used to estimate the impact of market share upon quality. Casemix was only controlled for in relation to the proportion of people over 65 and the proportion of women. Where a relationship was found, it tended to be in favour of lower market share (i.e. greater competition) being associated with higher quality. For cataract and for bladder tumor there was a ‘significant’ effect. So in this setting at least, competition seems to be good news for quality. But the effect sizes are neither huge nor certain. A look at each of the quality indicators separately showed plenty of ‘non-significant’ relationships in both directions. While a novelty of this study is the liberalised pricing context, the authors find that there is no relationship between price and quality scores. So even if we believe the competition-favouring results, we needn’t abandon the ‘non-price competition only’ mantra.

Cost-effectiveness thresholds in global health: taking a multisectoral perspective. Value in Health Published 3rd January 2017

We all know health care is not the only – and probably not even the most important – determinant of health. We call ourselves health economists, but most of us are simply health care economists. Rarely do we look beyond the domain of health care. If our goal as researchers is to help improve population health, then we should probably be allocating more of our mental resource beyond health care. The same goes for public spending. Publicly provided education might improve health in a way that the health service would be willing to fund. Likewise, health care might improve educational attainment. This study considers resource allocation decisions using the familiar ‘bookshelf approach’, but goes beyond the unisectoral perspective. The authors discuss a two-sector world of health and education, and demonstrate the ways in which there may be overlaps in costs and outcomes. In short, there are likely to be situations in which the optimal multisectoral decision would be for individual sectors to increase their threshold in order to incorporate the spillover benefits of an intervention in another sector. The authors acknowledge that – in a perfect world – a social-welfare-maximising government would have sufficient information to allocate resources earmarked for specific purposes (e.g. health improvement) across sectors. But this doesn’t happen. Instead the authors propose the use of a cofinancing mechanism, whereby funds would be transferred between sectors as needed. The paper provides an interesting and thought-provoking discussion, and the idea of transferring funds between sectors seems sensible. Personally I think the problem is slightly misspecified. I don’t believe other sectors face thresholds in the same way, because (generally speaking) they do not employ cost-effectiveness analysis. And I’m not sure they should. I’m convinced that for health we need to deviate from welfarism, but I’m not convinced of it for other sectors. So from my perspective it is simply a matter of health vs everything else, and we can incorporate the ‘everything else’ into a cost-effectiveness analysis (with a societal perspective) in monetary terms. Funds can be reallocated as necessary with each budget statement (of which there seem to be a lot nowadays).

Is the Rational Addiction model inherently impossible to estimate? Journal of Health Economics [RePEc] Published 28th December 2016

Saddle point dynamics. Something I’ve never managed to get my head around, but here goes… This paper starts from the problem that empirical tests of the Rational Addiction model serve up wildly variable and often ridiculous (implied) discount rates. That may be part of the reason why economists tend to support the RA model but at the same time believe that it has not been empirically proven. The paper sets out the basis for saddle point dynamics in the context of the RA model, and outlines the nature of the stable and unstable root within the function that determines a person’s consumption over time. The authors employ Monte Carlo estimation of RA-type equations, simulating panel data observations. These simulations demonstrate that the presence of the unstable root may make it very difficult to estimate the coefficients. So even if the RA model can truly represent behaviour, empirical estimation may contradict it. This raises the question of whether the RA model is essentially untestable. A key feature of the argument relates to use of the model where a person’s time horizon is not considered to be infinite. Some non-health economists like to assume it is, which, as the authors wryly note, is not particularly ‘rational’.

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