machine learning | The Academic Health Economists' Blog

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.

Machine learning: an applied econometric approach. Journal of Economic Perspectives [RePEc] Published Spring 2017

Machine learning tools have become ubiquitous in the software we use on a day to day basis. Facebook can identify faces in photos; Google can tell you the traffic for your journey; Netflix can recommend you movies based on what you’ve watched before. Machine learning algorithms provide a way to estimate an unknown function $f$ that predicts an outcome $Y$ given some data $x$ : $Y = f(x) + \epsilon$ . The potential application of these algorithms to many econometric problems is clear. This article outlines the principles of machine learning methods. It divides econometric problems into prediction, $\hat{y}$ , and parameter estimation, $\hat{\beta}$ and suggests machine learning is a useful tool for the former. However, this distinction is a false one, I believe. Parameters are typically estimated because they represent an average treatment effect, say $E(y|x=1) - E(y|x=0)$ . But, we can estimate these quantities in ‘ $\hat{y}$ problems’ since $f(x) = E(y|x)$ . Machine learning algorithms, therefore, represent a non-parametric (or very highly parametric) approach to the estimation of treatment effects. In cases where functional form is unknown, where there may be nonlinearities in the response function, and interactions between variables, this approach can be very useful. They do not represent a panacea to estimation problems of course, since interpretation rests on the assumptions. For example, as Jennifer Hill discusses, additive regression tree methods can be used to estimate conditional average treatment effects if we can assume the treatment is ignorable conditional on the covariates. This article, while providing a good summary of methods, doesn’t quite identify the right niche where these approaches might be useful in econometrics.

Incorporating equity in economic evaluations: a multi-attribute equity state approach. European Journal of Health Economics [PubMed] Published 1st June 2017

Efficiency is a key goal for the health service. Economic evaluation provides evidence to support investment decisions, whether displacing resources from one technology to another can produce greater health benefits. Equity is generally not formally considered except through the final investment decision-making process, which may lead to different decisions by different commissioning groups. One approach to incorporating equity considerations into economic evaluation is the weighting of benefits, such as QALYs, by group. For example, a number of studies have estimated that benefits of end-of-life treatments have a greater social valuation than other treatments. One way of incorporating this into economic evaluation is to raise the cost-effectiveness threshold by an appropriate amount for end-of-life treatments. However, multiple attributes may be relevant for equity considerations, negating a simplistic approach like this. This paper proposed a multi-attribute equity state approach to incorporating equity concerns formally in economic evaluation. The basic premise of this approach is to firstly define a set of morally relevant attributes, to secondly derive a weighting scheme for each set of characteristics (similarly to how QALY weights are derived from the EQ-5D questionnaire), and thirdly to apply these weights to economic evaluation. A key aspect of the last step is to weight both the QALYs gained by a population from a new technology and those displaced from another. Indeed, identifying where resources are displaced from is perhaps the biggest limitation to this approach. This displacement problem has also come up in other discussions revolving around the estimation of the cost-effectiveness threshold. This seems to be an important area for future research.

Financial incentives, hospital care, and health outcomes: evidence from fair pricing laws. American Economic Journal: Economic Policy [RePEc] Published May 2017

There is a not-insubstantial literature on the response of health care providers to financial incentives. Generally, providers behave as expected, which can often lead to adverse outcomes, such as overtreatment in cases where there is potential for revenue to be made. But empirical studies of this behaviour often rely upon the comparison of conditions with different incentive schedules; rarely is there the opportunity to study the effects of relative shifts in incentive within the same condition. This paper studies the effects of fair pricing laws in the US, which limited the amount uninsured patients would have to pay hospitals, thus providing the opportunity to study patients with the same conditions but who represent different levels of revenue for the hospital. The introduction of fair pricing laws was associated with a reduction in total billing costs and length of stay for uninsured patients but little association was seen with changes in quality. A similar effect was not seen in the insured suggesting the price ceiling introduced by the fair pricing laws led to an increase in efficiency.

Credits

Antony Theobald (CC BY-NC-ND 2.0)

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 learning, discrete 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.

Credits