# Chris Sampson’s journal round-up for 17th September 2018

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.

Does competition from private surgical centres improve public hospitals’ performance? Evidence from the English National Health Service. Journal of Public Economics Published 11th September 2018

This study looks at proper (supply-side) privatisation in the NHS. The subject is the government-backed introduction of Independent Sector Treatment Centres (ISTCs), which, in the name of profit, provide routine elective surgical procedures to NHS patients. ISTCs were directed to areas with high waiting times and began rolling out from 2003.

The authors take pre-surgery length of stay as a proxy for efficiency and hypothesise that the entry of ISTCs would improve efficiency in nearby NHS hospitals. They also hypothesise that the ISTCs would cream-skim healthier patients, leaving NHS hospitals to foot the bill for a more challenging casemix. Difference-in-difference regressions are used to test these hypotheses, the treatment group being those NHS hospitals close to ISTCs and the control being those not likely to be affected. The authors use patient-level Hospital Episode Statistics from 2002-2008 for elective hip and knee replacements.

The key difficulty here is that the trend in length of stay changed dramatically at the time ISTCs began to be introduced, regardless of whether a hospital was affected by their introduction. This is because there was a whole suite of policy and structural changes being implemented around this period, many targeting hospital efficiency. So we’re looking at comparing new trends, not comparing changes in existing levels or trends.

The authors’ hypotheses prove right. Pre-surgery length of stay fell in exposed hospitals by around 16%. The ISTCs engaged in risk selection, meaning that NHS hospitals were left with sicker patients. What’s more, the savings for NHS hospitals (from shorter pre-surgery length of stay) were more than undermined by an increase in post-surgery length of stay, which may have been due to the change in casemix.

I’m not sure how useful difference-in-difference is in this case. We don’t know what the trend would have been without the intervention because the pre-intervention trend provides no clues about it and, while the outcome is shown to be unrelated to selection into the intervention, we don’t know whether selection into the ISTC intervention was correlated with exposure to other policy changes. The authors do their best to quell these concerns about parallel trends and correlated policy shocks, and the results appear robust.

Broadly speaking, the study satisfies my prior view of for-profit providers as leeches on the NHS. Still, I’m left a bit unsure of the findings. The problem is, I don’t see the causal mechanism. Hospitals had the financial incentive to be efficient and achieve a budget surplus without competition from ISTCs. It’s hard (for me, at least) to see how reduced length of stay has anything to do with competition unless hospitals used it as a basis for getting more patients through the door, which, given that ISTCs were introduced in areas with high waiting times, the hospitals could have done anyway.

While the paper describes a smart and thorough analysis, the findings don’t tell us whether ISTCs are good or bad. Both the length of stay effect and the casemix effect are ambiguous with respect to patient outcomes. If only we had some PROMs to work with…

One method, many methodological choices: a structured review of discrete-choice experiments for health state valuation. PharmacoEconomics [PubMed] Published 8th September 2018

Discrete choice experiments (DCEs) are in vogue when it comes to health state valuation. But there is disagreement about how they should be conducted. Studies can differ in terms of the design of the choice task, the design of the experiment, and the analysis methods. The purpose of this study is to review what has been going on; how have studies differed and what could that mean for our use of the value sets that are estimated?

A search of PubMed for valuation studies using DCEs – including generic and condition-specific measures – turned up 1132 citations, of which 63 were ultimately included in the review. Data were extracted and quality assessed.

The ways in which the studies differed, and the ways in which they were similar, hint at what’s needed from future research. The majority of recent studies were conducted online. This could be problematic if we think self-selecting online panels aren’t representative. Most studies used five or six attributes to describe options and many included duration as an attribute. The methodological tweaks necessary to anchor at 0=dead were a key source of variation. Those using duration varied in terms of the number of levels presented and the range of duration (from 2 months to 50 years). Other studies adopted alternative strategies. In DCE design, there is a necessary trade-off between statistical efficiency and the difficulty of the task for respondents. A variety of methods have been employed to try and ease this difficulty, but there remains a lack of consensus on the best approach. An agreed criterion for this trade-off could facilitate consistency. Some of the consistency that does appear in the literature is due to conformity with EuroQol’s EQ-VT protocol.

Unfortunately, for casual users of DCE valuations, all of this means that we can’t just assume that a DCE is a DCE is a DCE. Understanding the methodological choices involved is important in the application of resultant value sets.

Trusting the results of model-based economic analyses: is there a pragmatic validation solution? PharmacoEconomics [PubMed] Published 6th September 2018

Decision models are almost never validated. This means that – save for a superficial assessment of their outputs – they are taken at good faith. That should be a worry. This article builds on the experience of the authors to outline why validation doesn’t take place and to try to identify solutions. This experience includes a pilot study in France, NICE Evidence Review Groups, and the perspective of a consulting company modeller.

There are a variety of reasons why validation is not conducted, but resource constraints are a big part of it. Neither HTA agencies, nor modellers themselves, have the time to conduct validation and verification exercises. The core of the authors’ proposed solution is to end the routine development of bespoke models. Models – or, at least, parts of models – need to be taken off the shelf. Thus, open source or otherwise transparent modelling standards are a prerequisite for this. The key idea is to create ‘standard’ or ‘reference’ models, which can be extensively validated and tweaked. The most radical aspect of this proposal is that they should be ‘freely available’.

But rather than offering a path to open source modelling, the authors offer recommendations for how we should conduct ourselves until open source modelling is realised. These include the adoption of a modular and incremental approach to modelling, combined with more transparent reporting. I agree; we need a shift in mindset. Yet, the barriers to open source models are – I believe – the same barriers that would prevent these recommendations from being realised. Modellers don’t have the time or the inclination to provide full and transparent reporting. There is no incentive for modellers to do so. The intellectual property value of models means that public release of incremental developments is not seen as a sensible thing to do. Thus, the authors’ recommendations appear to me to be dependent on open source modelling, rather than an interim solution while we wait for it. Nevertheless, this is the kind of innovative thinking that we need.

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# Method of the month: Synthetic control

Once a month we discuss a particular research method that may be of interest to people working in health economics. We’ll consider widely used key methodologies, as well as more novel approaches. Our reviews are not designed to be comprehensive but provide an introduction to the method, its underlying principles, some applied examples, and where to find out more. If you’d like to write a post for this series, get in touch. This month’s method is synthetic control.

## Principles

Health researchers are often interested in estimating the effect of a policy of change at the aggregate level. This might include a change in admissions policies at a particular hospital, or a new public health policy applied to a state or city. A common approach to inference in these settings is difference in differences (DiD) methods. Pre- and post-intervention outcomes in a treated unit are compared with outcomes in the same periods for a control unit. The aim is to estimate a counterfactual outcome for the treated unit in the post-intervention period. To do this, DiD assumes that the trend over time in the outcome is the same for both treated and control units.

It is often the case in practice that we have multiple possible control units and multiple time periods of data. To predict the post-intervention counterfactual outcomes, we can note that there are three sources of information: i) the outcomes in the treated unit prior to the intervention, ii) the behaviour of other time series predictive of that in the treated unit, including outcomes in similar but untreated units and exogenous predictors, and iii) prior knowledge of the effect of the intervention. The latter of these only really comes into play in Bayesian set-ups of this method. With longitudinal data we could just throw all this into a regression model and estimate the parameters. However, generally, this doesn’t allow for unobserved confounders to vary over time. The synthetic control method does.

## Implementation

Abadie, Diamond, and Haimueller motivate the synthetic control method using the following model:

$y_{it} = \delta_t + \theta_t Z_i + \lambda_t \mu_i + \epsilon_{it}$

where $y_{it}$ is the outcome for unit $i$ at time $t$, $\delta_t$ are common time effects, $Z_i$ are observed covariates with time-varying parameters $\theta_t$, $\lambda_t$ are unobserved common factors with $\mu_i$ as unobserved factor loadings, and $\epsilon_{it}$ is an error term. Abadie et al show in this paper that one can derive a set of weights for the outcomes of control units that can be used to estimate the post-intervention counterfactual outcomes in the treated unit. The weights are estimated as those that would minimise the distance between the outcome and covariates in the treated unit and the weighted outcomes and covariates in the control units. Kreif et al (2016) extended this idea to multiple treated units.

Inference is difficult in this framework. So to produce confidence intervals, ‘placebo’ methods are proposed. The essence of this is to re-estimate the models, but using a non-intervention point in time as the intervention date to determine the frequency with which differences of a given order of magnitude are observed.

Brodersen et al take a different approach to motivating these models. They begin with a structural time-series model, which is a form of state-space model:

$y_t = Z'_t \alpha_t + \epsilon_t$

$\alpha_{t+1} = T_t \alpha_t + R_t \eta_t$

where in this case, $y_t$ is the outcome at time $t$, $\alpha_t$ is the state vector and $Z_t$ is an output vector with $\epsilon_t$ as an error term. The second equation is the state equation that governs the evolution of the state vector over time where $T_t$ is a transition matrix, $R_t$ is a diffusion matrix, and $\eta_t$ is the system error.

From this setup, Brodersen et al expand the model to allow for control time series (e.g. $Z_t = X'_t \beta$), local linear time trends, seasonal components, and allowing for dynamic effects of covariates. In this sense the model is perhaps more flexible than that of Abadie et al. Not all of the large number of covariates may be necessary, so they propose a ‘slab and spike’ prior, which combines a point mass at zero with a weakly informative distribution over the non-zero values. This lets the data select the coefficients, as it were.

Inference in this framework is simpler than above. The posterior predictive distribution can be ‘simply’ estimated for the counterfactual time series to give posterior probabilities of differences of various magnitudes.

### Software

#### Stata

• Synth Implements the method of Abadie et al.

#### R

• Synth Implements the method of Abadie et al.
• CausalImpact Implements the method of Brodersen et al.

## Applications

Kreif et al (2016) estimate the effect of pay for performance schemes in hospitals in England and compare the synthetic control method to DiD. Pieters et al (2016) estimate the effects of democratic reform on under-five mortality. We previously covered this paper in a journal round-up and a subsequent post, for which we also used the Brodersen et al method described above. We recently featured a paper by Lépine et al (2017) in a discussion of user fees. The synthetic control method was used to estimate the impact that the removal of user fees had in various districts of Zambia on use of health care.

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