Thesis Thursday: Andrea Gabrio

On the third Thursday of every month, we speak to a recent graduate about their thesis and their studies. This month’s guest is Dr Andrea Gabrio who has a PhD from University College London. If you would like to suggest a candidate for an upcoming Thesis Thursday, get in touch.

Title
Full Bayesian methods to handle missing data in health economic evaluation
Supervisors
Gianluca Baio, Alexina Mason, Rachael Hunter
Repository link
http://discovery.ucl.ac.uk/10072087

What kind of assumptions about missing data are made in trial-based economic evaluations?

In any analysis, assumptions about the missing values are always made, about those values which are not observed. Since the final results may depend on these assumptions, it is important that they are as plausible as possible within the context considered. For example, in trial-based economic evaluations, missing values often occur when data are collected through self-reported patient questionnaires and in many cases it is plausible that patients with unobserved responses are different from the others (e.g. have worse health states). In general, it is very important that a range of plausible scenarios (defined according to the available information) are considered, and that the robustness of our conclusions across them is assessed in sensitivity analysis. Often, however, analysts prefer to ignore this uncertainty and rely on ‘default’ approaches (e.g. remove the missing data from the analysis) which implicitly make unrealistic assumptions and possibly lead to biased results. For a more in-depth overview of current practice, I refer to my published review.

Given that any assumption about the missing values cannot be checked from the data at hand, an ideal approach to handle missing data should combine a well-defined model for the observed data and explicit assumptions about missingness.

What do you mean by ‘full Bayesian’?

The term ‘full Bayesian’ is a technicality and typically indicates that, in the Bayesian analysis, the prior distributions are freely specified by the analyst, rather than being based on the data (e.g. ’empirical Bayesian’). Being ‘fully’ Bayesian has some key advantages for handling missingness compared to other approaches, especially in small samples. First, a flexible choice of the priors may help to stabilise inference and avoid giving too much weight to implausible parameter values. Second, external information about missingness (e.g. expert opinion) can be easily incorporated into the model through the priors. This is essential when performing sensitivity analysis to missingness, as it allows assessment of the robustness of the results to a range of assumptions, with the uncertainty of any unobserved quantity (parameters or missing data) being fully propagated and quantified in the posterior distribution.

How did you use case studies to support the development of your methods?

In my PhD I had access to economic data from two small trials, which were characterised by considerable amounts of missing outcome values and which I used as motivating examples to implement my methods. In particular, individual-level economic data are characterised by a series of complexities that make it difficult to justify the use of more ‘standardised’ methods and which, if not taken into account, may lead to biased results.

Examples of these include the correlation between effectiveness and costs, the skewness in the empirical distributions of both outcomes, the presence of identical values for many individuals (e.g. excess zeros or ones), and, on top of that, missingness. In many cases, the implementation of methods to handle these issues is not straightforward, especially when multiple types of complexities affect the data.

The flexibility of the Bayesian framework allows the specification of a model whose level of complexity can be increased in a relatively easy way to handle all these problems simultaneously, while also providing a natural way to perform probabilistic sensitivity analysis. I refer to my published work to see an example of how Bayesian models can be implemented to handle trial-based economic data.

How does your framework account for longitudinal data?

Since the data collected within a trial have a longitudinal nature (i.e. collected at different times), it is important that any missingness methods for trial-based economic evaluations take into account this feature. I therefore developed a Bayesian parametric model for a bivariate health economic longitudinal response which, together with accounting for the typical complexities of the data (e.g. skewness), can be fitted to all the effectiveness and cost variables in a trial.

Time dependence between the responses is formally taken into account by means of a series of regressions, where each variable can be modelled conditionally on other variables collected at the same or at previous time points. This also offers an efficient way to handle missingness, as the available evidence at each time is included in the model, which may provide valuable information for imputing the missing data and therefore improve the confidence in the final results. In addition, sensitivity analysis to a range of missingness assumptions can be performed using a ‘pattern mixture’ approach. This allows the identification of certain parameters, known as sensitivity parameters, on which priors can be specified to incorporate external information and quantify its impact on the conclusions. A detailed description of the longitudinal model and the missing data analyses explored is also available online.

Are your proposed methods easy to implement?

Most of the methods that I developed in my project were implemented in JAGS, a software specifically designed for the analysis of Bayesian models using Markov Chain Monte Carlo simulation. Like other Bayesian software (e.g. OpenBUGS and STAN), JAGS is freely available and can be interfaced with different statistical programs, such as R, SAS, Stata, etc. Therefore, I believe that, once people are willing to overcome the initial barrier of getting familiar with a new software language, these programs provide extremely powerful tools to implement Bayesian methods. Although in economic evaluations analysts are typically more familiar with frequentist methods (e.g. multiple imputations), it is clear that as the complexity of the analysis increases, the implementation of these methods would require tailor-made routines for the optimisation of non-standard likelihood functions, and a full Bayesian approach is likely to be a preferable option as it naturally allows the propagation of uncertainty to the wider economic model and to perform sensitivity analysis.

Thesis Thursday: Elizabeth Lemmon

On the third Thursday of every month, we speak to a recent graduate about their thesis and their studies. This month’s guest is Dr Elizabeth Lemmon who has a PhD from the University of Stirling. If you would like to suggest a candidate for an upcoming Thesis Thursday, get in touch.

Title
Essays on the provision of long term care to older adults in Scotland
Supervisors
David Bell, Alasdair Rutherford
Repository link
http://hdl.handle.net/1893/29369

What long term care provision is available to older people in Scotland?

Long term care (LTC) in Scotland comprises both formal care and unpaid care. Formal care encompasses care provided by professionals in a person’s own home as well as care in a residential care setting. Unpaid care is care that is provided by family members, friends, or neighbours. Long term care is provided to older people who need help because they are ill, frail or have a disability. It might mean help with more administrative tasks such as filling in forms, paying bills, shopping, and housework, but can also mean help with things of a more personal nature such as washing and dressing. Since 2002, individuals living in Scotland aged 65 or over are entitled to free personal care (FPC) at home, subject to a needs assessment. This makes Scotland quite different to England, where personal care costs are borne by the service user and their families, and provides a unique opportunity to conduct research.

What were the pros and cons of your chosen data sources?

I used three data sources in my PhD. Those included the Family Resources Survey (FRS), the Scottish Government’s administrative Social Care Survey (SCS) and publically available data zone level data. The key benefit of using survey data like the FRS was that they captured information about care recipients and their caregivers. I used these data in my third paper to look at unpaid carers’ Standard of Living (SoL). The down side of the FRS is that it only captures a subset of the population, which might be systematically different from the population at large. At the same time, although there is information on carers and the person they are caring for, this information is very limited for those who are not living with the care recipient. On the other hand, the benefit of using the SCS, which I used in my first two papers, is that it captures population level information about the provision of LTC services. However, unlike the FRS, the SCS was designed for administrative purposes meaning that it lacks the richness of information on client circumstances and characteristics. One solution to this is to use data zone level information as a proxy for those characteristics, but often this is not enough. Overall, the PhD highlighted both the strengths and weaknesses of working with these different data sources, pointing to the potential of using linked administrative and survey data in future research.

How did you identify sources of inequity in the provision of long term care?

Inequity in the provision of LTC exists if there are differences in LTC provision after accounting for differences in need. I investigated this issue of inequity in my first paper. In particular, we observed from the raw data that there are big differences in FPC provision between the 32 Scottish local authorities. As I mentioned, FPC is available to anyone in Scotland aged 65+ who needs it. Perhaps those differences are due to differences in need. But I didn’t find that this was the case. It seemed that, even after accounting for the need of local authority populations, via the proportion of disability benefit claims, there were still large differences in provision of FPC. I modelled this inequity using a simple regression framework. The results from the regressions found that there is evidence of geographic inequity in the provision of FPC in Scotland. In particular, the analysis suggests that the differences between the FPC rate and the rate of disability are not consistent across local authorities, suggesting that a needy individual might be more or less likely to receive care depending on where they live. One explanation for this is that local authorities differ in terms of their practices for managing the demand for FPC. However, this is an area that would require more detailed investigation with individual local authorities to understand their practices.

What is the role of unpaid care, and how did you model that?

Unpaid care is defined as care that is provided by family members, partners, or friends to those who require help because they are ill, frail, or have a disability. The care that they provide is unpaid and often considered as having a zero cost in economic evaluations. This might lead to inefficient resource allocation and poor policy decisions. In my second paper, I tried to model the effect that unpaid carers have on the FPC use of the cared for. This was difficult due to the potential reverse causality that occurs between the two. I compared different models to try to estimate this effect. Overall, my findings suggest that unpaid carers likely complement FPC services in Scotland. This relationship might be due to unpaid carers advocating on behalf of the cared for, and demanding services from the local authority for them. They might do this because they require more support to enable them to remain in the labour force. It could also be that the type of care unpaid carers provide is different to that provided by formal carers.

Why did you use a ‘standard of living’ approach and what can it tell us about the cost of unpaid care?

The motivation for using the SoL approach, as implemented by Morciano et al (2015), was really that we felt it might capture more of the trade-offs that are involved in providing care. Specifically, it is expected that unpaid carers have to divert resources in order to pay for goods and services for the person they are caring for. Compared to the conventional costing methods which have focused on attaching a monetary value to the time a carer gives up in order to provide care, we argue that the SoL approach may capture a wider array of the trade-offs that are involved in providing unpaid care. For example, are unpaid carers less able to afford to go on holiday or to take part in a regular leisure activity? If it is the case that unpaid carers have to invest resources into providing care then they might have fewer resources to devote to their own needs and wants, resulting in unpaid carers having a lower SoL compared to non-carers. The results suggest that unpaid carers who are living with the person they are caring for would require compensation of £229 per week in order for them to reach the same SoL as a non-carer.

What are the key steps necessary to identify and address unmet need in this context?

My research highlighted that there is possibly unmet need for FPC in Scotland and that this could potentially be more likely for older people who don’t have an unpaid carer helping them to access FPC services. Understanding this unmet need is a key area which requires further research. Unfortunately, it is difficult to measure and we only ever observe the met need for care, i.e. those who end up receiving formal care services. Thus, prior to addressing unmet need, it is important that we can measure it. One step necessary in doing so would be to carry out detailed investigations with individual local authorities. This would help us understand more about the needs of those individuals who apply for FPC but who are turned down. But this is only part of the picture. Understanding where individuals need FPC but don’t apply, either due to transaction costs, a lack of information on how to access those services, or other reasons, is far more difficult. One approach to gaining insight on these individuals could be to conduct qualitative interviews with them and their families.

Thesis Thursday: Feng-An Yang

On the third Thursday of every month, we speak to a recent graduate about their thesis and their studies. This month’s guest is Dr Feng-An Yang who has a PhD from Ohio State University. If you would like to suggest a candidate for an upcoming Thesis Thursday, get in touch.

Title
Three essays on access to health care in rural areas
Supervisors
Daeho Kim, Joyce Chen
Repository link
http://rave.ohiolink.edu/etdc/view?acc_num=osu152353045188255

What are the policy challenges for rural hospitals in the US?

Rural hospitals have been financially vulnerable, especially after the implementation of Medicare Prospective Payment System (PPS) in 1983, under which hospitals receive a predetermined, fixed reimbursement for their inpatient services. Under the PPS, they suffer from financial losses as their costs tend to exceed the reimbursement rate due to their smaller size and lower patient volume than their urban counterparts (Medicare Payment Advisory Commission, 2001 [PDF]). As a result, a noticeable number of rural hospitals have closed since the implementation of PPS (Congressional Budget Office, 1991 [PDF]).

This closure trend has slowed down thanks to public payment policies such as the Critical Access Hospitals (CAH) program, but rural hospitals are continuing to close their doors and a total of 107 rural hospitals have closed from 2010 to present according to the North Carolina Rural Health Research Program. This issue has raised public concern for rural residents’ access to health services and health status, and how to keep rural hospitals open has become an important policy priority.

Which data sources and models did you use to identify key events?

My dissertation investigated the impact of the CAH program and hospital closure by compiling data from various sources. The primary data come from the Medicare cost report, which contains detailed financial statements for nearly every U.S. hospital. Historical data on health care utilization at the county-level are obtained from the Area Health Resource File. County-level mortality rates are calculated from the national mortality files. Lastly, the list of CAHs and closed hospitals is obtained from the Flex Monitoring Team and American Hospital Association Annual Survey, respectively. This list contains information on the hospital identifier and year of event which is key to my empirical strategy.

To identify the impact of key events (i.e., CAH conversion and hospital closure), I use an event-study approach exploiting the variation in the timing of events. This approach estimates the changes in outcome for the time relative to the ‘event time’. A primary advantage of this approach is that it allows a visual examination of the evolution of changes in outcome before and after the event.

How can policies relating to rural hospitals benefit patients?

This question is not trivial because public payment policies are not directly linked to patients. The primary objective of these policies is to strengthen rural hospitals’ financial viability by providing them with enhanced reimbursement. As a result, it has been expected that, under these policies, rural hospitals will improve their financial conditions and stay open, thereby maintaining the access to health services for rural residents. Broadly speaking, public payment policies can lead to an increase in accessibility if we compare patient access to health services between counties with at least one hospital receiving financial support and counties without any hospitals receiving financial support.

I look at patient benefits from three aspects: accessibility, health care utilization, and mortality. My research shows that the CAH program has substantially improved CAHs’ financial conditions and as a result, some CAHs that otherwise would have been closed have stayed open. This in turn leads to an increase in rural residents’ access to and use of health services. We then provide suggestive evidence that the increased access to and use of health care services have improved patient health in rural areas.

Did you find any evidence that policies could have negative or unexpected consequences?

Certainly. The second chapter of my dissertation focused on skilled nursing care which can be provided in either swing beds (inpatient beds that can be used interchangeably for inpatient care or skilled nursing care) or hospital-based skilled nursing facilities (SNFs). Since the services provided in swing beds and SNFs are equivalent, differential payments, if present, may encourage hospitals to use one over the other.

While the CAH program provides enhanced reimbursement to rural hospitals, it also changes the swing bed reimbursement method such that swing bed payments are more favorable than SNF payments. As a result, CAHs may have a financial incentive to increase the use of swing beds over SNFs. By focusing on CAHs with a SNF, my research shows a remarkable increase in swing bed utilization and this increase is fully offset by the decrease in SNF utilization. These results suggest that CAHs substitute swing beds for SNFs in response to the change in swing bed reimbursement method.

Based on your research, what would be your key recommendations for policymakers?

Based on my research findings, I would make two recommendations for policymakers.

First, my research speaks to the ongoing debate over the elimination of CAH designation for certain hospitals. Loss of CAH designation could have serious financial consequences and subsequently have potentially adverse impacts on patient access to and use of health care. Therefore, I would recommend policymakers to maintain the CAH designation.

Second, while the CAH program has improved rural hospitals’ financial conditions, it has also created a financial incentive for hospitals to use the service with a higher reimbursement rate. Thus, my recommendation to policymakers would be to consider potentially substitutable health care services when designing reimbursement rates.