From time to time I post things that are essentially pages of my research notebook. It’s a way for me to keep track of important papers and methods. This is one such post. It may not appeal to everyone, especially the details. Read what you like, and trust that more posts of the types you love are forthcoming.
There are two ways of characterizing hospital market structure, or the degree of competitiveness or concentration among hospitals. One is based on patient flows, the other on prices, or specifically the degree to which prices charged by one hospital affect those charged by others. My prior reading of the literature on hospital mergers led me to believe that patient flow approaches have been discredited for that application. I now think that’s too strong a conclusion, and there is a legitimate role for them.
Nearly six months ago I described how one patient flow based approach–the Elzinga/Hogarty (E/H) method–is flawed, and I went on to discuss other price-based approaches that measure the degree of substitutability of one hospital for another. More recently, I’ve noticed that a certain patient flow approach is still employed in economic studies, the recent cost shifting paper by Vivian Wu among them. An important distinction is how the hospital market structure measure is used: as a covariate (a control variable) in the study of something else versus as the dependent variable (the focus of study). For the former, patient flow approaches may be OK. For the latter, it seems price-based approaches are to be preferred.
If a patient flow measure is less credible than a price-based one, why would it be OK even as a control variable? This question is on the boundary of art and science. There are a lot of less-than-perfect aspects to every study. Even methods and measures that are accepted and widely applied are known to be sub-optimal in some respects. That’s the price of tractability. To make progress on complex questions while expending a reasonable amount of resources one has to sacrifice the perfect for the good enough.
Price data are closely guarded. To obtain good measures of actual transaction prices is difficult for a study of a region or a few hospitals, and impossible nationally. Proxies for transaction prices and other ways of intuiting their effects exist but in using them one is already moving away from the perfect. In some cases, a large amount of heavy lifting is required, more than could be justified for the construction of a covariate in the study of something else. Finally, it is plausible that patient flow measures while flawed are only so to the extent many other measures are flawed. If those flaws lead to no or small bias in estimates of the measures of focus (which is plausible) then there is no harm in using them. As I said, this is as much art as science.
Now for the details. In the remainder of this post I will summarize some of the patient flow based measures used in the literature. My references for doing so are two papers by Zwanziger, Melnick, and Mann, one of which also includes Bamezai as a co-author: (1) Price competition and hospital cost growth in the United States (1989-1994) (Health Economics 8:233-243, 1999) and (2) Measures of hospital market structure: a review of the alternatives and a proposed approach (Socio-Econ. Plann. Sci. 24(2):81-95, 1990).
For a specific hospital, areas defined by zip codes that contribute more admissions in a period of time (a year, say) to that hospital than a cutoff are considered part of that hospital’s market area. There are three approaches to defining the cutoff denoted as “straight marginal,” “maximum marginal,” and “minimum marginal.” Each is summarized below.
Straight marginal. This is the most straight-forward way of specifying a cutoff. Just declare it. If a zip code contributes more than X% of hospital admissions then it is included in the market area. A limitation is that this approach comports poorly with respect to the variation across hospitals in geographic distribution of patients. Some have long tails, drawing a lot of patients from many distant zip codes. Others have a more compact catchment area. One can imagine that for hospitals of the former type, setting X to a value of, say, 1% might exclude a lot of patients. In the (unrealistic) extreme, where a hospital only draws up to 0.9% from any zip code from which it draws any patients, this cutoff would define a market area consisting of no zip codes. That’s not good.
Maximum marginal. This method avoids the limitation just described by defining a cutoff such that a fixed percentage of a hospital’s admissions are accounted for. In this way, one can be assured that zip codes that collectively account for, say, 80% of a hospital’s admissions are included in its market area. One can combine the straight marginal and the maximum marginal approaches and include only zip codes that contribute a certain proportion of patients such that a cumulative maximum is not exceeded. A concern with this approach is that once the maximum is reached–80% in the above example–some significant zip codes are excluded (imagine the largest one excluded contributes 5%–that’s big!).
Minimum marginal. This rule establishes a minimum cumulative proportion that must be reached. It is meant to be combined with the straight marginal approach. The idea is that one collects zip codes in order from largest to smallest contributor until (a) a minimum total proportion (50%, say) of admissions is accounted for and (b) the next largest contributing zip code contributes no more than a specified percentage (1%, say).
With a hospital’s market area defined by one or another of the aforementioned methods, one can then identify the hospital’s competitors. A competitor of a hospital is one that draws a significant proportion of patients from its market area (3%, say). With this information, one can then define a measure of competition, such as the Hirschmann-Herfindahl index (HHI). Note that all of the above can be done by diagnosis to reflect the fact that hospitals have different market areas and different sets of competitors by type of patient. Finally, one can examine how sensitive HHI is to the various methods (and variations in thresholds). In the work cited above, it has been found that HHI is very robust to such variations. In this sense, within some reasonable range, it doesn’t matter how market area is defined, so long as it is done so in a consistent and sensible way.
If you’ve read this far and understood everything, you should consider a career in health economics. Or maybe you already have one.
