Episode Choices and Bundled Payment Risk

Earlier in 2013 we wrote an article about the effect of selection of individual DRGs for participation in the Medicare Bundled Payment for Care Improvement (BPCI) program. Entitled Assessing Participation Risk in the Medicare Bundled Payment Initiative, it discusses the relationship between the population size (number of episodes) and the variation in costs among episodes on the overall financial effects of participation in this program.

This article continues that discussion by investigating the relationship between the number of different episode families[1] for which a provider elects to participate and the overall variation in payment that would occur by participating in an increasing number of episodes families. A PDF of this paper can be downloaded here.

Understanding the issue

Provider organizations have many reasons for selecting various DRGs for bundling. Opportunities for alignment with post-acute providers, physician participation, previous experience in the related clinical areas, and many other factors all play a part in these decisions. Assessment of risk and opportunity is also a significant consideration. In some cases variations in the costs between clinically similar episodes represents an opportunity to create savings through elimination of those variations, but in other cases these variations are due to random factors outside of the control of the provider. These factors create uncontrollable risk, and are generally undesirable.

In our previous article we explored the relationship between population size, inter-episode cost variation and risk. Since CMS has recently opened the opportunity for participating providers to include additional episode families (or for new hospitals to join an existing convener group), some potential BPCI participants are assessing the risk effect of adding additional clinical areas for BPCI participation. Will adding certain high-variation episode families, such as those associated with chronic diseases, significantly increase the overall risk of participation, or will the effect of an increasing population size actually reduce this risk? Understanding this relationship is the goal of this article.

Analytical process

This project utilizes the same data set as the previous article. Our source of data was 2011 Medicare 100% limited data set, which contains 100% of Medicare claims for hospitals, SNFs, HHA's, and DME suppliers, and 5% of the "carrier" (non-institutional part B) claims. From this data we constructed all of the episodes that would occur throughout this entire population. For the missing carrier claims, we substituted the average carrier claim cost for each DRGs into each episode for which carrier claims were not provided. Since carrier claims only constitute 10 to 15% of the episode cost and are not highly variable this substitution should not have a significant effect on the results.

Use of this extremely large database allowed us to simulate the variation in episodes that providers might encounter, yet had not yet encountered. This was possible by stratifying the total number of episodes in each DRG into groups, each group containing the number of episodes that a BPCI participant might encounter over a year. By creating multiple groups of episodes and averaging the episode cost over groups, we can determine the variation in episode cost (which is the total Medicare payment to all providers for that episode) that could occur for a specific patient population size. For example, in DRG 470 (major joint replacement) we selected a population size of about 125 cases per year. The national database contained approximately 165,000 episodes of DRG 470, so we were able to construct approximately 1300 samples, the episode cost of each sample representing the average of 125 episodes of this DRG. This sample of averages will, according to the central limit theorem, be normally distributed, and has a frequency distribution that appears like this:

Each point on the line represents the average cost per episode of a population of approximately 125 episodes that a BPCI participant might encounter in this episode family. As can be seen, most average episode costs are between $25,000 and $30,000, but a few are as high at $39,000 or as low as $21,000. There are small, but still finite, possibilities that the average episode costs might reach these amounts though randomness in the population. The metrics described below are derived from these cost distributions.

This process differs from that used in several other analyses that we have seen recently. Those analyses appear to use the episode population of a single hospital to estimate the variation in episode costs across the universe of all episodes that the hospital might encounter. But using only data from cases the hospital has encountered provides no information about possible cases that the hospital has not encountered. By utilizing the national data set and stratifying it into samples the size of an individual hospital's episode population, we can estimate the distribution of average episode costs through a much wider population range. This probably biases the amount of variation slightly upwards since the variation in the cases that an individual hospital may encounter is probably lower than the variation across the country, which means that the variability of costs described here is probably slightly higher than that which would be encountered by a single hospital.


We will use two main metrics in our analysis of risk. The first is the "coefficient of variation (CV)" of the total payment for all episodes occurring in a year. The CV is the standard deviation divided by the mean, and can be used to compare the relative variation among two different sets of data. The "total payments" amount is the sum of the payment amounts for all DRGs in which the organization is participating, and will obviously increase as the number of episode families increases. Since it is a percentage, the CV doesn't increase as total payments increase.

The other metric is the "maximum loss amount" for a participating organization, and is expressed in dollars. This reflects the difference in the total covered episode population cost between the overall average population cost (as a surrogate for the target payment) and the population cost of each sample. In graphical terms, it's the difference between the height of each bar on the above graph and the average height of all bars. That difference is graphed below.

The maximum loss per episode amount is indicated by the red arrow in the graph. This is the amount at the "tail" of the distribution of all participant costs, above which three standard deviations (97.5%) of episode costs will lie. This means that there's only a 2.5% chance that loss per episode will exceed this amount.

Also note that in this example the cost distribution isn’t exactly symmetrical – the maximum loss is higher than the maximum savings. This is because the theoretical minimum episode cost is zero (the actual minimum episode cost is the hospital’s DRG payment plus physician payments for the inpatient stay, assuming no post-discharge services), but there’s no maximum episode cost.

Selecting episodes

Although there is a virtually limitless combination of episode families that could be selected by BPCI participants, we chose to model three alternatives - a single episode family, a group of five families and all families. These selections fit with the choices made by current BPCI participants. For the single episode family we selected "Major Joint Replacement of the Lower Extremity", composed of DRGs 469 and 470. This is a relatively low CV episode family with a long history of inclusion in other Medicare demonstration projects, which may be why it's the most popular choice for BPCI.

For the group of five families we reviewed the initial episode choices published by CMS and selected the episode families most frequently chosen by participants. The episode families added were heart failure, pneumonia, asthma and PCI.

In the third sample set, we included all episode families. Some participants have selected this option, presumably to have the greatest possibility of creating savings. It has also been suggested that this large population reduces participation risk, and testing that assertion is one goal of this analysis.

Results of the analysis

For each of the alternatives we computed the following measures for an average participating provider:

  • Number of episodes from all participating episode families
  • Total cost - the total of all Medicare payments for episodes in which the participant in participating
  • Coefficient of variation of the average cost of the population of all episodes
  • The "maximum loss", which is the difference between the target payment and the average episode payment at three standard deviations from the mean episode payment, multiplied by the number of episodes.


Top 1 Episode Family

Top 5 Episode Families

All Episode Families

Coefficient of Variation










Total Episode Payments


 $ 3,128,981



 $ 12,890,827



 $ 40,041,173


Maximum Payment Loss


 $  450,003



 $ 1,214,278



 $ 2,876,488




This analysis results in some interesting conclusions. First, the CV almost always decreases as episode families are added to the population. The CV of the combination of two episode families is almost always lower than the CVs of each family alone. Combining participation in a relatively low CV family such as major joint replacements with a high CV family such as CHF resulted in a lower CV than in major joint replacements alone. From this perspective, statistical risk is reduced by participating in a larger number of episode families, even those families that have high CVs themselves.

This risk reduction comes at a price, however. To obtain a lower CV, more dollars must be put into play, with the possibility of larger financial loss. In our example, to achieve the reduction in CV from 4.8%, (arising from participating in major joint replacements) to 2.4%, (arising from participation in all episode families), the maximum dollar loss increases from $450,000  to $2.8 million, more than six times the financial exposure of the smaller episode family group. The loss per episode (which is measured by the CV) is lower, but that loss is multiplied by a larger number of episodes.

Which alternative is more preferable? This gets into the issue of "utility theory“ in which this author claims no significant expertise. Utility theory relates the amount of possible loss to the odds of winning and losing, and presumably explains why there are no $1,000 slot machines that offer the same odds as $1 slot machines. Individuals and organizations make the different decisions when different amounts of money are at risk, even with the same odds. An organization may choose a statistically risker (higher CV) alternative that has a lower dollar risk over a lower-CV alternative with greater financial risk based on the organization’s perception of the utility of the situation.

Of course, risk isn't the only consideration for participation in an episode family.  The organization should have an implementable plan to reduce the costs of each episode family in which it participates. This generally requires the committed involvement of the medical staff in each of the clinical areas involved, although some initiatives may span all clinical areas. Absent an implementable plan, the organization is simply playing the odds of encountering a relatively low-cost population rather than a higher-cost group of patients in the additional episode families. This may indeed reduce some statistical risk but meets none of the "triple aim" goals of the BPCI. It’s a Las Vegas-type of gamble that probably isn’t appropriate for a healthcare provider.

So what’s the right answer? Well, it’s the same answer as readers might have assumed before reading this article. Providers should participate in episode families where they have opportunities, through care management activities focused on those patients, to improve care and reduce cost. They shouldn’t avoid those families because of the added risk, since adding episode families will reduce statistical risk. However, they shouldn’t include episode families in which they have no opportunity for clinical improvements, since the added dollars at risk simply represent risk, not opportunity.

[1] CMS refers to a group of related DRG that must all be included in a participation contract as an “episode”. Since that term can also refer to an individual occurrence (an index admission followed by a post-discharge period), we use the term "episode family" to refer to these groups of DRGs.