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A Grand (or First-Rate) Idea

Bill Farrell, Ph.D.
Senior Analyst
Sutter Health

Sutter Health is a family of not-for-profit hospitals and physician organizations that share resources and expertise to advance health care quality. Serving more than 100 communities in Northern California, Sutter Health is a regional leader in cardiac care, cancer treatment, orthopedics, obstetrics, and newborn intensive care, and is a pioneer in advanced patient safety technology.

Two common measures of quality in health care are "medication errors per 10,000 prescriptions" and "falls per thousand patient days." If you're following St. Elsewhere's "New Moms" initiative, you know they're reporting low APGAR scores per thousand, as in "St. Elsewhere had 9.4 low APGAR scores per thousand deliveries in the fourth quarter." Finally, those of you in a managed care environment will be familiar with statements like "Hospital utilization for commercial members at St. Eligius Medical Group is running at 115 bed days per thousand."

What is it with this "per thousand" thing? It's actually a little more complicated than you might expect, since there are two distinct scenarios where the terminology arises. The first is what I'll call rare events, and the second is utilization. Let's start with rare events. If St. Elsewhere has 8 low APGAR scores in 853 deliveries, we could calculate the percentage as 0.9%, but that's a little hard to interpret. Instead we might do the following calculation:

(8 / 853) x 1,000 = 9.4

and report that St. Elsewhere had 9.4 low APGAR scores per thousand deliveries. Similarly, if the hospital had 3 medication errors in 23,000 prescriptions, we might be better understood if we reported

(3 / 23,000) x 10,000 = 1.3

1.3 med errors per 10,000 prescriptions, as opposed to .01% medication errors.

The 9.4 and 1.3 are known technically as rates, one of three things that can result from dividing two numbers. So 2 / 50 = .04, a proportion; 2 / 50 x 100 = 4, a percentage; and 2 / 50 x 1,000 = 40 per thousand, a rate.

You'll note that in the case of rates, the numbers themselves are fictitious. In the first example (9.4 low APGARs per thousand) the hospital did not have 9.4 low APGARs and it did not have 1,000 deliveries. We simply calculate and report these rates to make small numbers easier to grasp.

And in the second example you can see that we don't always use "thousand" as the denominator in this kind of reporting. The rule of thumb is that we choose a denominator that allows us to state the numerator as a number greater than or equal to 1. For medication errors, the most commonly used denominator is 10,000. Other examples (outside of health care) might include "4.3 accidents per 100,000 miles driven," and "7.6 satisfactory airline meals per million passenger miles flown."

We'll turn now to the second case where "per thousand" comes into play: managed care utilization. To illustrate the point, let's ask Dr. d'Arcangelis how he's doing at keeping his pediatric patients out of the ER. He says, "I'm doing great. Only four of my pediatric patients went to the ER." This is not very useful, since we don't know

a. how many pediatric patients he has,
b. what time period he's talking about, or
b. the total number of ER visits for those four children.

If we know that Dr. d'Arcangelis has 500 pediatric patients and that he's talking about 3Q04, we can say that 4 / 500 or .8% of his pediatric patients visited the ER in the third quarter. Given that .8% is a little difficult to interpret, we might (as we did above) note that Dr. d'Arcangelis' pediatric patients visited the ER at a rate of 8 per thousand in the third quarter (4 / 500 x 1,000 = 8).

Suppose we now learn that those four pediatric patients visited the ER a total of 10 times during the third quarter. The 10 visits are what we commonly refer to as "utilization," and while we COULD calculate a percentage as above (10 / 500 = 2%), this percentage is meaningless, since numerator and denominator are not comparable.

Typically we use member months as the denominator in calculating utilization. Since individual members can move in and out of a physician's panel (or medical group) almost at will, member months is seen as the fairest count of "opportunities" for utilization to occur. So if someone is enrolled with a medical group for three months, that counts as three member months. If three different people are enrolled in a group for one month, that's also three member months.

Because utilization can be a difficult concept to grasp, we'll switch to a new physician, Dr. Gabriel, who has 1,000 patients in her panel for each of the three months of 3Q04. We see 10 ER visits in July, 10 visits in August, and 10 in September. It seems obvious in this case that Dr. Gabriel's utilization is going to work out to 30 visits per thousand members for the quarter, but getting there will be a little tricky.

First, we divide the 10 visits in July by the 1,000 member months in July, getting .01 visits per 1 member month. If we multiply both sides of this by 1,000 to scale it up, we get 10 visits per 1,000 member months. Realizing that this is a one-month period, a more general statement of the result is "10 visits per thousand member months per month." Since "month" is now in both denominators, it cancels out, leaving us with "10 visits per thousand members." So with 10 visits per thousand members in each of three months, we end up with 30 visits per thousand members for the quarter. The actual calculation would look like this:

30 total visits / 3,000 total member months x 3 months x 1,000 = 30

Turning back to Dr. d'Arcangelis, we recall that he had 500 pediatric patients with a total of 10 ER visits in the quarter. His quarterly utilization would be calculated as:

10 total visits / 1,500 total member months x 3 months x 1,000 = 20

As a reminder, when we say "20 ER visits per thousand members" we're actually saying "20 ER visits per thousand EQUIVALENT members," since we'll almost always see some enrollment changes during a quarter.

We've calculated utilization for a quarter, but in managed care circles this number is almost always annualized (multiplied by 4). So in this case an analyst would look at a quarter's worth of Dr. d'Arcangelis' data, run the numbers, and state that "Dr. d'Arcangelis' pediatric ER utilization is running at 80 per thousand." This shorthand expresses the following concept: IF Dr. d'Arcangelis had 1,000 pediatric patients, and IF they visited the ER for a year at the same frequency that was observed for a quarter, we could expect to see 80 visits.

Let's summarize: Dr. d'Arcangelis has 500 pediatric patients. Four of them (.8%) went to the ER in the first quarter, for a rate of 8 per thousand. With a total of 10 visits, Dr. d'Arcangelis' utilization is reported as 80 ER visits per thousand equivalent children per year.

A final word on using statistical process control to track these kinds of measures: rare events are usually best suited to the U chart, while utilization can only be tracked using the I chart.

Technical Note: Discerning readers will have noticed that there are two classes of "rare events": one where the numerator is a subset of the denominator and percentaging is appropriate (low APGAR scores / all APGAR scores) and one where numerator and denominator are not comparable and rates are appropriate (falls / patient days). Mathematically, P charts and U charts will give identical results with these two classes of data. It probably makes more sense to stick with U charts in both cases, however, since (a) the U chart is strictly appropriate in the latter case (falls), and (b) the U chart gets you thinking "per thousand" rather than "percent" in the former case (APGAR).