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Rare Events in Healthcare

Rare events in healthcare can pose a daunting issue with Quality Professionals, particularly in deciding how to monitor them with SPC charts. There are many examples of rare event data in healthcare including Medication Errors, Patient Falls, Nosocomial Infections, Surgical Complications and VAP events all representing important measures. Because these events occur so infrequently, conventional charts exhibit problems with them.

The problems with conventional charts are related to data collection and to theory behind the conventional chart. In the u chart and the p chart, we need some knowledge of the denominator which may not be easy to come by. With the u chart, we often use a surrogate number such as patient days to represent the area of opportunity simply because the opportunities are very difficult, if not impossible, to count. This helps us over the issue with collecting denominator data. With the p chart, using a binomial distribution, we would need to count each opportunity for an event to occur. It may be difficult to collect this data as well.

In order for these control charts to be effective, there are some "rules of thumb" for the amount of data related to the theory behind them. For the p chart, the rule of thumb is that np >= 5 where n is the subgroup size and p is the probability that the event will occur. This means that for a process with a p of .01 we need an n of 500. If we have a med error probability of 1 in 100 doses, our subgroups would need to be at least 500 doses to properly use a p chart. In other words, our period length would need to be long enough to capture this many doses for our p chart to be effective, in this case 500 doses in the period. This also translates into a longer period before we can detect that something has changed affecting the med error rate. Ideally, we would like to detect this process shift as soon as possible. If our probability is smaller, we would need even larger subgroups. Similar caveats exist for the u chart.

In the happy occurrence where we have very few of these events, our charts drawn using a reasonable time period subgroup would probably show a lot of zeros with little valuable information.

This is where the g chart enters. Developed in several papers by James Benneyan of Northeastern University, the g chart is based on the geometric distribution. An example of a geometric distribution histogram is given below.

You probably have a lot of data that exhibit this behavior. Remember, you can't find an exact geometric distribution any more than you can find an exact normal distribution.

The simplest implementation of the g chart is measuring time between events such as days between VAP events. This data is relatively easy to collect. You would only need to record the dates that events occurred.

Statit has developed a g chart based on Benneyan's formulas and will be deploying it in the next update of Statit piMD. With the piMD g chart, your data would only need the date that the event occurred. Statit piMD would do the rest.

It takes a little change in thinking to evaluate a g chart. A higher value on the chart means that the rate of the event occurring has actually decreased because the time between events is longer. For adverse events this is a good thing. Similarly, a smaller value plotted on the chart means that the rate of the event occurring has increased.

Let's take a look at a g chart with some fairly rare event data. Statit piMD needs only the date of the event occurrence. The Days_Betw_Event is included here to illustrate the rarity of the events.

154 03-Jun-2004
19 22-Jun-2004
19 11-Jul-2004
47 27-Aug-2004
2 29-Aug-2004
10 08-Sep-2004
47 25-Oct-2004
76 09-Jan-2005
2 11-Jan-2005
43 23-Feb-2005
9 04-Mar-2005
6 10-Mar-2005
37 16-Apr-2005
131 25-Aug-2005
17 11-Sep-2005
43 24-Oct-2005
9 02-Nov-2005
395 02-Dec-2006
75 15-Feb-2007
135 30-Jun-2007

The following g chart is interesting in that it does show a hint of improvement in the last few points. But notice that, with the rare occurrence of these events, it took several years to get 20 points.

Java is not enabled in browser, data tips cannot work for this graph.
g chart (click chart to activate data tips, then mouse over points for underlying data)

Following is a monthly p chart over the same time period using a constant denominator of 1000.

Java is not enabled in browser, data tips cannot work for this graph.
p chart (click chart to activate data tips, then mouse over points for underlying data)

Notice that we certainly see stratification in this chart and that we don't get much useful information from this chart. The p chart is not useful for monitoring this process, but one can certainly see the value of a g chart in detecting process changes in rare events. In future newsletters we will talk more about the Statit piMD g chart.

James Benneyan has published several articles on the g chart. The IHI website has a link to a presentation and a couple of his articles: