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.
Days_Betw_Event

Date 
154 
03Jun2004 
19 
22Jun2004 
19 
11Jul2004 
47 
27Aug2004 
2 
29Aug2004 
10 
08Sep2004 
47 
25Oct2004 
76 
09Jan2005 
2 
11Jan2005 
43 
23Feb2005 
9 
04Mar2005 
6 
10Mar2005 
37 
16Apr2005 
131 
25Aug2005 
17 
11Sep2005 
43 
24Oct2005 
9 
02Nov2005 
395 
02Dec2006 
75 
15Feb2007 
135 
30Jun2007 
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.
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.
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:
