Turning SPC Charts into Confidence Interval Charts
Bill Farrell, Ph.D.
Senior Analyst
Sutter Health
Sutter Health is a family of notforprofit
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.
As Sutter Health has promulgated statistical
process control for tracking outcomes, some
confusion has arisen regarding the interpretation
of SPC charts and the kind of information that
can be placed on them.
Specifically, people have wanted to see Sutter
Health norms, California norms, national benchmarks,
etc. drawn on SPC charts, so they can get an
idea of where they stand with respect to a target.
The problem with doing this is that it fosters
a mentality where attention is focused on the
target, rather than the process. Statistical
process control concerns itself with the variability
of the process, not the level of the process.
When we see a significant trigger on a patient
satisfaction SPC chart, that data point is significant
because of the past history of the process,
not because the point is above or below some
norm.
Still, people have every right to know where
they stand in relation to others. How can we
present this information in a meaningful and
statistically valid way? The answer lies in
confidence intervals.
Let's say that a sample of 300 patients discharged
from a hospital in 1Q 2004 gives a rating of
86 on nursing satisfaction. If we asked every
patient discharged in the first quarter to rate
nursing satisfaction, would we still get 86?
Probably notthere is some uncertainty associated
with that number. How much uncertainty? Let's
say there were 1,000 patients discharged from
the hospital in the second quarter. How confident
would we be in our conclusions if we had sampled
two patients? How confident would we be if we
had sampled 993 patients?
Confidence intervals are intimately tied to
sample size. The larger the sample, the narrower
the confidence interval; the smaller the sample,
the wider the confidence intervalall other
things being equal. Statements about confidence
intervals usually take the following form: "The
nursing satisfaction score is 86, and the 95%
confidence interval ranges from 82 to 90."
We can interpret this statement as saying that
we are 95% confident that the "true"
nursing satisfaction score lies between 82 and
90. If we had sampled 900 patients instead of
300, the 95% confidence interval would have
been narrower (85 to 87, say); and if we had
sampled only 50 of the 1,000 patients, the 95%
confidence interval would have been wider (maybe
76 to 96).
We hear people using confidence intervals almost
every day, though we may not realize it. If
a news anchor tells us "The president's
approval rating is 67%, subject to a 3% margin
of error," we can be 95% certain that the
true rating lies between 64% and 70%.
Why do we use 95% confidence intervals, when
we could just as easily calculate 90% or 99%
confidence intervals? It's directly related
to the p value criterion of .05 (or 5%) that
researchers have used for decades. What we're
saying is that we're willing to take a 1 in
20 chance of being wrong when we claim that
something is statistically significant. People
use different p values and confidence intervals
in special situations, but .05 and 95% seem
to work most of the time.
Some years ago Dr. Brent James of Intermountain
Health Care developed a technique whereby an
SPC chart can quickly be converted into a (pseudo)
confidence interval chart. The first chart below
is a standard threesigma SPC chart showing
fictitious patient satisfaction scores for St.
Elsewhere Hospital.
From the alphabet soup of significant triggers,
it's clear that the folks at St. Elsewhere have
been doing something right over the last 45
years. Looking at the centerline of the chart,
however, we note that it's around 68, which
seems a little low.
Suppose we know that the national norm for
patient satisfaction is 75. With two simple
tricks we can turn this threesigma SPC chart
into a 95% confidence interval chart. First,
we change the "number of sigmas" from
the default of three to two. Second, we "fix"
the centerline at 75, rather than letting it
default to the mean of (around) 68. The chart
below shows the result.
These two charts look a little different because
of different yaxis scales, but they are plotting
exactly the same data (note, for example, that
the first data point is just under 65). The
"rule letters" have been turned off
in the second chart, since they have no bearing
in its interpretation. We interpret this chart
as follows: if a data point is inside the twosigma
envelope, it is not different (statistically)
from the target. If it lies outside the envelope,
it is significantly above (or below) the target.
I made up this example deliberately to show
how two very different conclusions could be
drawn from the same set of data. The SPC chart
shows significant positive progress; the CI
chart shows five years of significant negative
performance. Looking at the SPC chart alone,
leadership at St. Elsewhere might have been
content to rest on their laurels. Looking at
the CI chart, they realize that given their
very low starting point, they still have some
work to do.
Patterns like this have shown up at Sutter
Health, but so have many others. There are several
cases where a process has been completely under
control for 67 years, with every data point
significantly favorable to target. The variations
are endless, and looking at our data this way
has been eye opening.
Technical Note: I called this a pseudo confidence
interval chart because, with the exception of
p charts, two sigma is not identical to 2 (1.96)
standard errors. It is very close, however,
and I should point out that we're using these
CI charts at Sutter Health for directional guidance,
not precision reporting or inferential statistics.
