Q: We would like to compare the relative
performances of a large group of service providers.
How can we identify those providers with especially
good service and those providers who we may
need to work with to improve quality?
A: P-charts are a handy tool for comparing
performances since the control limits will provide
an easy method to determine those performers
who appear to be "different" than
the others in the group. Using the "Phases"
capability of the Statit products can further
enhance the chart's usefulness.
(Note: The following article is reprinted from
the March/April 2000 issue of The Quality Resource,
the Newsletter of the Quality Management Section
of the American Health Information Management
Association.)
Comparing Performance Measures Using P-Charts
By Carole Shlaes, PhD, CQE
Quality and Statistics Training
Corvallis, OR
Health care providers today are looking for
new ways to objectively study and compare performance
measures to improve outcomes, cut costs, identify
"best practices" and increase patient
satisfaction. Control charts, used for years
in industrial settings, are being put to new
uses everyday in health care. Based on proven
statistical principles, control charts provide
powerful tools to improve quality.
A proportion chart, or p-chart, is a statistical
quality control device commonly used to track
the proportion or rate of defective items from
a production line over time. This versatile
chart can be used to track the proportion of
any classification over time and can easily
be used in health care quality management situations
to compare many types of performance measures
among providers. Examples of proportions or
rates that could be tracked are the rate of
a particular procedure among all patients or
the rate of patients who are readmitted within
a certain time frame.
Data for Control Charts
There are two types of data typically collected
to monitor any process. The first type of data
is called attribute data, which simply counts
the number of occurrences (or nonoccurrences)
of a particular event. When an event can either
occur or not, the p-chart is used to monitor
the proportion of units for which the event
occurred based on the total number of units
available. For example, an obstetrics patient
either had a C-section or did not. Other attribute
data charts are useful to monitor data where
the event can occur multiple times, such as
the number of times per day that special lab
work is requested for a patient.
The second type of data typically collected
is called variables data, which is based on
measurements, such as time, cost, heart rate,
and the like. There is a wide variety of control
charts for use with variables data.
Anatomy of a Control Chart
Most control charts have the same basic structure.
Summary data is plotted on a simple graph with
the x-axis (horizontal axis) representing time
or a collection of entities such as providers.
The y-axis (vertical axis) measures the data
itself. A horizontal center line is typically
based on the overall average of the quality
data being charted.
Control charts also have an upper control limit
(UCL) and a lower control limit (LCL). These
control limits on either side of the center
line are used to indicate whether the current
data value differs significantly from the prior
or average behavior. The width of the control
limits depends on the amount of variability
found in the data and the number of samples
making up each plotted point.
Construction of a P-Chart
P-charts are usually constructed using a computer,
but they are based on very simple mathematics.
The individual points on the p-chart represent
the rate of occurrence of an event in the samples
for each time period or entity. These proportions
are calculated as:
The subscript i is used to represent
the individual time periods or entities such
as providers.
The center line of the chart is the overall
average proportion based on all of the samples.
It is denoted as 
(pronounced
"p-bar") and is calculated as:
The control limits are then calculated based
on the average proportion and the individual
sample sizes:
Note that there is an inverse relationship
between the number of samples and the width
of the control limits: smaller sample sizes
require a greater actual difference before being
declared statistically different while larger
samples require a smaller difference. This is
due to the uncertainty, or variability, that
exists when making statistical decisions based
on samples.
A Typical Scenario
The use of a p-chart for health information
can be illustrated using VBAC rate data from
southeast Michigan hospitals which is found
in the 1998 Michigan Hospital Report (www.mha.org).
The rate of vaginal birth after cesarean section
(VBAC) represents the proportion of women at
the hospital who had a normal delivery after
having had a C-section for a prior birth. A
higher VBAC rate is generally preferred because
fewer mothers are exposed to the complications
that may be associated with surgery. To create
this rate, hospitals collect data on the number
of women having a VBAC and the total number
of deliveries for woman who have had a previous
C-section.
In the Michigan Hospital Report there are also
obstetric care classifications for the hospitals.
Hospitals are categorized into one of three
levels:
Preliminary Findings
Shown below is a p-chart for VBAC’s with
no distinction between the hospitals’ obstetrical
level of care classification. Each point on
the chart represents an individual hospital’s
VBAC rate, which is simply the number of VBAC’s
divided by the number of births to mothers who
had previously undergone a C-section. As shown
by the center line of the control chart, the
average VBAC rate for all the hospitals is just
less than 0.40 or 40 percent.
The control limits associated with each provider’s
VBAC rate is shown by the stepped lines on either
side of the center line. The control limits
for each provider are a function of the overall
average rate and the number of data points making
up each sample. Since each provider has a different
number of previous C-section mothers, these
control limits are different for each provider.
The width of the control limits is inversely
proportional to the number of previous C-section
mothers.
Since a higher VBAC rate is desired, the hospitals
with rates above its upper control limits are
significantly better than the average hospital.
These points are designated with the letter
"A" on the control chart to indicate
a point above the upper control limit. These
hospitals can be studied to find out what they
are doing to achieve this desirable outcome.
Similarly, the letter "B" on the control
chart indicates a point below the lower control
limit. These hospitals have VBAC rates that
are significantly lower than the average hospital.
These hospitals can be studied to find out where
they can improve.
Grouping Increases Sensitivity
A p-chart for the same data with hospitals
grouped according to the level of obstetrical
care is shown below (using the "Phases"
capability of the Statit products). The hospital
numbers and individual data points are the same
as in the earlier chart. However, now each group
of hospitals has its own center line representing
the average VBAC rate for the hospitals in that
classification level only. The p-chart shows
that there are some pronounced differences between
the VBAC rate for the different groups of hospitals.
This phenomenon itself can be studied, if desired.
The grouped p-chart also results in a more equitable
review of hospitals with similar characteristics.
For example, look at the VBAC rate for Hospital
20, designated by the vertical line on the control
charts. In the first p-chart, Hospital 20 appears
to have a fairly average VBAC rate when compared
to all hospitals. However, this rate can be
seen to be significantly higher than most other
Level 2 hospitals in the second chart. Hospital
20’s control limits are also quite narrow,
indicating that the hospital’s rate was
based on many patients. Therefore, it would
be very worthwhile for other Level 2 hospitals
to study this hospital’s practices.
Control Charts are Simple, Yet Powerful
P-charts, and control charts in general, can
have a wide variety of uses in health care quality
management. They allow an easy, objective review
of the many types of data captured in today’s
environment. Using the p-chart, it is possible
to objectively determine when the proportion
or rate of an occurrence for a particular provider
or time period differs significantly from the
average proportion among all providers or over
time. The conditions surrounding rates that
are significantly worse than average can be
examined to determine what went wrong and where
improvements can be made. Equally important,
conditions surrounding rates that are significantly
better than average can be examined to determine
if there are techniques that can be used by
other providers and or in other situations to
help improve overall patient outcomes.
