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Comparing Performance of Individuals

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 ( 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:

  • Level 1 hospitals have all the capabilities for normal births and births with minor complications.
  • Level 2 hospitals have additional equipment and staff to deal with more complicated deliveries.
  • Level 3 hospitals have equipment and staff to handle very complicated cases requiring intensive care, such as premature births.

Preliminary Findings

Shown below is a p-chart for VBACís with no distinction between the hospitalsí obstetrical level of care classification. Each point on the chart represents an individual hospitalís VBAC rate, which is simply the number of VBACís 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 providerís 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 20ís control limits are also quite narrow, indicating that the hospitalís rate was based on many patients. Therefore, it would be very worthwhile for other Level 2 hospitals to study this hospitalís 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 todayís 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.

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