What is the Difference Between a Percentage and a Rate?


Often we hear the question, "What is the difference between a percentage and a rate?"

They are both calculated using a numerator and a denominator. However, the relationship between the numerator and denominator makes the difference.

Percentages

Indicators which use percentage are the most commonly used indicator type in healthcare. Most of the Joint Commission measures monitor percentages to measure compliance. A percentage measures the number of a certain set of events which have a particular outcome when there are two outcomes possible, either Yes or No. For example, either the AMI patient received aspirin on arrival or they did not. For each of these outcomes (received aspirin or did not receive aspirin), there can never be more than 100 percent. We cannot see a situation where 110% of the patients admitted received aspirin on arrival.

Guidelines for Percentages:

  • Numerator and denominator are the same unit of measure
  • Both the numerator and denominator are positive whole numbers
  • The numerator is never greater than the denominator

Example: An AMI patient is admitted. Did that patient receive aspirin on arrival? If we look at all the AMI patients admitted during a period, some subset of those patients receive aspirin on arrival. To get the percentage, we divide the number of AMI patients admitted and who received aspirin (numerator) by the total number of AMI patients admitted (denominator). The patients who received aspirin are a subset of the patients admitted.

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Percentages are charted on a p chart, where p stands for proportion. Statit piMD™ translates that to a percentage, a simple transformation that has no effect on the results except to provide the viewer a standard view that is easier to understand.

Rates

A rate, on the other hand, does not have the same numerator-denominator relationship as a percentage. For example, if we look at falls per patient days, the patient days did not fall. So the numerator is not a subset of the denominator; that is, it does not have the same unit of measure.

If we answer the question, "Can an outcome happen more than once in an area of opportunity?" in the affirmative, then we are talking about a rate.

We probably cannot count the number of opportunities for a patient to fall, so we use a surrogate measure that will give us an indication of the magnitude of the area of opportunity. Patient days fits well with several such measures. Using such surrogate measures produces standard measures across different size hospitals with different numbers of patients.

Guidelines for rates:

  • Numerator and denominator do not use the same unit of measure
  • There can be more than one countable outcome for a unit in the denominator
  • We may not be able to count the opportunities for the outcome

Example:

We might measure the number of falls per 1000 patient days. The numerator is the number of falls during the period. The denominator is the number of patient days in that period divided by 1000. We use the 1000 patient days as a denominator to produce a number that will make a little more sense to the viewer. Four (4) falls per 1000 patient days seems to make more sense to the human mind than .04 falls per patient day. You would probably choose the denominator (1000 patient days or 100 patient days) based on how you would want to compare your measures to other hospitals. If most of the hospitals you are comparing are using 1000 patient days, then you would probably want to use 1000 patient days.

This type of data is charted on a u chart where the u stands for unit, as in number of defects per unit. An important thing to remember is that there can be more than one defect per unit. In the above example, the unit is 1000 patient days and the defect is falls.

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The rate might be expressed in a form that looks like a percentage but is not and can produce confusion. For example, falls per 1000 patient days is a rate not a percentage. The number produced is not the number of patient days that fell but is the rate of falls per 1000 patient days.

Let me give you one more example that may help to illustrate the difference. With med errors, each dose could have more than one error. We administer a dose of medicine. There could be more than one error with that dose, such as wrong time, wrong dose, wrong patient, or wrong delivery. A percentage would be the number of doses that were in error divided by the total number of doses administered. Doses in error would be any dose that had a least one error. A rate would be the count of individual errors divided by the number of doses. The percentage would be expressed as the percent of doses that had at least one error. The rate would be expressed as the number of individual errors per 1000 doses.

The Statit piMD online demo and the 10 Minute guided tour of Statit piMD give you some illustration of the use of these measures. Most of the indicators under the group Competency are percentage type; however, Adverse Drug Events is a rate type. Please take a look at these charts for a better understanding of the difference between the two types.

A more in-depth discussion of these data and chart types can be found at:
http://www.statit.com/support/quality_practice_tips/ucharts_pcharts_icharts.shtml.

If you would like additional information, please send email to statit.support@acs-inc.com.