Statistical Process Improvement
Georgetown University

Comparison of Rates

Assigned Reading

  1. Comparison of rates Read►


There are three sets of presentations for this lecture:

  1. Lecture on P-chart Slides► Video► SWF►
  2. Lecture on risk adjusted P-charts  Slides► IE Video► SWF►
  3. Introduction to control chart  Slides► SWF►
  4. Calculate expected deviations  IE Video► SWF►
  5. Student t-values.  More►

Narrated slides and videos require Flash.


  • See a recent tutorial on how to create a risk adjust control chart.  More►
  • See published examples PubMed►
  • Michael Cleary, Ph.D. and Six Sigma give a case study for on-time medication delivery. More►
  • See an example of use of control charts in preventing hospital falls.  More►
  • For an example of risk-adjusted quality control charts see Gustafson's approach to infection control.  More►


Question 1: This exercise allows you to examine how quality of hospital care is evaluated through data obtained from electronic health records.  This exercise is discussed in several health administration courses, including courses on quality improvement, informatics, or statistics. In practice, the need to analyze these types of data arises in improvement teams, where managers, clinicians and sometimes patients work together to systematically improve healthcare processes. In this assignment, you are asked to examine if prophylactic antibiotics are discontinued within 24 hours after end of surgery.  Instead of providing you with the data, we ask that you download the data on the web so that you learn more about the source of the data and peculiar organization of the data.  Hospital Compare provides information on many quality indicators.  In this assignment, you are asked to focus on failure to stop use of antibiotics post surgery. The Hospital Compare web site provides the following rationale for why this measure of quality is helpful:  "A goal of prophylaxis with antibiotics is to provide benefit to the patient with as little risk as possible. It is important to maintain therapeutic serum and tissue levels throughout the operation. Intra-operative re-dosing may be needed for long operations. However, administration of antibiotics for more than a few hours after the incision is closed offers no additional benefit to the surgical patient. Prolonged administration does increase the risk of clostridium difficile infection and the development of antimicrobial resistant pathogens."  To complete this assignment complete the following tasks:

  1. Download Hospital Compare data for the year 2015 and 2016.  Merge the file " HQI_HOSP_TimelyEffectiveCare" across all databases for different years. 
  2. Create a query for each year.  Select measure ID "SCIP_INF_3"; this measure refers to prophylactic antibiotic use. Select to work with data from "Southeast Alabama Medical Center"; this is provider ID "010001". 
  3. Calculate rate of overuse of antibiotics.  In these data, the field "Score" refers to the number of patients with overuse of antibiotics.  The field "Sample" refers to all selected surgical patients with no evidence of prior infection. The ratio of Score to Sample provides the rate of overuse of antibiotics.  

Construct a control chart showing rate of overuse of prophylactic antibiotic over time in Southeast Alabama Medical Center.  Download the needed data using the following databases:►►►►►►►►►   Guide► Answer►

Question 2:  Nursing home and hospital administrators implement many initiatives to reduce falls.  This problem shows how these initiatives can be measured and evaluated.  Prepare a risk-adjusted control chart for data on falls in a nursing home. Data►  Video► SWF► Answer►

Question 3: Following data were obtained on post surgical infection rates.  Are we having more infections than expected from the patients' conditions? Answer►

Week Risk of Infection for each Patient Number Infected
1 0.9 0.8 0.7 0.8 0.9 0.85 6
2 0.7 0.8 0.7 0.6 0.8 0.9 5
3 0.8 0.95 0.92 0.87     4
4 0.5 0.6 0.66 0.67     3
5 0.3 0.4 0.5 0.4 0.5 0.34 2
6 0.3 0.4 0.5       1

Question 4: Download Hospital Compare data for the year 2015 and 2016.  Start from 1/1/2015 till the most recent available database. Since the data on AMI payments does not change in the files, you can save time and read only the following 3 files into a new database:

File Database Field Start End
HQI_HOSP_AMI_Payment   HOSArchive_20150122 Compared to National 2010 2013
HQI_HOSP_Payment HOSArchive_20150716 Category 2011 2014
HQI_HOSP_PaymentAndValueOfCare Hospital_20161110 or HOSArchive_20161110 Payment Category 2012 2015

In these files the denominator indicates the number of patients.  Whether the hospital had above average payments are reported in different fields: [Compared to National], [Category], and [Payment Category]  Select data that meet the following conditions:

  1. Select the "PAYM_30_AMI" measure
  2. Select hospitals that in the denominator do not have "Not Available".

Construct a control chart showing probability of change over time.  Download using the following files:►►►►►►►►► Guide► Answer►

Question 5: On average 1 in 10 patients have some sort of medication error in our facility; what is the probability that out of 10 patients none will have medication errors?

Question 6: The probability of a patient recovering from a heart operation is 0.9. Assuming that heart operations are not related to each other, what is the probability that exactly 4 out of 8 next patients will survive the operation?

Question 7: An insurance salesperson is about to sell life insurance policies to 7 unrelated women, all of whom are of the same age, belong to the same race, and are in good health. According to independent actuarial estimates, the probability of a woman of this age, race, and health status being alive 20 years from now is 80%. What is the probability that in 20 years all 3 women are alive?


  1. Risk adjusted probability charts More►

  2. Independence of observations  More►

This page is part of the course on Statistical Process Control, the lecture on Comparison of Rates.  This presentation was based on Alemi F, Rom W,  Eisenstein E. Risk adjusted control charts for health care assessment.  Annals of Operations Research, 1996. Created on Tuesday, September 17, 1996.  Most recent revision 05/07/17.