Statistical Process Improvement
Georgetown University
 

Time to Adverse Events


 

This topic examines control charts that require only 1 observation per time period.  These include time-between and Tukey control charts. Since there is one observation per time period, you can easily apply these methods to analysis of your own habits.  Want to know if you have really lost weight or kept up with exercise, use the control charts this week to examine your own data. We continue as before to also look at real data from hospitals.  Now we look at rare events such as wrong side surgery or medication errors. We also help you think through which chart is appropriate with what kind of data.

Assigned Reading

  • Chapter 8 in Big Data in Health Care: Statistical Analysis of Electronic Health Record Read►

Presentations

Assignments

Instruction for Submission of Assignments: Assignments should be submitted directly on Blackboard.  In rare situations assignments can be sent directly by email to the instructor. Submission should follow these rules:

  1. Make sure that any control charts follow the visual rules below:  (1) Control limits must be in red and without markers, (2) Observed lines must have markers, (3) X and Y axis must be labeled, and (4) Charts must be linked to the data. 
  2. The first sheet/section in the file, or a separate file, should be a summary page.  In the summary page you should list how your answers to the question differs from answers provided within the assignment (inside Teach One or other answers).  You must indicate for each question if your control chart is exactly the same as seen in Teach One or other formats.  For each question, you must indicate if the answers you have provided is the same as the answers supplied on the web.  If there are no answers provided, you must indicate that there were no answers available on the web to compare your answers to.

Question 1: We have received a set of comments over time on the web. Check if we have improved?   Please note that there are no pre- and post intervention periods and therefore control limits must be calculated from the entire period.

Question 2: The following data show the speed with which Alabama Medical Center's Emergency Room provides a patient who has fractured long bone with pain medication.  Examine if the organization has been able to reduce the response time to less than 73 minutes?

Measure Start Date Measure End Date Minutes to Pain Medication Sample
4/1/2013 3/31/2014 78 132
7/1/2013 6/30/2014 68 124
7/1/2013 6/30/2014 68 124
10/1/2013 9/30/2014 72 122
1/1/2014 12/31/2014 76 138
4/1/2014 3/31/2015 85 144
7/1/2014 6/30/2015 86 137
10/1/2014 9/30/2015 95 121
1/1/2015 12/31/2015 99 111

Question 3: A control chart requires independent repeated observations over time.  In addition, based on other factors, different charts are appropriate. For each of the following conditions, select a measure in Hospital Compare and describe its denominator and numerator.  You can find measure definitions under CMS's definition of measures.  Select hospital compare program and focus on measures used in hospital compare program. Then, identify one or more control charts that are appropriate.  If more than one control chart is appropriate, the usual approach is to try both charts and select the chart with tighter controls (i.e. control limits with smaller absolute difference): 

Hospital Compare Measure Code Short Definition of Denominator Short Definition of Score Is there one observation per time period? Is the score a continuous (interval) scale? Are outliers likely? Recommended Chart
Yes Yes Yes
      Yes Yes No  
      Yes No -  
      No Yes  -  
      No No  -  

Question 4: In the following data, we have tracked whether 352 infants in our pre-natal clinic eventually showed for various services in post-natal care. Each clinic is reporting if these 352 patients showed at their clinic and on what dates. Given these data, calculate the referral rate to each clinic. Has the rate of days-of-referrals to ultrasound clinic changed over time (does the control chart show points outside the limit)? In analyzing these data you may wish to use combination of if and match commands within excel. The command may look like

=if(match(A2,C:C, 0), 1,0).

This command says the value that should be matched is in A2, the look-up array is in column C, and 0 indicates that it should be exact match. Here is a pointer on how to answer this question. The data provide dates of visits. To calculate the daily probability of a visit follow these steps:

  1. Sort the dates from smaller to larger values.
  2. Calculate the difference between two consecutive visits. In Excel the difference of dates can be calculated through subtraction.
  3.  Average the difference, this provides "A", the average number of days between two consecutive visits. In Excel, the difference between two dates is calculated by subtracting the two dates from each other.  Write this as a cell formula, so you can copy it for all the dates.
  4.  The daily probability of a visit is 1/A
  5.  To examine if there has been a change, split the data into two equal sets and calculate the probability for each half of the data.  The difference in these two probabilities shows the change in the rates.

Question 5: Using the data from previous question, what is the daily probability of referrals to each of the ultrasound, neurology and combination of the two clinics.   To calculate the daily probability of a visit follow these steps:

  1. Sort the dates from smaller to larger
  2. Calculate the difference between two consecutive visits. In Excel, the difference between two dates is calculated by subtracting the two dates from each other.  Write this as a cell formula, so you can copy it for all consecutive dates.
  3. Average the difference, this provides "a", the average number of days between two consecutive visits.  
  4. The daily probability of a visit is 1/a To examine if there has been a change, split the data into two equal sets and calculate the probability for each half of the data. 
  5. The difference in these two probabilities shows the change in the rates.  

Here is what I calculated as the daily rates of referrals to neurology, ultrasound, and combination of the two clinics:

  Days to Next Event
First Half of Data Second Half of Data
Average of Next Daily Probability Average of Next Daily Probability
Neurology 9.74 0.10 8.47 0.12
Ultrasound  4.61 0.22 4.83 0.21
Neurology & Ultrasound 3.13 0.32 3.15 0.32

Question 6: In the past 3 years, there have been the following incidences of privacy violations:  A disgruntled employees sold information on May 11 of year 1.  Another disgruntled x-employee sold password to the system on Dec 12 of year 3.  There have been four incidences of clinician discussing patient information in social gathering on the following dates: December 5 year 2, January 25 Year 3, May 27 year 3, and September 1 year 3. Days of incidences of any other types of privacy violations were May 11 year 1, Nov 22 year 2, Dec 27 year 3.  Which types of privacy violations are more frequent? Use Excel formulas to calculate the average days to event and daily probability of the event. 

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Copyright 1996 Farrokh Alemi, Ph.D. Most recent revision 11/04/2021.  This page is part of the course on Statistical Process Improvement, this is the lecture on Introduction to the Course.