statistical process control tim wiemken, phd mph cic assistant professor, university of louisville...

Statistical Process Control

Tim Wiemken, PhD MPH CICAssistant Professor, University of Louisville School of Medicine, Division of Infectious DiseasesDirector, University of Louisville Hospital Epidemiology ProgramAssistant Director of Epidemiology and Biostatistics, Clinical and Translational Research Support CenterLouisville, KYtim.wiemken@louisville.edu

Overview

• Appropriate use of charts• Run Charts• Statistical Process Control Charts• Examples…

Appropriate Use of Charts

1. Pie is to eat, not to display your data.

Appropriate Use of Charts

1. Pie is to eat, not to display your data.

“Use a pie chart when you don’t have anything to say”

- Dr. Julio Ramirez

Appropriate Use of Charts

2. Bars are for buying booze, not for displaying consecutive data points.

Don’t do this

Appropriate Use of Charts

2. Bars are for drinking, not for displaying consecutive data points.

Or this

Appropriate Use of Charts

3. Line charts are good. They display consecutive data points. That’s all.

Do this

Overview

• Appropriate use of charts• Run Charts• Statistical Process Control Charts• Examples…

Run Charts

• Line chart when you have few time periods (e.g. <25 months).

Run Charts

Anatomy• Center Line / Median –represents the median of

all of the data points. • X-axis –represents the time period of interest

(days, weeks, months, quarters, years).• Y-axis –represents the scale of the plotted data

points (e.g. rate or count of infection).• Data points – the actual data values.

Y-axis (Rate)

X-axis (Month)

Center Line (Median)

Data Points (<25)

Run Charts

Use to identify when the data are different than you expect (for better or worse) through

detecting abnormal variation

Run Charts

Rules for abnormal variation

1. Seven or more consecutive points on either side of the Center Line (median).

2. Five or more consecutive points increasing or decreasing.

3. Fourteen or more consecutive points alternating up and down.

Run Charts

Rule 17 points below median

Rule 25 consecutive points increasing

Run Charts

Overview

• Appropriate use of charts• Run Charts• Statistical Process Control Charts• Examples…

• Use when you have many time periods (e.g. ≥25 months).– These are much better than run charts.

Statistical Process Control Charts

• Use when you have many time periods (e.g. ≥25 months).– These are much better than run charts.

• But not more than 50 points

Statistical Process Control Charts

They help identify the difference between

Statistical Process Control Charts

1. Common cause variation (in-control)

2. Special cause variation (out of control)

• Anatomy• Center Line / Mean–represents the average of all

of the data points. • X-axis –represents the time period of interest

(days, weeks, months, quarters, years).• Y-axis –represents the scale of the plotted data

points (e.g. rate or count of infection).• Data points – the actual data values.• Standard deviation lines (control limits) –

represent 1, 2 or 3 standard deviations on each side of the center line

Statistical Process Control Charts

• What’s up with the standard deviation?

Statistical Process Control Charts

• What’s up with the standard deviation?• All data have a distribution.

Statistical Process Control Charts

• What’s up with the standard deviation?• All data have a distribution. • This distribution can be broken up into

standard deviations – measures of variation from the average

Statistical Process Control Charts

Statistical Process Control Charts

1. 68% of data fall in 1 standard deviation of the average

2. 95% of the data will fall within 2 standard deviations

3. 99% will fall within 3 standard deviations

Statistical Process Control Charts

1. 68% of data fall in 1 standard deviation of the average

2. 95% of the data will fall within 2 standard deviations

3. 99% will fall within 3 standard deviations

One point outside of 3 standard deviations would be abnormal

Statistical Process Control Charts

Statistical Process Control Charts

Statistical Process Control Charts99

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• one point above or below 3SD

• two of three points above/below 2SD

• four of five points above/below 1SD

• eight points in a row on either side of the mean

• trends of 6 points in a row increasing or decreasing

• fourteen points in a row alternating up and down

• eight points in a row outside of 1SD

Statistical Process Control Charts

• There are many different types of charts

• Using the wrong chart will give you the wrong results

• You may miss an outbreak

• You may institute interventions that are not necessary (e.g. waste your time!)

Statistical Process Control Charts

P Chart

Use for:

1. Microbiological surveillance rates

2. Compliance rates

U Chart

Use for:

1. Device-associated infections

Statistical Process Control Charts

• Put all of your data into a nice clean report!

• Not all reports are appropriate for all audiences.

• Remember it is about the audience’s interests, not yours!

Statistical Process Control Charts

Example introductory slide for MRSA rates

Hospital-associated Methicillin-resistant Staphylococcus aureus

(MRSA)

Case of MRSA (Numerator): A case of MRSA was defined as a new and unique, hospital-associated (isolated >48 hours after admission), microbiological isolate from a patient admitted to hospital x during the month of interest without a prior history of MRSA.

Patient days (Denominator): The denominator for the calculation of the rate of MRSA was defined as the number of patient-days for hospital x during the month of interest, regardless of risk status.

Rate: (Numerator / Denominator) * 1,000

UCL 0.003

CL 0.001

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0.0040

0.0045

0.0050

Ra

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Date

June 2006:Rate peaked to 4.30. Suspect increase was due to a change in MRSA precautions implemented affected staff compliance with when to wear PPE.

Hospital-Associated Methicillin-resistant Staphylococcus aureus Isolates: Hospital X, MICU, January 2006 – January 2010

# HA MRSA Isolates divided by # Bed-days of Care

Date

Number of Isolates

Number of Bed-Days of Care

Rate Per 1000 Bed-days of Care

Jan 10

Feb 10

Mar 10

Apr 10

May 10

Jun 10

Jul 10Aug 10

Sep 10

Oct 10

Nov 10

Dec 10

0 2

1319 1117

0.0 1.8

Average Rate per 1000 Bed-days of Care 2008

Average Rate per 1000 Bed-days of Care 2009

Average Rate per 1000 Bed-days of Care 2010 YTD

0.4 0.6 0.9

Assessment: Process is in statistical control.

Plan: Continue surveillance activities.

Statistical Process Control Charts

Examples

Statistical Tools Workbook

you must use clinical judgement in addition to statistics

Conclusion