Boating Beyond Simple Shewhart

Model 11

Destinations

• Purpose—To provide a quick long distance view.• Content

– Time or observations between events (g, h, t charts).– CUSUM and EWMA– Following a panel of patients

• Small Multiples (Thanks to Jerry Langley)• Problem of changing denominators.

– Comparing beginning and ending performance• Prevalence difference vs. Percent Improvement• Scatterplots

– Smoothed Curves vs. Control Charts

Analyzing Rare Events

Using Time or Occurrences Between Them

One way to analyze rare events

Another way to analyze rare events

t and g chart summary

• t-chart measures the time between events

• g-chart measures the number of incidents (procedures, admission) between events

• Both charts are useful when looking at rare events– Eliminates the need to wait for a long time

period to collect enough data points

CUSUM and EWMA

Early detection of shifts

Anatomy of a CUSUM chart

Monitoring CO2 in a NurseryCUSUM Chart

Monitoring CO2 in a NurseryCUSUM Chart

Or, you can use an exponentially weighted moving average chart.

Surgeries DeathsSource: Benneyan, 2001

CUSUM vs. EWMA

CUSUM EWMA

Y-axis Cumulative sum of the difference between the observed mean and the target or average.

Avg. of surrounding values, weighting close values very high and far away values very low (exponential weighting).

X-axis Measurement number (observation).

Time interval.

Advantage Detects small shifts

More sensitive than EWMA.

Partially immune to autocorrelation.

Detects small shifts.

Partially Immune to autocorrelation.

Easier to understand than CUSUM

Following a Panel of Patients

Small Multiple Graphs

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A-07 J -07 O-07 J -08 A-08 J -08 O-08 J -09

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IPC Site

Denominator in blue

Screening rate in red

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Small Multiple GraphsThink-Pair-Share

• Why are they powerful?

• What are their limitations?

An Alternative:Percent of Patients Screened for Depression:

A Period-Cohort Analysis.

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1 2 3 4 5 6 7 8 9

Quarter beginning Jan 2009

Percent Screened

1st QTR Cohort

3rd QTR Cohort

5th QTR Cohort

A cohort is a group of patients empanelled within a particular quarter.

Summarizing beginning and ending results

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-80 -60 -40 -20 0 20 40 60 80 1,334 2,052 3,129Percent Improvement

95% Confidence Interval Percent Improvement

over 12 months in 2009 by IPC site.Figure 1. Percent improvement in the Health Risk Screening Bundle

Compare to change in percent screened

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-20 -10 0 10 20 30 40 50 60 70 80 90 100Percent

95% Confidence Interval

Change in Percent Screened (5th Q-1st Q)

Scatter plot comparing beginning and ending of period of observation.

Control Charts vs. Smoothed, Descriptive Data

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0 20 40 60Month beginning January 2004

Number of Preventable Hospitalizations Curve fit by Median Spline

Preventable hospitalizations due to any one of the 11 conditions defined by AHRQ asPrevention Quality Indicators

Number of preventable hospitalizations by month for site 1

Compare to corresponding c-Chart

Your Turn!

1. Think about your work and select a key quality characteristic (KQC).

2. Develop an operational Definition for the KQC.

3. Evaluate your definition with the criteria from the NQF in module 2.

4. Answer: What kind of chart or analysis would you use?