Time%20Between%20Charts

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Time Between Charts

• Farrokh Alemi, Ph.D.

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Steps in construction of time in between charts

1. Verify the chart assumptions
2. Select to draw time to success or time to failure
3. Calculate time to success or failure
4. Calculate control limits
5. Plot chart
6. Interpret findings
7. Distribute chart

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Step 1 Check assumptions

• One observation per time period
• Dichotomous discrete rare event
• Independent observations over time
• Geometric Distribution of observations (Longer
  time to event is increasingly rare)

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Step 2 Select the event to trace

• Plot time to failure if failure is more rare than
  success
• Plot time to success if success is more rare than
  failure

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Step 3 Calculate time to event
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Step 4 Calculate control limits

• If failures are rare, calculate R as the ratio of
  failure days to success days 
• If success is rare, calculate R as the ratio of
  successful days to failure days
• UCL R 3 R (1R) 0.5

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Step 5 Plot control chart

• X-axis is time
• Y-axis is either length of failures or length of
  successes
• UCL is drawn as straight line

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Steps 6 7 Interpret findings distribute chart

• Any series exceeding UCL cannot be due to chance
  and is a statistically significant deviation from
  historical patterns
• If any point in a series is above the UCL, then
  the entire series is unusual not just the point
  exceeding the limit.
• In distributing chart include
• Assumptions
• Plot
• Interpretation

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Example in asthma care

• Patient followed for 19 days
• Personal best 310
• 80 of personal best is 248
• Is the patients asthma improving?

if(A2lt248,Yes,No)
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Calculate attack free days
IF(B2"Yes",0,1)
IF(B3"Yes",0,B21)
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Calculate control limits
COUNTIF(B2B20,"Yes")
COUNTIF(B2B20,No")
F53(F5(1F5))0.5
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Plot chart
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Interpret findings distribute

1. Recovery on the 5th day was not statistically
   significant
2. From 9th to 14th day, when patient was away from
   home, there was significant recovery.
3. After the 14th day, the patient returns home and
   so do the asthma attacks

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Example in Court Ordered Substance Abuse Treatment

• Different corrective actions are needed for
  relapse or return to poor habits

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What Is Relapse?

1. A working definition of relapse is difficult.
2. It is a relapse, if I say it is. Otherwise it is
   not.
3. Behavioral definitions have been offered
   recently.
4. We provide a statistical definition.

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Sample Case

• Client was tested weekly for 20 weeks
• There has been failures on 6th, 10th and 15th
  through 17th week
• Are these failures return to poor habits or
  merely temporary relapses?

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How to score length of relapses?
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Calculating Length of Relapse in Excel
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Check Assumptions

• Time to success should have a geometrically
  decaying shape
• Eye examination suggests the assumption is
  reasonable
• Frequency of failures are low.

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Calculate Upper Control Limit
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Step 4 Plot the Relapse Chart
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Interpret the Chart

• Points below control limit could be due to chance
  events. Despite failures, the underlying habit
  is repeating as before.
• There were two lapses
• Series with one point above control limit have
  less than 1 chance of occurring due to chance
  alone. They represent changes in the underlying
  repetition of the habit.
• There is one return to drug use

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Take Home Lesson

• Time in between charts are effective tools for
  examining rare events