time between charts
DESCRIPTION
Time Between Charts. Farrokh Alemi, Ph.D. Steps in construction of time in between charts. Verify the chart assumptions Select to draw time to success or time to failure Calculate time to success or failure Calculate control limits Plot chart Interpret findings Distribute chart. - PowerPoint PPT PresentationTRANSCRIPT
Time Between Charts
Farrokh Alemi, Ph.D.
Steps in construction of time in between charts1. 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
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)
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
Step 3: Calculate time to event
Yesterday Today Number of days to
successNumber of days to
failureStart of data collection Success 1 day 0 dayStart of data collection Failure 0 day 1 day
Success Failure 0 day 1 dayFailure Failure 0 day 1 + yesterday’s duration
of failuresFailure Success 1 day 0 day
Success Success 1 + yesterday’s length of success days
0 day
Rules for counting time to events
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 * (1+R)] 0.5
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
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
Example in asthma care
Patient followed for 19 days
Personal best 310
80% of personal best is 248
Is the patient’s asthma improving?
PEFRAsthma Attack
120 Yes140 Yes100 Yes150 Yes260 No150 Yes100 Yes120 Yes160 Yes300 No300 No275 No300 No200 Yes140 Yes170 Yes150 Yes150 Yes190 Yes
=if(A2<248,”Yes”,”No”)
Calculate attack free days
=IF(B2="Yes",0,1)
=IF(B3="Yes",0,B2+1)
Calculate control limits
=COUNTIF(B2:B20,"Yes")
=COUNTIF(B2:B20,“No")
=F5+3*(F5*(1+F5))^0.5
Plot chart
0
1
2
3
4
5
1 3 5 7 9 11 13 15 17 19
Time since start
Du
rati
on
of
sy
mp
tom
fr
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da
ys
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
0
1
2
3
4
5
1 3 5 7 9 11 13 15 17 19
Time since start
Du
rati
on
of
sy
mp
tom
fr
ee
da
ys
Example in Court Ordered Substance Abuse Treatment
Different corrective actions are needed for relapse or return to
poor habits
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.
Sample Case
1. Client was tested weekly for 20 weeks
There has been failures on 6th, 10th and 15th through 17th week
2. Are these failures return to poor habits or merely temporary relapses?
Week AbstinentWeeks
Abstinent1 Yes 1 02 Yes 2 03 Yes 3 04 Yes 4 05 Yes 5 06 No 17 Yes 6 08 Yes 7 09 Yes 8 010 No 111 Yes 9 012 Yes 10 013 Yes 11 014 Yes 12 015 No 116 No 217 No 318 Yes 13 019 Yes 14 020 Yes 15 0
How to score length of relapses?
Last week This week Length of relapseStart of data collection Success 0 dayStart of data collection Failure 1 day
Success Failure 1 dayFailure Failure 1 + yesterday’s length of relapse
Success Success 0 day
Rules for counting consecutive days of relapse
Calculating Length of Relapse in Excel
If current date is success, then 0
Otherwise, if previous day is relapse
then add 1 to previous days count, if not relapse
Then set current count to 1 day of relapse
Check Assumptions
1. Time to success should have a geometrically decaying shape
Eye examination suggests the assumption is reasonable
2. Frequency of failures are low.
Histogram
0
2
4
6
8
10
12
0 1 2 3
Days in betweenF
req
ue
ncy
Calculate Upper Control Limit
=COUNT(C2:C21)-COUNTIF(C2:C21, 0)
=COUNTIF(C2:C21,0)
=E2/E3
=E4+3*(E4*(1+E4))^0.5
Step 4: Plot the Relapse Chart
0
1
2
3
4
1 3 5 7 9 11 13 15 17 19
Weeks
Len
gth
of
rela
pse
UCL
Interpret the Chart
1. Points below control limit could be due to chance events. Despite failures, the underlying habit is repeating as before.
There were two lapses
2. 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
Take Home Lesson
Time in between charts are effective tools for examining rare
events