1. Time Between Charts Farrokh Alemi, Ph.D.

2. 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

3. 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)

4. 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

5. Step 3: Calculate time to event

6. 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

7. 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

8. 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

9. Example in asthma care Patient followed for 19 days Personal best 310 80% of personal best is 248 Is the patient’s asthma improving? =if(A2<248,”Yes”,”No”)

10. Calculate attack free days =IF(B2="Yes",0,1) =IF(B3="Yes",0,B2+1)

11. Calculate control limits =COUNTIF(B2:B20,"Yes") =COUNTIF(B2:B20,“No") =F5+3*(F5*(1+F5))^0.5

12. Plot chart

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

14. Example in Court Ordered Substance Abuse Treatment Different corrective actions are needed for relapse or return to poor habits

15. 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.

16. Sample Case 1. Client was tested weekly for 20 weeks There has been failures on 6 th, 10 th and 15 th through 17 th week 2. Are these failures return to poor habits or merely temporary relapses?

17. How to score length of relapses?

18. 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

19. 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.

20. Calculate Upper Control Limit =COUNT(C2:C21)- COUNTIF(C2:C21, 0) =COUNTIF(C2:C21,0) =E2/E3 =E4+3*(E4*(1+E4))^0.5

21. Step 4: Plot the Relapse Chart

22. 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

23. Take Home Lesson Time in between charts are effective tools for examining rare events