# Presentation: 394041

## Time-Specific Measurements vs. Time-Weighted Average for Pain in Chronic and Acute Analgesia Trials

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**Time-Specific Measurements ****vs. Time-Weighted Average for Pain in Chronic and Acute Analgesia Trials**

**Laura Lu, Ph.D**
**Office of Biostatistics, CDER, FDA**

## Outline

**Time-specific measurements and time-weighted average (TWA)  **
**Issues in chronic analgesia trials**
**interpretation of drug benefit**
**data imputation **
**Issues in acute analgesia trials**
**interpretation of drug benefit**
**data imputation**
**Summary**

## Change from Baseline in Pain

- 0

- 2

- 4

- 8

- 12

**Change from Baseline in Pain Score**

- 20

- 40

- 60

**Time Post-Randomization**

**Notes:**
I’ll use an individual patient’s change from baseline in pain score to introduce those measurements. This graph plots an individual patient’s pain curve in terms of change from baseline in pain score. Suppose the patient's pain was measured at time 2, 4, 6, and 12 (acute: hours  chronic: weeks). The red vertical segments represent the change from baseline in pain at each time point. These are what we call time-specific measurements. Later I will refer the area under this pain curve as AUC.

## Change from Baseline in Pain

- 0

- 2

- 4

- 8

- 12

**Change from Baseline in Pain Score**

- 20

- 40

- 60

**Time Post-Randomization**

**t****1**

**t****2**

**t****3**

**t****4**

**d****1**

**d****2**

**d****3**

**d****4**

**Notes:**
Let me call the time interval between time points as t.... And the time specific measurments as d ....

## Time-Weighted Average (TWA)

- TWA**=**
-          **=**
*         *
*         **** ***

**Notes:**
The tine-weighted average of a measurement  is AUC of the measurement normalized by the patient’s treatment period. In mathematical form, it is a weighted average of time-specific measurements. The weight is related to the neighbor hood time intervals of each time-specific measurements. The AUC approach actually refer to TWA. Because of the relationship between TWA and AUC, sometimes the TWA measurement was referred as AUC approach.  

## Chronic Analgesia Trials

**Interpretation of drug benefit**
**Data imputation**

**Notes:**
Next I will talk about issues in chronic analgesia trials with different measurements in terms of interpretation of drug effect and data imputation method. 

## Drug Benefit

**End-of-the-trial (time-specific) measurement: drug effect at the end of the trial**
**TWA: average effect through the trial**
**Consistency of drug benefit over time**

**Notes:**
The end of trial measurements for pain improvement was a time specific measurement commonly used as a primary endpoint in chronic analgesia trials. It represent the treatment effect at the end of the trial.
The TWA for pain improvement also has been proposed as a primary endpoint. This measurement represent average treatment effect through the trial.
These two measurements represent different aspect of drug effect, but when there is no consistent drug effect over time, none of the measurements can really represent the drug benefit.  

## Inconsistent Drug Effect  

**Time**

**Notes:**
For example, these two curves represent mean pain improvement in two treatments. The advantage of treatments shift along time. In this case, no single measurement  can describ drug effect.

## Imputation for Missing Values

**End of the trial measurements: last-observation-carried-forward (LOCF)  **
**imputes measurement at withdrawal time to later period  **
**TWA: no imputation?**
**uses average treatment effect before withdrawal time to represent (impute) average effect in overall treatment period  **

**Notes:**
When we have missing value, 

## Imputation for Missing Value(continued)

**Both methods imply assumptions: later evaluations of drug efficacy is similar to that of earlier evaluation.**
**Results generally favor drug with imputation than without imputation due to different drop-out mechanisms in treatment groups (drop-out rates and drop-out reasons).**

**Notes:**
Artificial assumptions

## Improvement?

**Continuing efficacy evaluation even after a patient’s withdrawal can provide additional treatment information (ITT analysis).**
**Responder analysis?**
**time to respond**
**percentage of responder**
**duration of response**

**Notes:**
Seeing theses problems in data imputation, can we make improvement through  trial design and analysis? First, in terms of  trial design, we should continue to 
Also, we can thhink about responder analysis including .. To better characterize drug effect and avoid artificial imputation methods by taking drop-out status into consideration. 

## Acute Analgesia Trials

**Interpretation of drug benefit**
**Data imputation**

##  Drug Benefit  

**Single-dose trial**
**onset**
**duration**
**pain curves**
**Multiple-dose trial**
**duration of effect**

## Drug Benefit (continued)

**In single-dose trials, time specific pain measurements provide more information about onset and duration. TWA (SPID, SPRID) does not.**
**In multiple-dose trials, time-specific measurements and TWA face similar issues as those in chronic analgesia trials. **

**Notes:**
So in single-dose trial, time specific measurements are preferred than SPRID.

## Data Imputation for Time-Specific Measurements in Single-Dose Trial

**Last-observation-carried-forward (LOCF) **
**Baseline-observation-carried-forward (BOCF) **
**Worst-observation-carried-forward (WOCF)**

**Notes:**
I will focus on single-dose trial. LOCF and BOCF are commonly seen imputation methods. Although BOCF are often more conservative than LOCF method, both of them are based on urealistic assumptions hta lter pain intensity is the same as earlier or baseline pain intensity--not consistent with self-healing nature of acute pain. And, when with imputation, the results usually favor drug than without imputaiton.  

## Observed Curves

- 0

**Pain Intensity**

**--- placebo**
**__ testing drug**

- 4

- 8

- 12

- 16

- 20

- 24

**Hours**

**Notes:**
An extreme example: when we evaluate analgesic effect of a drug using dental model. Suppose we have pain measuremnt until 24 hours post baseline. No mater how many patient left in the end of the trial, if you plot the observed curve without imputation, because of the shot duration of dental pain, the pain intensity would be very mild in both drug and placebo groups.

## Observed and Imputed Curves

- 0

**Pain Intensity**

**--- placebo**
**__ testing drug**

- 4

- 8

- 12

- 16

- 20

- 24

**Hours**

**Notes:**
This is usually what happens when imputing  earlier drop-out’s data into later period. The separation here is due to higher drop-out rate in placebo group and mostly due to lack of efficacy. The imputed curve gives the impression that the pain persist and the drug effect still last at 24 hours. 

## Summary

**Chronic analgesia trial:**
**end-of-the-trial measurement and TWA represent different aspects of drug effect **
**consistent drug benefit through the trial is important**
**Acute analgesia trial: time-specific measurements are more informative than TWA (SPID, SPRID) in single-dose trials. **

## Summary

**Continuing efficacy evaluation even after a patient’s withdrawal can provide additional treatment information for drug effect.**
**Responder analysis**

**Notes:**
Responder analysis may be a better way to characterized drug effect and avoid artificial imputation methods