# Presentation: 257750

## Statistical Considerations in Design and Analysis of Drug Abuse Clinical Trials

- Ling Chen, Ph.D.
- Quantitative Methods and Research Staff
- OB/CDER/FDA
- Acknowledgement
- The presenter thanks Drs. Yi Tsong and Michael Klein for helpful discussion and useful comments.
- The views expressed in this talk represent the opinions of the presenter, and do not necessarily represent the views of the U.S. Food and Drug Administration.
- June 30, 2005, DIA meeting

## Outline

- Statistical assessment criteria
- Advantages and disadvantages of currently used study designs
- Design issues and statistical analysis issues
- Summary

## Statistical Assessment Criteria

- To claim that there is no potential for abuse liability of a new drug, an applicant needs to show that for each primary variable,
- The positive control drug has statistically larger mean response than placebo (validating the trial)
- All doses of the new drug have statistically lower mean response than each dose of the positive control drug.
- All doses of the new drug have mean response that is “not worse than” the mean response of placebo (e.g. no more than twice the mean response of placebo)

## Designs of Drug Abuse Potential Studies

- Repeated Williams Square design
-         For example: 4 treatments crossover, A, B, C, and D denote treatments.
- A D B C	Three replications
- B A C D	 Sixteen degrees of freedom is available to assess fixed
- C B D A	 effects
- D C A B
-    	_Advantage:_
-    	It is a variance-balanced design. The balance can be achieved by one particular Latin square for an even number of treatments or two particular Latin squares for an odd number of treatments.
-    	_Disadvantage:_
-    	Insufficient enough degrees of freedom to assess direct-by-carryover interaction.

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- Complete set of orthogonal Latin squares
-    	For example, for 4 treatments crossover, it needs 3 Latin squares to achieve the balance.
- 	A B C D	A D B C		A C D B
- 	B A D C	B C A D		B D C A		Forty eight degrees of
- 	C D A B	C B D A		C A B D		freedom are available for
- 	D C B A	D A C B		D B A C		assessing fixed effects.
-  	_Advantage:_
-    	It is also a variance balanced design. There are enough degrees of freedom to assess mixed carryover effect (direct-by-carryover interaction).
-    	_Disadvantage:_
-    	It needs more squares to achieve the balance.

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- When one treatment has an extremely long half life, a suggestion made by the sponsor is to include one more placebo and randomly assign placebo and this treatment in the last two periods.
-    _Disadvantage:_
-    It will affect blinding of the trial.
-    It is not a balanced design.

## Design Issues

- Which drugs are necessary to include in the study?
-     Placebo
-     An active control drug (multiple dose)
-     Low, median and high doses of the new drug
- If the objective of a study is to show a new drug lacks  abuse liability, the positive control should be a schedule IV drug or V drug.
- Unnecessary treatments used in the study may bring additional variability in the analysis.

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-  What is the required washout period?
- We suggest to be at least five times the maximum T1/2 of all treatments in the study.
- Insufficient washout period results in carryover effects and complicates assessing the treatment difference.

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- What is a good choice of Latin squares for a crossover design for such a study? Repeated Williams squares? A complete set of Latin squares? Or others?
-    An algorithm developed by John, Russell and Whitaker (2004) (*Statistics in Medicine*, Vol. 23, pp 2645-2658) allows the user to choose a design from a variety of models for the carry-over effects. One of the models includes direct-by-carryover interaction.

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- What sample size should be chosen for such a study?
- One of the reasons that many such studies failed to demonstrate the absence of abuse liability of the new drug is lack of power of the statistical tests due to small sample sizes.
- Due to the difficulty in recruiting appropriate study subjects, the desirable sample size is not necessarily feasible in a one center trial. But this difficulty may be overcome by a multi-center trial.
- The best way to reduce the sample size is to not put unnecessary treatments in the study.

## Statistical Analysis Issues

## Models for the Primary Analysis

- We consider period, treatment, first-order-carryover and direct-by-carryover interaction as fixed effects and subject as a random effect.
- If repeated Latin squares are used, sequence should be considered as a fixed effect and subject nested with sequence as a random effect.

## Assessment of carryover effects

- Since no carryover effect (or no mixed carryover effect) is in the null hypothesis, in this case, the type II error (falsely accepting the claim of no carryover effect) concerns the FDA. A* *larger than 5% level of significance should be chosen for this test to decrease the probability of making type II error.
- If the test is not statistically significant,  the carryover effect (or mixed carryover effect) may be dropped from the study model for a sensitive analysis.

## Summary

- The design of a drug abuse potential study should be based on the objective of the study and the study model used in statistical analysis.
- Unnecessary treatments included in the study may bring unnecessary variability into the analysis and would increase the duration of the trial and the sample size needed.

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- We suggest the washout period of a crossover designed study to be at least 5 times the maximum T1/2 of the treatments in the study. A sufficient washout period is key to the success of a study based on a crossover design.
- The challenges of such studies are: large number of treatments crossover, carryover effects, small sample sizes.

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- The history of drug abuse potential studies is relatively young.
-  There are many opportunities for improving the existing designs and developing statistical methodologies for such a study.

## Thank You!