1 Statistics in Drug Development Mark Rothmann, Ph. D.* Division of Biometrics I Food and Drug Administration * The views expressed here are those of the author and not necessarily those of the FDA.

2 Various Indications for Drugs For example: Headache/Pain medicine, psychiatric drugs, AIDS treatments, Cancer drugs, etc. Details about the design and goal of a study depends on the indication of the drug (how the drug will be used).

3 Goal of New Drug Development Develop a safe and effective drug.

4 Phases of Drug Development Pre-clinical - Animal testing Phase 1 - Dose ranging (toxicity) Phase 2 - Use of the drug in a small number of studies (efficacy screening) Phase 3 - Comparative study with a placebo or an active drug (usually the standard therapy) Phase 4 - Post-marketing studies

5 Comparative Phase 3 Trials Aspects of a quality comparative study - Randomization (patients are randomly divided into groups) - Stratification - Double-Blind (eliminate a placebo-effect and diagnosis bias) - Control

6 Endpoints (Variables of Interest) Examples of Oncology Endpoints: Survival Time Tumor response (binary or ordinal variable) Time to tumor progression Quality of Life

7 Hypotheses H 0 : experimental drug and the standard drug (or placebo) have the same effectiveness H 1 : experimental drug and the standard drug (or placebo) have different effectiveness Alternative hypotheses are two-sided. Hypotheses are formally for those patients in the study. One or more endpoints may tested.

8 Potential Errors Type I error: Rejecting H 0 when H 0 is true (false positive rate) Type II error: Failing to reject H 0 when H 1 is true ( or for the drug company the type II error of interest is failing to conclude the drug is effective when it is effective) An overall probability of a type I error is maintained at 0.05 for the primary efficacy analysis. If more than one endpoint is involved in the primary efficacy analysis, individual type I errors are adjusted for the total number of comparisons.

9 Sample Size Determination Aspects considered for the sample size calculation: - A primary method of analysis is selected. - Desired Type II error probability at a clinically meaningful effectiveness alternative. - Accrual Period - Follow-up time - Fraction of dropouts

10 Analysis Populations Intent-to-treat Population: All patients as randomized Evaluable Population: All patients who received study therapy that have measurements for the primary efficacy endpoint and comply with the protocol.

11 Statistical Conclusions Patients in the study are volunteers - not randomly selected from some group. Formally, any conclusions of statistical significance is good only for that set of patients in the study.

12 Other Issues - Formal Definitions of Endpoints - Missing Data (common in quality of life measurements) - Crossover to other therapies - Censoring - Robustness with respect to the method of analysis chosen - Interim Efficacy Analyses