## Properties of biased coin designs in sequential clinical trials.(English)Zbl 0553.62068

Several authors have proposed and studied designs in a clinical trial experiment of testing treatments. For example B. Efron [cf. Biometrika 58, 403-417 (1971; Zbl 0226.62086)] proposed and studied a sequential biased design for two treatments $$R=2$$. A number of generalizations have been studied when $$R>2.$$
The author uses the methods of martingale and martingale invariance principle to derive central limit theorems and related results for biased coin designs. The method applies to an arbitrary number of treatments with no prognostic factors. The case $$R=2$$ with arbitrary number of prognostic factors is also studied.
Reviewer: R.A.Khan

### MSC:

 62L05 Sequential statistical design 62P10 Applications of statistics to biology and medical sciences; meta analysis 60F05 Central limit and other weak theorems 60F17 Functional limit theorems; invariance principles

Zbl 0226.62086
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