Multi-part balanced incomplete-block designs

TL;DR

This paper develops new combinatorial designs for cancer trials that accommodate multiple treatment types and constraints across medical centers, with generalizations to more complex scenarios involving additional object types.

Contribution

It introduces novel design constructions for multi-part balanced incomplete-block designs and extends them to scenarios with three or more object types.

Findings

Proved properties of these designs.

Provided multiple construction methods.

Generalized designs to complex multi-object scenarios.

Abstract

We consider designs for cancer trials which allow each medical centre to treat only a limited number of cancer types with only a limited number of drugs. We specify desirable properties of these designs, and prove some consequences. Then we give several different constructions. Finally we generalise this to three or more types of object, such as biomarkers.