Integral evaluation for continual reassessment method

In this paper we show how the exact analytical solutions to the numerical integrals required in the implementation of the continual reassessment method can be evaluated. The formulas have been given but, with increasing sample size, rapidly become unwieldy. We develop an algorithm which uses the numerical binary representation of the subset size and, in the process, enables us to easily identify those members of the subset needed in the integral evaluation. The complex combinatorial problem of selecting the set of all subsets with a particular characteristic is then greatly simplified. We describe the nature and type of all the variables and parameters used in a PASCAL procedure.