The bivariate probit model of uncomplicated control of tumor: a heuristic exposition of the methodology

To describe the concept, models, and methods for the construction of estimates of joint probability of uncomplicated control of tumors in radiation oncology. Interpolations using this model can lead to the identification of more efficient treatment regimens for an individual patient. The requirement to find the treatment regimen that will maximize the joint probability of uncomplicated control of tumors suggests a new class of evolutionary experimental designs--Response Surface Methods--for clinical trials in radiation oncology.

The software developed by Lesaffre and Molenberghs is used to construct bivariate probit models of the joint probability of uncomplicated control of cancer of the oropharynx from a set of 45 patients for each of whom the presence/absence of recurrent tumor (the binary event E1/E1) and the presence/absence of necrosis (the binary event E2/E2) of the normal tissues of the target volume is recorded, together with the treatment variables dose, time, and fractionation.

The bivariate probit model can be used to select a treatment regime that will give a specified probability, say P(S) = 0.60, of uncomplicated control of tumor by interpolation within a set of treatment regimens with known outcomes of recurrence and necrosis. The bivariate probit model can be used to guide a sequence of clinical trials to find the maximum probability of uncomplicated control of tumor for patients in a given prognostic stratum using Response Surface Methods by extrapolation from an initial set of treatment regimens.

The design of treatments for individual patients and the design of clinical trials might be improved by use of a bivariate probit model and Response Surface Methods.