The Single-Dependence Sequential Testing Problem for the Living Kidney Donor Workup Process

Abstract

The Sequential Testing Problem (STP) seeks to minimize the total expected cost of administering a series of tests which determine the quality of a system. When the probabilities of passing or failing a test are independent there exist many methods to solve the problem efficiently, but there is little research exploring the effect of dependency between tests. Motivated by the process of evaluating living kidney donors, we explore a variant of the STP which assumes that the probability of passing a given test is conditional upon passing the preceding test, and refer to this variant as the Single-Dependence Sequential Testing Problem (SDSTP). We present an optimization model to solve the SDSTP to optimality and simple - but effective methods to approximate the solution. Though we conjecture that the problem is NP-Complete, our experiments show that the model can be solved to optimality for many practical applications where the set of tests is small (say, less than 20), and our proposed algorithms also find near-optimal solutions in rapid time even for large numbers of tests.