The Stochastic Score Classification Problem

TL;DR

This paper addresses the problem of optimally sequencing medical tests with probabilistic outcomes to classify patient risk levels while minimizing expected costs, providing approximation algorithms for different testing strategies.

Contribution

It introduces approximation algorithms for both adaptive and non-adaptive test sequencing in the stochastic score classification problem, advancing cost-effective risk classification methods.

Findings

Developed approximation algorithms for adaptive testing strategies.

Proposed solutions for non-adaptive testing sequences.

Identified open questions for future research.

Abstract

Consider the following Stochastic Score Classification Problem. A doctor is assessing a patient's risk of developing a certain disease, and can perform $n$ tests on the patient. Each test has a binary outcome, positive or negative. A positive test result is an indication of risk, and a patient's score is the total number of positive test results. The doctor needs to classify the patient into one of $B$ risk classes, depending on the score (e.g., LOW, MEDIUM, and HIGH risk). Each of these classes corresponds to a contiguous range of scores. Test $i$ has probability $p_i$ of being positive, and it costs $c_i$ to perform the test. To reduce costs, instead of performing all tests, the doctor will perform them sequentially and stop testing when it is possible to determine the risk category for the patient. The problem is to determine the order in which the doctor should perform the tests, so as to minimize the expected testing cost. We provide approximation algorithms for adaptive and non-adaptive versions of this problem, and pose a number of open questions.