Determination of Optimal Timing for Non-Invasive Prenatal Testing and Robustness Analysis of Errors Based on Multi-Objective Optimization and K-Means Clustering

Abstract

This study addresses the challenge of determining the optimal timing for non-invasive prenatal testing (NIPT) based on BMI grouping. It aims to identify the optimal NIPT testing window for different pregnant women populations to minimize potential risks and maximize the pass rate for Y chromosome concentration. First, to eliminate subjective bias and uncover potential associations between BMI and test performance, virtual data were generated via Monte Carlo simulation to compensate for sparse real samples. Combined with the K-means elbow point method, pregnant women carrying male fetuses were grouped into four BMI intervals: [20.0, 25.7), [25.7, 32.2), [32.2, 39.4), and [39.4, 47.0). Second, a segmented sigmoid function was constructed to quantitatively define maternal potential risk, aligning with clinical risk trends. This function exhibits a three-stage progression: “initial slow growth,” “rapid growth,” and “extremely slow growth.” Subsequently, a multi-objective optimization model was established to minimize potential risk while maximizing Y chromosome concentration compliance rates. Solving this model using the NSGA-II algorithm yielded optimal NIPT timing points of 11.21, 12.69, 14.25, and 15.83 weeks for each BMI interval. Finally, error analysis revealed that detection errors significantly amplify false-negative risks in high-BMI and early-pregnancy-week cases, markedly narrowing the feasible testing window.