Quantum Neural Networks Reduce Bias in Colorectal Cancer Surgery Outcomes.

Addressing selection bias remains a persistent challenge in observational biomedical studies, frequently hindering accurate comparisons of treatment outcomes. Researchers are increasingly exploring machine learning techniques to refine propensity score estimation, a statistical method used to account for confounding variables. A new study, led by Vojtěch Novák, Ivan Zelinka, Lenka Přibylová from VSB-Technical University of Ostrava, and Lubomír Martínek from the University of Ostrava and University Hospital Ostrava, investigates the application of quantum neural networks (QNNs) to this problem. Their work, entitled “Quantum Neural Networks for Propensity Score Estimation and Survival Analysis in Observational Biomedical Studies”, details the development and evaluation of QNN models applied to a cohort of 1177 patients undergoing colorectal carcinoma surgery at University Hospital Ostrava between 2001 and 2009. The team employed a QNN architecture incorporating a linear feature map, summed Pauli operators, and the Covariance Matrix Adaptation Evolution Strategy for optimisation, demonstrating improved performance over classical machine learning algorithms, particularly when dealing with limited data and noisy environments.

Quantum neural networks present a refined approach to causal inference, particularly valuable when analysing limited biomedical data and high-dimensional datasets. Researchers have recently applied these networks to estimate propensity scores, effectively addressing selection bias within a retrospective analysis of patients with colorectal carcinoma who underwent either laparoscopic or open surgery. This work demonstrates that quantum neural networks, when combined with robust optimisation strategies, improve propensity score estimation, especially when sample sizes are limited and data structures are complex, conditions frequently encountered in biomedical investigations.

The investigation utilised a quantum neural network architecture featuring a linear ZFeatureMap for data encoding and a SummedPaulis operator for predictions. A feature map transforms classical data into a quantum state, allowing the quantum computer to process it. The ZFeatureMap specifically encodes data using rotations around the Z-axis of the quantum state. The SummedPaulis operator then facilitates predictions based on this encoded data. Crucially, the model employs the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for training. CMA-ES is a gradient-free optimisation algorithm, meaning it doesn’t rely on calculating derivatives, which can be problematic in quantum systems. This algorithm effectively navigates complex data landscapes and converges on optimal solutions. Furthermore, variance regularisation actively mitigates the impact of measurement noise, the inherent inaccuracies in reading quantum states, enhancing the reliability of the propensity score estimates.

Comparative analyses, conducted under ideal, sampling, and noisy hardware conditions, consistently demonstrated the quantum neural network’s ability to maintain performance even with significant quantum noise. The resulting propensity scores were successfully employed in both matching and weighting techniques to achieve substantial balance in covariates between the surgical groups. Covariate balance ensures that groups being compared are similar in terms of characteristics that could influence the outcome, reducing the risk of spurious associations. Standardised mean differences of 0.0849 and 0.0869 were achieved using genetic matching and matching weights, respectively, indicating effective reduction of confounding variables and a more reliable comparison between the two surgical approaches.

Subsequent survival analyses, utilising Kaplan-Meier estimation, Cox proportional hazards modelling, and Aalen regression, revealed no statistically significant differences in survival outcomes between the laparoscopic and open surgery groups following adjustment for confounding factors, with p-values ranging from 0.287 to 0.851. Kaplan-Meier estimation provides a non-parametric estimate of survival probabilities. At the same time, Cox proportional hazards modelling and Aalen regression are parametric methods used to assess the relationship between covariates and survival time. These findings strongly suggest that observed differences in unadjusted survival outcomes were likely attributable to confounding variables, rather than the surgical approach itself, highlighting the importance of careful statistical adjustment.

The study highlights the potential of quantum neural networks, enhanced by CMA-ES optimisation and noise-aware strategies, to enhance causal inference in biomedical research, providing a new tool for clinicians and researchers. The study suggests that quantum neural networks offer a promising avenue for reducing bias and obtaining more accurate estimates of treatment effects, ultimately contributing to improved patient care and more informed clinical decision-making.