This study investigates the application of quantum neural networks (QNNs) for propensity score estimation to address selection bias in comparing survival outcomes between laparoscopic and open surgical techniques in a cohort of 1177 colorectal carcinoma patients treated at University Hospital Ostrava (2001-2009). Using a dataset with 77 variables, including patient demographics and tumor characteristics, we developed QNN-based propensity score models focusing on four key covariates (Age, Sex, Stage, BMI). The QNN architecture employed a linear ZFeatureMap for data encoding, a SummedPaulis operator for predictions, and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for robust, gradient-free optimization in noisy quantum environments. Variance regularization was integrated to mitigate quantum measurement noise, with simulations conducted under exact, sampling (1024 shots), and noisy hardware (FakeManhattanV2) conditions. QNNs, particularly with simulated hardware noise, outperformed classical logistic regression and gradient boosted machines in small samples (AUC up to 0.750 for n=100), with noise modeling enhancing predictive stability. Propensity score matching and weighting, optimized via genetic matching and matching weights, achieved covariate balance with standardized mean differences of 0.0849 and 0.0869, respectively. Survival analyses using Kaplan-Meier estimation, Cox proportional hazards, and Aalen additive regression revealed no significant survival differences post-adjustment (p-values 0.287-0.851), indicating confounding bias in unadjusted outcomes. These results highlight QNNs' potential, enhanced by CMA-ES and noise-aware strategies, to improve causal inference in biomedical research, particularly for small-sample, high-dimensional datasets.