Propensity Score Matching for Causal Inference: Comparing Classical and Bayesian Approaches

Naomi Kollongei — 2026-10-03

Propensity-score matching (PSM) is widely used to reduce measured confounding in observational studies, but treatment-effect estimates can be sensitive to matching restrictions and to uncertainty in the estimated propensity score. This study compares classical and Bayesian PSM using the 996-record Lindner abciximab dataset distributed with the LocalControl R package. The treatment was abciximab use during percutaneous coronary intervention, and the outcome was life-years preserved (lifepres), coded 0 for patients who died within 1 year and 11.6 for patients who survived at least 1 year in this public data distribution. The reported analysis used a six-covariate treatment-assignment model (stent use, height, sex, diabetes, recent acute myocardial infarction, and left ventricular ejection fraction). Classical analyses used 1:1 nearest-neighbour matching without replacement, first unrestricted and then with a caliper of 0.2 standard deviations of the logit propensity score. The classical model had an AUC of 0.6192 (95% CI 0.5820-0.6565). Unrestricted matching paired 298 of 698 treated patients with 298 controls and yielded a matched-sample mean difference of 0.3503 life-year units but poor residual balance. Caliper matching retained 288 treated-control pairs and yielded 0.4833 life-year units; balance improved materially for several covariates, although residual imbalance remained for stent use, height, sex, and the propensity score. Bayesian caliper matching propagated uncertainty in the treatment-assignment model through repeated posterior propensity-score draws and matching, generating 1,000 matched-sample treatment-effect draws. The posterior mean was 0.4098 life-year units (SD 0.2340; 95% credible interval -0.0410 to 0.8736), with P(effect > 0 | data) = 0.960. These results illustrate that matching restrictions can alter both the analysed treated population and the estimated treatment contrast. Given the remaining important residual imbalance, the omission of the number of vessels involved in the first PCI from the fitted treatment model, and the possibility of unmeasured confounding, the empirical estimates should be interpreted as a methodological illustration rather than as definitive clinical causal effects.

Numerical Analysis of Magnetohydrodynamic Turbulent Fluid Flow Over a Vertical Semi: Infinite Plate with Joules Heat

Wycliffe Odhiambo Juma — 2026-10-14

Magnetohydrodynamic (MHD) turbulent fluid flow plays a significant role in many engineering and industrial processes, including nuclear reactor cooling, metallurgical operations, electromagnetic pumps, petroleum transportation, liquid metal technology, geothermal energy extraction, thermal management systems, MHD power generation, biomedical fluid systems and other industrial heat transfer technologies where magnetic fields and Joule heating significantly influence fluid behaviour. Despite the extensive literature on MHD fluid flow, relatively limited attention has been given to the numerical analysis of turbulent MHD flow over a vertical semi-infinite plate under the combined influence of Joule heating and buoyancy effects. This study addresses this gap by developing and numerically analysing a mathematical model describing turbulent magnetohydrodynamic fluid flow over a vertical semi-infinite plate with Joule heating. The governing continuity, momentum, and energy equations were formulated based on the principles of fluid dynamics and electromagnetism. Reynolds time-Averaging (RANS) together with the Boussinesq approximation was employed to simplify the turbulence terms, while the resulting dimensionless governing equations were solved numerically using the finite difference method. Numerical simulations were conducted to investigate the influence of key dimensionless parameters, including the Grashof number, Joule heating parameter, magnetic parameter, and decay parameter, on the velocity and temperature distributions within the flow field. The numerical results demonstrate that increasing the Grashof number significantly enhances fluid velocity and heat transfer due to stronger buoyancy forces. The study further establishes that higher Joule heating intensities increase both fluid temperature and velocity by supplying additional thermal energy to the flow. Conversely, larger decay parameters reduce the influence of Joule heating, resulting in lower temperature and velocity profiles. The imposed magnetic field was observed to regulate fluid motion by introducing Lorentz forces that modify the velocity distribution, while turbulence effects were effectively represented through the Reynolds-Averaged Navier-Stokes formulation. Comparison of the numerical solutions with established results in the literature showed good agreement, confirming the accuracy and reliability of the developed numerical model. The findings contribute to the advancement of computational studies on turbulent magnetohydrodynamic flows and provide useful insights for the design and optimisation of engineering systems involving electrically conducting fluids.

Journal of Advances in Mathematics and Computer Science

Propensity Score Matching for Causal Inference: Comparing Classical and Bayesian Approaches

Numerical Analysis of Magnetohydrodynamic Turbulent Fluid Flow Over a Vertical Semi: Infinite Plate with Joules Heat