#Propensity Score Matching underestimates Treatment Effect, in a simulated theoretical multivariate model

Propensity Score Matching (PSM) is an useful method to reduce the impact of treatment-selection bias in the estimation of causal effects in observational studies. Despite the fact of the Treatment - Selection Bias reduction, the overall behaviour of this PSM compared with a Multivariate Regression Model (MRM) has never been tested. Monte Carlo Simulations are made to construct groups with different effects in order to compare the behaviour of PSM and MRM estimating this effects. Also the Treatment - Selection Bias reduction for the PSM is calculated. With the PSM a reduction in the Treatment - Selection Bias is achieved, with a reduction in the Relative Real Treatment Effect Estimation Error, but despite of this bias reduction and estimation error reduction, the MRM significantly reduces more this estimation error compared with the PSM. Also the PSM leads to a not insignificant reduction of the sample, which may lead to another not known bias, and thus, to the inaccurate of the effect estimation compared with the MRM.