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

## TL;DR

This study compares Propensity Score Matching and Multivariate Regression Model in estimating treatment effects, revealing that PSM underestimates effects and reduces sample size, potentially introducing new biases.

## Contribution

The paper provides a simulation-based analysis showing PSM's limitations in effect estimation and sample retention compared to MRM.

## Key findings

- PSM reduces treatment bias but underestimates true effects.
- MRM outperforms PSM in effect estimation accuracy.
- Sample size reduction in PSM may introduce new biases.

## Abstract

Propensity Score Matching (PSM) is an useful method to reduce the impact ofTreatment - Selection Bias in the estimation of causal effects in observational studies. After matching, the PSM significantly reduces the sample under investigation, which may lead to other possible biases. In this sense, we want to analyse the behaviour of this PSM compared with other widely used method to deal with non-comparable groups, as is the Multivariate Regression Model (MRM). 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. This loss of information derived from the matching process may lead to another not known bias, and thus, to the inaccurate of the effect estimation compared with the MRM.