Table 4 Overview of four different PS-based approaches

Principle

Matching one or more control cases with a propensity score almost equal to the PS for each treatment case

Stratifying the sample based on rank-ordered PSs and performing comparisons between groups within each stratum

Incorporating PS values as a covariate in regression analysis models

Utilizing the PS to develop weights and applying all outcomes of interest

Ability to control confounding bias

Superior to the PS hierarchy and PS correction

Weaker than other methods in particular to survival analysis

Weaker than PS matching and PS weight

Superior to PS hierarchy and PS correction

Data utilization

Removing data that does not match the study objectives

Retaining data from all study objectives

Retaining data from all study objectives

Retaining data from all study objectives

Causal effect estimation

Matching can estimate only the ATT

Hierarchy can estimate only marginal effect but neither the ATT nor the ATE

Correction can estimate only marginal effect but neither the ATT nor the ATE

Weighting can estimate either effect (ATT or ATE) according to the way weights are defined

Advantages

Addressing the confounding from multiple variables to guarantee equalization between individuals; The strength of the argument is strong and mirrors a closer randomized experiment

Achieving equilibrium of intergroup covariates within each stratum

Model-based analysis with a straightforward application

The strength of the argument is strong and mirrors a closer randomized experiment

Disadvantages

As only areas of the domain that are mutually supported by PS values can be matched, the sample size is reduced

Inadequate covariate equalization, particularly for the uppermost and lowest tiers

A model-dependent approach that can sometimes be challenging to meet the assumptions of the model

The sample in the study is only theoretical; Excessive weight will have an impact on the effect estimates