## 7 Discussions
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Method** & **Advantage** & **Disadvantage** \\ \hline \multirow{6}{*}{**Traditional regression**} & \multirow{6}{*}{\(\bullet\)} & \multirow{6}{*}{Simplest and easy to fit} & \(\bullet\) & Model mis-specification decreases precision in unbalanced design May be implausible with a large number of covariates Treatment effect is assumed to be the same for different levels of the covariates \\  & & & & \\ \cline{1-1}  & & & & \\ \cline{1-1}  & & & & \\ \hline \multirow{6}{*}{**G-computation**} & \multirow{6}{*}{\(\bullet\)} & Treatment effect can be different for different levels of the covariates Robust to model mis-specification & \(\bullet\) & Needs more time to compute confidence intervals \\ \cline{1-1} \cline{2-4}  & & & & \\ \cline{1-1}  & & & & \\ \cline{1-1}  & & & & \\ \hline \multirow{6}{*}{**PS Stratification**} & \multirow{6}{*}{\(\bullet\)} & Keeps all the data and divides into strata Gives estimates for all strata Explores interactions of treatment and PS & \(\bullet\) & Has bias when a small number of strata strata are used Unstable when the number of strata is large and/or the data size is small \\ \cline{1-1} \cline{2-4}  & & & & \\ \cline{1-1}  & & & & \\ \cline{1-1}  & & & & \\ \cline{1-1}  & & & & \\ \hline \multirow{6}{*}{**PS Matching**} & \multirow{6}{*}{\(\bullet\)} & Simple to perform and interpret Often provides good balance among matched pairs in most cases & \(\bullet\) & Loses data due to unmatching May not be precise Need to choose matching algorithm \\ \cline{1-1} \cline{2-4}  & & & & \\ \cline{1-1}  & & & & \\ \cline{1-1}  & & & & \\ \cline{1-1}  & & & & \\ \cline{1-1}  & & & & \\ \hline \multirow{6}{*}{**PS Weighting**} & \multirow{6}{*}{\(\bullet\)} & Keeps all the data Often provides good balance in covariates Easy to implement and intuitive to understand understand & \(\bullet\) & May be unstable with the presence of extreme weights Needs to decide whether to take out Needs large and small weights \\ \cline{1-1} \cline{2-4}  & & & & \\ \cline{1-1}  & & & & \\ \cline{1-1} \cline{2-4}  & & & & \\ \cline{1-1} \cline{2-4}  & & & & \\ \cline{1-1} \cline{2-4}  & & & & \\ \hline \multirow{6}{*}{**Traditional Regression with PS as a Covariate**} & \multirow{6}{*}{\(\bullet\)} & Simple to implement & \(\bullet\) & May not be necessary Removes less difference compared with matching and weighting. \\ \cline{1-1} \cline{2-4}  & & & & \\ \cline{1-1} \cline{2-4}  & & & & \\ \cline{1-1} \cline{2-4}  & & & & \\ \cline{1-1} \cline{2-4}  & & & & \\ \hline \multirow{6}{*}{**Oenly Robust Estimator**} & \multirow{6}{*}{\(\bullet\)} & Unbiased if one of the treatment model and response model is correct & \(\bullet\) & More difficult to implement Takes a longer time \\ \cline{1-1} \cline{2-4}  & & & & \\ \cline{1-1} \cline{2-4}  & & & & \\ \cline{1-1} \cline{2-4}  & & & & \\ \cline{1-1} \cline{2-4}  & & & & \\ \hline \multirow{6}{*}{**Overlap Weighting**} & \multirow{6}{*}{\(\bullet\)} & Weights are bounded between 0 and 1 Minimize the asymptotic variance Define a population of substantial clinical relevance and policy interest Doubly robust estimator can be applied & \(\bullet\) & Not available in some software languages except for PSWeight package in R \\ \cline{1-1} \cline{2-4}  & & & & \\ \cline{1-1} \cline{2-4}  & & & & \\ \cline{1-1} \cline{2-4}  & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of different confounding adjustment methods. is applied, treatment effects can be differentiated by covariates. G-computation is effective in reducing confounding bias and balancing covariates. However, variance estimation is more complex, relying on either bootstrapping or the empirical sandwich variance estimator [72; 73]. PS stratification has the advantage of keeping the whole data and exploring possible interactions between the treatment variable and PS. It tends to work well with small to moderate covariate imbalances [35].