Propensity Score Weighting

Introduction

Propensity score (PS) weighting is a statistical technique widely employed in Real World Evidence (RWE) studies to address confounding bias and facilitate the estimation of causal treatment effects. By using the estimated probability of treatment assignment to create weights, PS weighting aims to balance the observed covariates across treatment groups. While both SAS and R provide methods to do PS weighting, the syntax and available options differ considerably. The PS weighting process generally involves several key stages: first, the estimation of propensity scores using a regression model; second, the calculation of weights for each subject based on their propensity score; and third, the use of these weights in the analysis of choice.

Differences

Given the extensive number of parameters and arguments available in both PROC PSMATCH and weightit(), we will focus only on the observed differences.

Options

Option	PROC PSMATCH	weightit
PS methods	logistic regression	glm, gbm, covariate balancing propensity score (CBPS) algorithm, non-parametric CBPS, entropy balancing, inverse probability tilting, optimization-based weighting, PS weighting using SuperLearner, bayesian additive regression trees (BART), energy balancing
Estimands	ATT, ATE	ATT, ATE, ATC, for some methods ATO, ATM, ATOS
Region	Always used; allobs, treated or cs (common support), with allowed extension	Not available
Stabilize weights	Available as logical, only for ATE	Available as logical or formula when used with continuous treatments or when estimand is ATE
Moments	Not available	Some methods allows to set the greatest power of each covariate to be balanced
Interactions	Not available	Some methods allows to set the first-order interactions of the covariates to be balanced

Output

The way SAS and R output the weights is similar - they are given as a column (SAS) / vector in the output list (R) with a computed weight for each observation. However, seems to be due to the different rounding rules, the PS weights may differ on the last digit.

Statistics

In SAS, descriptive statistics for assessing balance are primarily generated through the ASSESS statement within PROC PSMATCH. Conversely, in R, descriptive statistics for weights could be obtained by applying the summary() function to the output object returned by the weightit(). The balance assessment after weighting could be performed using the cobalt package. The following table summarizes the statistics available in SAS and R:

Stat or info	SAS	R
N	+	+
Weights range	-	+
Extreme weights	+	+
ESS	-	+
Coefficient of Variation	-	+
Mean absolute deviation	-	+
Negative Entropy	-	+
Number of zero weights	-	+
Weighted covariates stats	+	-*

*available from cobalt package

Figures

Plot type	R	SAS
Love plot	plot(): - cobalt: many different settings.	Displayed for: all/region/matched/weighted matched, trt/control. Includes PS, all numeric and binary variables.
General distribution plots	plot(): - cobalt : Highly customizable plots.	Displayed for: all/region/weighted, trt/control. Includes PS and all variables. For PS and numeric - boxplots, character - barplots.
eCDF plots	plot(): -	Displayed for: all/region/weighted, trt/control. Includes PS and all numeric variables.
Cloud plots	plot(): -	Displayed for: all/region, trt/control. Includes PS, weights and all numeric variables. Presented as 2 separate clouds per variable.
PS weights histogram	plot(): Displayed for: trt/control. Includes PS weigths. cobalt: Highly customizable plots.	-

Dataset

The dataset used in the example below can be found here: [ps_data.csv](https://github.com/PSIAIMS/CAMIS/blob/main/data/ps_data.csv)

                           trt              control       Standardized
Characteristic          (N = 120)          (N = 180)       Mean Diff.

  sex                                                        0.1690
    F                  70 (58.3 %)        90 (50.0 %)        
    M                  50 (41.7 %)        90 (50.0 %)
    
  age                 61.5 (17.12)       49.4 (10.55)        0.7057
  
  weight              67.3 ( 7.33)       63.8 ( 9.64)        0.4741
  
  bmi_cat   
    underweight        34 (28.3 %)        63 (35.0 %)       -0.1479  
    normal             57 (47.5 %)        61 (33.9 %)        0.2726
    overweight         29 (24.2 %)        56 (31.1 %)       -0.1622

Matching Examples

Average Treatment Effect in Treated (ATT)

SAS

proc psmatch data=data;
    class trtp sex bmi_cat;
    psmodel trtp(Treated="trt")= sex weight age bmi_cat;
    psweight weight=ATTWGT;
    output out(obs=all)=ps_res ps=_PScore weight=_PSweight;
run;

R

ps_res <- weightit(trtp ~ sex + weight + age + bmi_cat,
                    data=data_gen,
                    method="glm",
                    estimand="ATT",
                    focal="trt")

Average Treatment Effect (ATE)

SAS

proc psmatch data=data;
    class trtp sex bmi_cat;
    psmodel trtp(Treated="trt")= sex weight age bmi_cat;
    psweight weight=ATEWGT;
    output out(obs=all)=ps_res ps=_PScore weight=_PSweight;
run;

R

ps_res <- weightit(trtp ~ sex + weight + age + bmi_cat,
                    data=data_gen,
                    method="glm",
                    estimand="ATE")

Average Treatment Effect (ATE), stabilized weights

SAS

proc psmatch data=data;
    class trtp sex bmi_cat;
    psmodel trtp(Treated="trt")= sex weight age bmi_cat;
    psweight weight=ATEWGT(stabilize=YES);
    output out(obs=all)=ps_res ps=_PScore weight=_PSweight;
run;

R

ps_res <- weightit(trtp ~ sex + weight + age + bmi_cat,
                    data=data_gen,
                    method="glm",
                    estimand="ATE",
                    stabilize=TRUE)