Propensity score and IPW with imputed data

[Liamb]

Hello,

I used the codes at below to estimate the propensity score and logistic regression for inverse probability weighting.

How can I test the balance of the standardised mean differences before and after adjustment?

How to obtain the synthetic n values derived from weights?

Thanks

/***CREATING PROPENSITY SCORES********/

proc sort data=tab_imput; by _imputation_;run;
proc logistic data=tab_imput desc;
class var1 var2 var3 var4 var5 var6 var7 var8 var9 ;
model mut= var var1 var2 var3 var4 var5 var6 var7 var8 var9/link=logit rsquare ;
output out=denom p=d;
by _imputation_;
run;
		
proc logistic data=tab_imput desc;
model mut=;
output out=num p=n;
by _imputation_;
run;

proc sort data=tab_imput ;
by anonymat;run;
proc sort data=denom;
by anonymat;run;
proc sort data=num;
by anonymat;run;

data tab_imput_pscore;
merge tab_imput denom num;
by anonymat;
if mut=1 then uw=1/d; else if mut=0 then uw=1/(1-d);
if mut=1 then sw=n/d; else if mut=0 then sw=(1-n)/(1-d);
run;
proc sort data=tab_imput_pscore; by _imputation_;run;

/***PROPENSITY SCORE WEIGHTED OUTCOME MODEL****/

ods graphics on;
proc logistic data=tab_imput_pscore desc; 
	class mut(ref='no') / param=reference ; 
	model vif (event='no') = mut/ rsquare clodds=wald lackfit ;
	weight sw ;
    by _imputation_;
    oddsratio mut;
    ods output parameterEstimates  = ipw_mut ;
run;
ods graphics off;
proc mianalyze parms=ipw_mut ;
modeleffects mut;
ods output parameterEstimates  = ipw_mut1;
run;

data ipw_mut2; set ipw_mut1;
OR_est=EXP(ESTIMATE);
LCI_OR=OR_est*EXP(-1.96*STDERR);
UCI_OR=OR_est*EXP(+1.96*STDERR);
run;

proc print data=ipw_mut2;
var Parm OR_est LCI_OR UCI_OR Probt ;
run;

[SAS_Rob]

In order to combine any statistics from multiply imputed data you need the point estimate and a standard error.  Do you know how the standard errors for standardized mean differences and synthetic Ns would be calculated?

[Liamb]

Standrd erros will be estimated according to Rubin's rules. For parameter estimates, averages are taken. Their variance is basically a combination of the average squared standard errors plus the variance of the parameter estimates across the imputed data sets.

[SAS_Rob]

The standard errors that I was referring to were associated with the point estimates themselves, not the combined estimates.  In other words, do you have a formula that reflects the standard errors that you will eventually average in the first half of Rubin's methodology?

[Liamb]

I'm not sure but I think it is the following formula for standard mean difference (SMD):