**A. Appendix**

Below, we present code from SAS 9.3 (SAS Institute, Cary, NC) to implement the statistical analyses for the application in Section 5.4. See Leslie and Ghomrawi [35] for additional details on the implementation of instrumental variables regression using the QLIM procedure in SAS.

/\*For each implementation below, we begin with *analysis\_data*, which is the cleaned version of the registry data with all coded variables necessary for analyses. The variable *Tobi* is the indicator variable for whether the subject received tobramycin; *dfev1* refers to the outcome variable (change in FEV1% predicted). First, we examine the initial difference between the treated and untreated groups.\*/

```
title 'Unadjusted Analysis';
proc ttest data=analysis_data;
class Tobi;
var dfev1;
run;
```
/\*The code below performs a multivariable linear regression to determine the association between tobramycin and change in lung function, with adjustment for the previously described measured confounders. The variables below correspond to sex (*gender*), baseline measures of age (*age*), FEV1% predicted (*base\_fev1*), weightfor-age percentile (*wtpct*), insurance coverage (*inscat*), CF-related diabetes (*cfrd*), dornase alfa (*dnase*), pancreatic insufficiency (*pancr*), and number of hospitalizations in year prior to baseline year (*numhosp*), categorized as 0, 1, 2, 3 or more\*/

title 'Model (1): Traditional Regression';

proc glm data=analysis\_data;

class Tobi inscat cfrd dnase pancr numhosp gender;

model dfev1=Tobi base\_fev1 wtpct age inscat cfrd dnase pancr numhosp gender/ cl solution;

lsmeans Tobi/pdiff cl; run;

*Evaluating Clinical Effectiveness with CF Registries DOI: http://dx.doi.org/10.5772/intechopen.84269*

/\*Next, we implement the propensity score regression model previously described. First, we use logistic regression to estimate propensity scores for each subject.\*/

title 'Model (2): Propensity Score Regression';

proc logistic data=analysis\_data;

class inscat cfrd dnase pancr numhosp gender;

model Tobi=base\_fev1 wtpct age inscat cfrd dnase pancr numhosp gender/ link=logit;

output out=props pred=ps;

run;

/\*We use the commands below to assign a subject-specific weight that corresponds to his or her propensity score from the logistic regression above. Since the propensity score, denoted *ps* below, corresponds to predicted probability of receiving the treatment, each subject who received the treatment will have weight *1*/*ps*, while each subject who did not receive the treatment will have weight *1*/(*1-ps*). The resulting dataset, *props2*, will consist of the *analysis\_data*, propensity scores that were previously created and stored in *props*, and the *ps\_weight* corresponding to each subject's weighting derived from the propensity score.\*/

data props2; set props; if Tobi=1 then ps\_weight=1/ps; if Tobi=0 then ps\_weight=1/(1-ps); run;

/\*We now implement the weighted multivariable regression. The commands are similar to our previous regression, except for our use here of the *weight* statement. By using this statement, we request computation of weighted means and variance estimates that are inversely proportional to the corresponding sum of weights.\*/

proc glm data=props2;

class Tobi inscat cfrd dnase pancr numhosp gender;

model dfev1=Tobi base\_fev1 wtpct age inscat cfrd dnase pancr numhosp gender/ cl solution;

lsmeans Tobi/pdiff cl; weight ps\_weight;

run;

/\*Finally, we present commands for the instrumental variables regression. The first model statement performs the first-stage regression of the treatment indicator *Tobi* on the instrument (*cid\_iv*) and all measured confounders. The result is a probit model with predicted probabilities of tobramycin use for each subject. The second model statement performs multiple linear regression with the instrumented version of the tobramycin variable from the first model statement.

title 'Model (3): Instrumental Variables Regression';

proc qlim data=analysis\_data;

class inscat cfrd dnase pancr numhosp gender;

model Tobi=cid\_iv base\_fev1 wtpct age inscat cfrd dnase pancr numhosp gender /discrete;

model dfev1=base\_fev1 wtpct age inscat cfrd dnase pancr numhosp gender / select(Tobi=1);

output out=Tobi prob proball predicted residual; run;

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*Evaluating Clinical Effectiveness with CF Registries DOI: http://dx.doi.org/10.5772/intechopen.84269*

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