1. Propensity Scores Friday, June 1 st, 10:15am-12:00pm Deborah Rosenberg, PhDKristin Rankin, PhD Research Associate ProfessorResearch Assistant Professor Division of Epidemiology and Biostatistics University of IL School of Public Health Training Course in MCH Epidemiology

2. 11 Propensity Scores The goal of using propensity scores is to more completely and efficiently address observed confounding of an exposure- outcome relationship. Program evaluation – Addresses selection bias Epidemiology – Addresses non-randomization of exposure Propensity scores are the predicted probabilities from a regression model of this form: Exposure = pool of observed confounders “Conditional probability of being exposed or treated (or both)”

3. 22 Propensity Scores When exposed and unexposed groups are not equivalent such that the distribution on covariates is not only different, but includes non-overlapping sets of values, then the usual methods for controlling for confounding may be inadequate. Non-overlapping distributions (lack of common support) means that individuals in one group have values on some of the covariates that don’t exist in the other group and vice versa.

4. 3 Sturmer, et al 2006, J Clin Epidemiol Area of “Common Support”

5. 4 Benefits of Propensity Score Methods The accessibility of multivariable regression methods means they are often misused, with reporting of estimates that are extrapolations beyond available data. The process of generating propensity scores: –focuses attention on model specification to account for covariate imbalance across exposure groups, and support of data with regard to “exchangeability” of exposed and unexposed –Allows for trying to mimic randomization by simultaneously matching people on large sets of known covariates –Forces researcher to design study/check covariate balance before looking at outcomes Oakes and Johnson, Methods in Social Epidemiology

6. 5 Propensity Scores Propensity scores might be used in three ways: 1. as a covariate in a model along with exposure, or as weights for the observations in a crude model (not recommended due to possible off-support inference) 2. as values on which to stratify/subclassify data to form more comparable groups 3. as values on which to match an exposed to an unexposed observation, then using the matched pair in an analysis that accounts for the matching

7. 66 Propensity Scores Propensity scores are the predicted probabilities from a regression model of this form: Exposure = pool of observed confounders proc logistic data=analysis desc; class &propenvars / param=ref ref=first; model adeq=&propenvars; output out=predvalues p=propscore; run; Once the propensity scores are generated, they are used to run the real model of interest: outcome = exposure *Note: Make sure you start with a dataset with no missing values on outcome, or you will end up with unmatched pairs

8. 7 Generating Propensity Scores Consider only covariates that are measured pre- program/intervention/exposure or do not change over time; value shouldn’t be affected by exposure or in causal pathway between exposure and outcome Covariates should be based on theory or prior empirical findings; never use model selection procedures such as stepwise selection for these covariates – if conceptually based, they should stay in the model regardless of statistical significance Include higher order terms and interactions to get best estimated probability of exposure and balance across covariates; trade-off between fully accounting for confounding and including so many unnecessary variables/terms that common support becomes an issue and PS distributions are more likely to be non-overlapping 7 Oakes and Johnson, Methods in Social Epidemiology

9. 8 Propensity Score Distributions Examine the distribution of propensity scores in exposed and unexposed If there is not enough overlap (not enough “common support”), then these data cannot be used to answer the research question Observations with no overlap cannot be used in matched analysis If there are areas that don’t overlap, the matched sample may not be representative (examine characteristics of excluded individuals to assess this) 8

10. 9 Propensity Scores Sometimes propensity scores are used to verify that pre-defined comparison groups are actually equivalent; If they are, then the propensity scores may not have to be used in analysis

11. 10 Propensity Scores Florida Healthy Start Evaluation: from Bill Sappenfield.5.6.7.8.91 Propensity Score Reference 1Care Coordination

12. 11.2.3.4.5.6.7 Propensity Score Reference 2Care Coordination Propensity Scores Florida Healthy Start Evaluation: from Bill Sappenfield

13. 12 Analysis Approach 1: Propensity Score as a Covariate or Weight in Model Use the propensity score as a covariate in model –1 degree of freedom as opposed to 1 or more for each original covariate; particularly useful when the prevalence of outcome is small relative to the number of covariates that must be controlled, leading to small cell sizes Weight data using the propensity scores –the weight for an “exposed” subject is the inverse of the propensity score –the weight for an “unexposed” subject is the inverse of 1 minus propensity score; weights must be normalized These approaches do not handle the issue of off-support data unless data are restricted to the range of propensity scores common to both the exposed and unexposed 12

14. 13 Analysis Approach 2: Subclassification by Categories of the Propensity Scores  Stratifying by quintiles of the overall distribution of propensity scores can remove approx 90% of the bias caused by the propensity score  The measure of effect is then computed in each stratum and a weighted average is estimated based on the number of observations in each stratum 13

15. 14 Analysis Approach 3: Propensity Score Matching Several matching techniques are available: Nearest Neighbor (with or without replacement) Caliper and Radius Kernal and Local Linear Several software solutions available to perform matching. Two examples include: PSMATCH2 in STATA GREEDY macro in SAS 14

16. 15 Analysis Approach 3: Propensity Score Matching PSMATCH2 (STATA): PSMATCH2 is flexible and user-controlled with regard to matching techniques GREEDY (5  1 digit) macro in SAS: The GREEDY (5  1 digit) Macro in SAS performs one to one nearest neighbor within-caliper matching: First, matches are made within a caliper width of 0.00001 (“best matches”), then caliper width decreases incrementally for unmatched cases to 0.1 At each stage, “unexposed” subject with “closest” ; propensity score is selected as the match to the exposed; in the case of ties, the unexposed is randomly selected Sampling is without replacement 15

17. 16 After Matching… 1. Check for balance in the covariates between the exposed and unexposed groups 2. If not balanced, re-specify the model and re- generate propensity scores; consider adding interactions or higher order terms for variables that were not balanced 3. If balanced, calculate a measure of association from an analysis that accounts for matched nature of data Relative Risk / Odds Ratio / Hazard Ratio/ Rate Ratio and 95% CI Risk Difference (Attributable Risk) and 95% CI 16

18. Matched Analysis Analysis to estimate effect of exposure on outcome should account for matched design in estimation of standard errors, since matched pairs are no longer statistically independent Estimates of effect need not be adjusted for matching because exposed are matched to unexposed; therefore a selection bias is not imposed on the data as it is in a matched case- control study where conditional logistic regression is needed 17

19. Matched Analysis Multivariable regression not necessary (but GEE can be used) since matching addresses confounding, so a simple 2x2 table can be used, but this 2x2 table must reflect the matched nature of the data 18 Exposed Experiences Outcome Unexposed Experiences Outcome

20. Matched Analysis: Measures of Effect (95% CI) Relative Risk (RR) = (a+c)/(a+b) SE (lnRR) = sqrt [(b+c) / {(a+b)(a+c)}] 95% CI = exp[lnRR ± (1.96*SE)] Risk Difference (RD) / Attributable Risk (AR) = (b-c)/n SE (RD) = ((c + b)−(b−c) 2 /n)/n 2 95% CI = RD ± 1.96(SE) Note: Measures of effect from propensity score-matched analyses are often called “Average Treatment Effect in the Treated (ATT)” in the propensity score literature. This usually refers to RD, but sometimes ATT ratio is reported 19

21. 20 Propensity Scores Using the 2007 National Survey of Children’s Health (NSCH) for Illinois

22. 21 Example: Association between receiving care in a medical home and reported overall health Exposure Outcome Output from SAS proc surveryfreq Children (age 0-17) Receiving Care that Meets the Medical Home Criteria Medical HomeFreq Weighted Freq Weighted Percent Yes1059173066355.9095 No801136481144.0905 Total18603095474100.000 Frequency Missing = 72 Description of Child’s General Health (Recode of k2q01) general healthFreq Weighted Freq Weighted Percent Excellent,Very good1650271517684.9019 Good, Fair, Poor28248284015.0981 Total19323198016100.000

23. 22 Example: Association between medical home (Y/N) and reported overall health % of children whose overall health was reported as excellent or very good, according to whether the care they received met the medical home criteria. Medical Home by General Health Medical Home General HealthFreq Weighted Freq Weighted Row Percent YesEVG981159469192.1434 GFP781359727.8566 Total10591730663100.000 NoEVG616103934676.1531 GFP18532546523.8469 Total8011364811100.000 TotalEVG15972634037 GFP263461437 Total18603095474 Frequency Missing = 72

24. 23 Crude Logistic Regression Model Output from SAS proc surveylogistic The odds of a child’s overall health being described as at least very good are 3.7 times greater for those who receive care that met the medical home criteria compared to those whose care did not. Odds Ratio Estimates Effect Point Estimate 95% Wald Confidence Limits Medical Home3.672.515.37

25. 24 Creating Propensity Scores for the Medical Home  Many factors—sociodemographic as well as medical—are likely to confound the association between medical home and reported overall health.  It may not be feasible to adjust for all of these factors in a conventional regression model.  Instead, propensity scores will be generated to simultaneously account for many factors.

26. 25 Creating Propensity Scores for the Medical Home: 3 Versions 1.12 variables—demographic variables only 2.14 variables—12 demographic variables plus a composite variable used to identify children with special health care needs (CSHCN) and a composite variable indicating severity of any health conditions 3.38 variables—12 demographic variables plus 5 individual CSHCN screener variables and 21 indicators of condition severity

27. 26 Distribution of Propensity Scores Before Matching Version 3 – 38 Variables Before Matching (n=1428) Medical Home = NO Medical Home = YES

28. 27 Creating Propensity Scores for the Medical Home: 3 Versions Pool of Variables Used to Create Propensity scores— Predicted Probabilities from Modeling: medical home (Y/N) = pool of variables # obs. used 12 variables ageyr_child racernew msa_stat totkids4 sex planguage coverage totadult3 famstruct k9q16r marstat_par neighbsupport 1629 14 variables ageyr_child racernew msa_stat totkids4 sex planguage coverage totadult3 famstruct k9q16r marstat_par neighbsupport screenscale severityscale 1629 38 variables ageyr_child racernew msa_stat totkids4 sex planguage coverage totadult3 famstruct k9q16r marstat_par neighbsupport k2q12_s k2q15_s k2q18_s k2q21_s k2q23_s K2Q30_s K2Q31_s K2Q32_s K2Q33_s K2Q34_s K2Q35_s K2Q36_s K2Q37_s K2Q38_s K2Q40_s K2Q41_s K2Q42_s K2Q43_s K2Q44_s K2Q45_s K2Q46_s K2Q47_s K2Q48_s K2Q49_s K2Q50_s K2Q51_s 1578

29. 28 Creating Propensity Scores for the Medical Home Sample SAS code for outputting the predicted values that are the propensity scores: proc surveylogistic data=datasetname; title1 “text”; strata state; cluster idnumr; weight nschwt; class classvars (ref=“ “)/ param=ref; model medical_home (descending) = confounder pool; output out=outputdataset p=name for pred. value; run;

30. 29 Creating Propensity Scores for the Medical Home: Excerpt from SAS proc print Obs.pscore1pscore2pscore3 811Medical Home Yes0.823140.823440.77917 812Medical Home Yes0.790930.807060.79674 813Medical Home No0.573220.45131. 814Medical Home No... 815Medical Home Yes0.823520.828990.83309 816Medical Home No0.317320.374600.36290 817Medical Home Yes0.813000.824090.82015 818Medical Home No0.721700.763840.78867 819Medical Home No... 820Medical Home No0.099050.112170.11435 821Medical Home Yes0.441070.507130.47309 822Medical Home Yes0.754590.761510.77425 823Medical Home Yes0.870600.891120.88204

31. 30 Modeling General Health: 3 approaches for each of 3 pools of Variables Modeling the Impact of Having a Medical Home on the Respondent’s Rating of Child’s General Health # obs. usedOR 95% CI Crude Model: genhealth = medical home(Y/N) genhealth = medical home (Y/N) – for non-miss covariates 1860 1629 3.67 (2.51, 5.37) 3.72 (2.44, 5.66) Using 12 variable version of the propensity scores: genhealth = medical home(Y/N) + 12 orig. vars genhealth = medical home(Y/N) + prop score (12) genhealth = medical home(Y/N) (matched on prop score)* 1629 509 pairs 1.99 (1.22,3.24) 1.89 (1.16,3.08) 2.52 (1.72,3.70) Using 14 variable version of the propensity scores: genhealth = medical home(Y/N) + 14 orig. vars genhealth = medical home(Y/N) + prop score (14) genhealth = medical home(Y/N) (matched on prop score)* 1629 503 pairs 1.49 (0.90,2.47) 1.44 (0.89,2.34) 1.55 (1.09,2.22) Using 38 variable version of the propensity scores: genhealth = medical home(Y/N) + 38 orig. vars genhealth = medical home(Y/N) + prop score (38) genhealth = medical home(Y/N) (matched on prop score)* 1578 482 pairs 1.75 (0.99,3.08) 1.57 (0.93,2.65) 1.93 (1.30,2.86) *SAS Greedy Macro used for matches; PROC GENMOD used for GEE logistic regression with no weights or survey design variables.

32. 31 Modeling General Health: 3 approaches for each of 3 pools of Variables Example of statistical results when including the medical home plus 12 covariates:

33. 32 Modeling General Health: 3 approaches for each of 3 pools of Variables As the number of variables increases, it becomes more difficult to implement a conventional model. With the medical home plus 38 variables, there were convergence problems: Warning: Ridging has failed to improve the loglikelihood. You may want to increase the initial ridge value (RIDGEINIT= option), or use a different ridging technique (RIDGING= option), or switch to using linesearch to reduce the step size (RIDGING=NONE), or specify a new set of initial estimates (INEST= option). Warning: The SURVEYLOGISTIC procedure continues in spite of the above warning. Results shown are based on the last maximum likelihood iteration. Validity of the model fit is questionable. Fortunately, convergence was not a problem when using the 38 variables to create the propensity scores.

34. 33 Modeling General Health: 3 approaches for each of 3 pools of Variables Using the propensity scores as a covariate in the model only requires 1 df making it feasible to account for many variables simultaneously Odds Ratio Estimates Medical Home + Propensity Scores (12 Vars) Predicting General Health (EVG V. GFP) Effect Point Estimate 95% Wald Confidence Limits ind4_8_071.8861.1563.075 pscore124.2228.48169.182 Odds Ratio Estimates Medical Home + Propensity Scores (14 Vars) Predicting General Health (EVG V. GFP) Effect Point Estimate 95% Wald Confidence Limits ind4_8_071.440.892.337 pscore265.61423.088186.470 Odds Ratio Estimates Medical Home + Propensity Scores (38 Vars) Predicting General Health (EVG V. GFP) Effect Point Estimate 95% Wald Confidence Limits ind4_8_071.5670.9282.647 pscore338.07313.230109.565

35. Distribution of Propensity Scores Before and After Matching Version 3 – 38 Variables Before After Medical Home = NO Medical Home = YES Medical Home = NO Medical Home = YES

36. 35 Modeling General Health: Stratified by Whether the Child is Screened as CSHCN 12 Variable Version Modeling the Impact of Having a Medical Home on the Respondent’s Rating of Child’s General Health # obs. used OR 95% CI Among Children WITHOUT Special Health Care Needs Using 12 variable version of the propensity scores^: genhealth = medical home(Y/N) + 12 orig. vars genhealth = medical home(Y/N) + prop score (12) genhealth = medical home(Y/N) (matched on prop score)* 1309 389 pairs 1.28 (0.69,2.34) 1.31 (0.76,2.26) 2.12 (1.26,3.56) Among Children WITH Special Health Care Needs Using 12 variable version of the propensity scores^: genhealth = medical home(Y/N) + 12 orig. vars genhealth = medical home(Y/N) + prop score (12) genhealth = medical home(Y/N) (matched on prop score)* 320 114 pairs 2.76 (1.21,6.29) 2.26 (1.05,4.88) 2.49 (1.40,4.41) *PROC GENMOD was used for GEE logistic regression with no weights or survey design variables; Matching was performed separately within CSHCN and non-CSHCN ^Stratum-specific estimates for the unmatched analyses were obtained using a DOMAIN statement in PROC SURVEYLOGISTIC in SAS 9.2

37. 36 Modeling General Health: Stratified by Whether the Child is Screened as CSHCN Rather than stratified analysis, obtain stratified results by including a product term in the model: genhealth = medical home(Y/N) + prop score (12) + medical home*cshcn Use contrast statements in SAS to generate the stratum- specific results: contrast 'odds ratio among cshcn y' medicalhome 1 medicalhome*cshcn 1 / estimate=exp; contrast 'odds ratio among cshcn n' medicalhome 1 / estimate=exp; These results attenuated compared to the matched, stratified results. ContrastEstimateConfidence Limits odds ratio among cshcn n1.550.892.70 odds ratio among cshcn y1.960.934.14

38. Propensity Score Example: Using 2003 Natality Data for Illinois 37

39. 38 Example: Association between receiving adequate prenatal care and Preterm Birth Exposure Outcome Output from SAS PROC FREQ Prenatal Care Adequacy (Kotelchuck) for Mothers of Singleton Infants (PNC) PNCFreqPercent Intermediate/Adequate/Adeq Plus147,41690.5 Inadequate/No PNC15,5039.5 Total162,919100.0 Frequency Missing =9,439 Preterm Birth (PTB) FreqPercent Preterm Birth (<37 wks)16,92310.4 Term Birth145,99689.6 Total162,919100.0 Frequency Missing =9,439

40. 39 Crude Measures of Effect proc freq data=analysis order=formatted; tables adeq*ptb/relrisk riskdiff; format adeq ptb yn.; run; Measures of Effect and 95% Cis Type of StudyValue95% Confidence Limits Case-Control (Odds Ratio) Cohort (Col 1 Risk) Risk Difference 0.76 0.78 -0.03 0.72 0.75 -0.03 0.80 0.82 -0.02 PTB PNCPreterm BirthTerm BirthTotal Adequate14,919 (10.1)132,497 (89.9)147,416 Not Adequate 2,004 (12.9) 13,499 (87.1) 15,503 Total17,454 (10.5)148,423 (89.5)162,919

41. 40 Creating Propensity Scores for PNC Adequacy Variable NameDescriptionValues AGECATMaternal age at delivery1=<20, 2=20-34, 3=35+ RACEETHRace/Ethnicity1=White, 2=Af-Am, 3=Hisp, 4=Other EDUCATEducation1= HS PARITY2Parity0=Primp, 1=1-2 previous LB, 3=3+ MARRIEDMarital Status1=Married, 0=Not Married SMOKESmoking Status1=Smoker, 0=Non-smoker RISKFANAnemia (HCT.<30/HGB.<10) 1=Yes, 0=No RISKFCARCardiac Disease 1=Yes, 0=No RISKFLUNAcute or Chronic Lung Disease 1=Yes, 0=No RISKFDIADiabetes 1=Yes, 0=No RISKFHERGenital Herpes 1=Yes, 0=No RISKFHEMHemoglobinopathy 1=Yes, 0=No RISKFCHYHypertension, Chronic 1=Yes, 0=No RISKFPHYHypertension, Pregnancy-Associated 1=Yes, 0=No RISKFINCIncompetent Cervix 1=Yes, 0=No RISKFPREPrevious Infant 4000+ Grams 1=Yes, 0=No RISKFPRTPrev Preterm or SGA 1=Yes, 0=No RISKFRENRenal Disease 1=Yes, 0=No RISKFRHRH Sensitization 1=Yes, 0=No RISKFUTEUterine bleeding 1=Yes, 0=No RISKFOTHOther Medical Risk Factors 1=Yes, 0=No How might variables be different if exposure was entry into PNC?

42. 41 Creating Propensity Scores for PNC Adequacy Sample SAS code for outputting the predicted values that are the propensity scores: proc logistic data=datasetname desc; title1 “text”; class classvars / param=ref ref=first; model adeq = confounder pool; output out=outputdataset p=name for pred. value; run;

43. 42 Creating Propensity Scores for PNC Adequacy: Excerpts from SAS proc print n=160,642 IDAdeqpropscore 100.79507 210.87975 310.88361 410.96668 500.94172 600.77970 710.95197 800.87975 910.85336 1010.95197 1110.97350 1210.95197

44. 43 Distribution of Propensity Score by PNC Adequacy, before Matching 43 On Support = 0.386-0.988 Adequate (range): 0.366-0.995 Inadequate (range): 0.386-0.988 38 observations at top and 2 at bottom of distribution in Adequate group

45. 44 Analyzing Data: Four Approaches 44 ApproachSAS Code 1.Model adequacy of PNC plus all 28 covariates Proc genmod data=OUTPUTDATASET desc; class CLASSVARS / param=ref ref=first; model PTB = ADEQ AGECAT…RISKFOTH/link=log dist=bin; run; 2.Model adequacy of PNC plus the propensity score proc genmod data=OUTPUTDATASET desc; model PTB = ADEQ PROPSCORE/link=log dist=bin; run; 3.Weight analysis on propensity score proc genmod data=OUTPUTDATASET desc; model PTB = ADEQ/link=log dist=bin; weight pweight; run; 4.Match women with adequate PNC to those without by propensity score and conduct matched analysis Call GREEDY macro: %GREEDMTCH(work,outputdataset,adeq,matched,propscore,idnumr); proc genmod data=matched desc; class matchto; model ptb = adeq/dist=bin link=log; repeated subject=matchto/type=IND corrw covb; estimate 'adeq' adeq 1/exp; run;

46. 45 Checking Covariate Balance Before Propensity Score Matching (GREEDY 1:1 Match) Selected Variables Before PS MatchStandardized Difference* Adequate (n=147,416) Inadequate (n=15,503) AgeMean (SD) <200.09 (0.21)0.21 (0.41)-34.61 20-340.76 (0.43)0.70 (0.46)14.72 35+0.15 (0.36)0.10 (0.30)16.96 Race/Ethnicity NH White0.57 (0.50)0.32 (0.47)53.04 NH African American 0.15 (0.36)0.347 (0.48)-46.37 Hispanic0.23 (0.42)0.30 (0.46)-16.73 Other0.05 (0.22)0.04 (0.19)6.94 Preg-Induced Hypertension 0.03 (0.18)0.02 (0.15)7.06 45 *Calculated as: 100*(mean exp - mean unexp ) SQRT((s 2 exp + s 2 unexp ) / 2 ) where s=std dev of mean Commonly, a Standardized Difference of >=10% or indicates imbalance Note: All factors are significantly associated with adequate PNC at p<0.0001

47. 46 Checking Covariate Balance Before and After Propensity Score Matching (GREEDY 1:1 Match) Selected Variables After PS Match (GREEDY in SAS) Standardized Difference % Bias Reduction^ Adequate (n=15,002) Inadequate (n=15,002) AgeMean (SD) <200.21 (0.41) 0.0399.9% 20-340.70 (0.46) 0.4896.7% 35+0.09 (0.29) -0.8095.3% Race/Ethnicity NH White NH African American 0.35 (0.48) 0.0100% Hispanic0.30 (0.46) 0.0499.8% Other0.04 (0.19)0.04 (0.18)0.4493.7% Preg-Induced Hypertension 0.02 (0.14)0.02 (0.15)-1.6177.2% 46 ^Calculated as:

48. 47 Distribution of Propensity Score by PNC Adequacy, after Matching (GREEDY) 47

49. 48 Modeling the Impact of Having Adequate PNC on Preterm Birth # obs. used RR (95% CI)RD (95% CI) Crude Model: PTB = Adequate PNC (Y/N)162,919 0.78 (0.75, 0.82)-0.03 (-0.03, -0.02) Using 26 variable version of the propensity scores: PTB = Adeq PNC (Y/N)+ 26 orig. vars PTB = Adeq PNC (Y/N) + prop score PTB = Adeq PNC (Y/N) (weighted to inverse of propensity score) PTB = Adeq PNC (Y/N) (matched on prop score using GREEDY macro (1:1 match) 160,642 15,010 pairs 0.94 (0.90, 0.99) 0.99 (0.95, 1.04) 1.04 (1.01, 1.07) 0.98 (0.93, 1.04) -0.007 (-0.01, -0.002) 0.0003 (-0.005, 0.006) 0.004 (0.001, 0.006) -0.00247 (-0.0249, 0.00244) Results: Four Approaches Using SAS Is PNC Associated with Reduced Risk of Preterm Birth?

50. Results: Restructuring data for matched 2x2 table /*Restructuring data from one observation per infant to one observation per matched pair (n obs from 30020  15010)*/ data adeq (rename=(ptb=InAdeqPTB)); set matched; where adeq=0; run; proc sort data=adeq; by matchto; run; data inadeq (rename=(ptb=AdeqPTB)); set matched; where adeq=1; run; proc sort data=inadeq; by matchto; run; data matchedpair; merge adeq inadeq; by matchto; run; 49

51. Results: Matched Analysis from 2x2 Table /*Producing 2x2 table for matched pairs, with McNemar test*/ proc freq data=matchedpair order=formatted; table InadeqPTB*AdeqPTB/norow nocol; exact mcnem; format AdeqPTB InadeqPTB yn.; run; RR = (a+c) / (a+b) SE (lnRR) = sqrt [(b+c) / {(a+b)(a+c)}] 95% CI = exp[lnRR ± (1.96*SE)] RR = (288+1623) / (288+1660) = 0.981 SE = sqrt [(1660+1623) / {(288+1660)(288+1623)}] = 0.0297 95% CI = 0.926, 1.040

52. 51 Some Limitations of Propensity Score Methods Like multivariable regression: Cannot account for unobserved characteristics (unmeasured confounders) Must consider how to approach the issue of missing data on covariates of interest (complete-case analysis, separate dummy variable for missing, imputation) Unlike multivariable regression: In most accessible form, methods are limited to binary exposures (though work is being done in this area) Mis-specification of model to generate propensity score can have a large impact on resulting estimates 51

53. 52 Some Limitations of Propensity Score Methods Propensity score techniques may not result in different findings than multivariable regression; it’s not always clear that there is a benefit to performing the analysis in this way Some exceptions include: Datasets in which sample size is limited or the outcome is rare, and multiple covariates need to be controlled; propensity scores provide a way to adjust for all covariates with fewer degrees of freedom Datasets in which some of the data is off-support; though care must be taken in interpretation as generalizability is affected and, in some cases, bias can be introduced when sample is restricted 52 Sturmer, et al 2006, J Clin Epidemiol.

54. 53 Questions and Challenges 1.What if there is interest in the independent effects of a few other variables besides the 'exposure' – as in any matched design, should these variables not be included in the pool used to create the propensity scores so that they can then be included as covariates in a final model?

55. 54 Questions and Challenges 2.While the model to create the propensity scores can include many variables regardless of their statistical significance, the number of observations lost due to missing values likely increases as the number of variables used increases. What is the balance here? Does this call for imputation?

56. 55 Questions and Challenges 3.For a given sample size, at some point the model to produce the propensity scores will get too big, so although theoretically many variables can be included, mechanically there may be convergence problems. With very small samples, this may mean that fully controlling for observed confounding may not be possible even with propensity scores. With a small number of variables, is it still worth it to gain the efficiency of matching—creating comparable groups.

57. 56 Questions and Challenges 4.One approach to using propensity scores is to weight the observations. Is this possible with a complex sampling design in which the observations are already weighted?

58. 57 Questions and Challenges 5. Choices about level of measurement might be made differently when modeling to generate propensity scores. For example, variables might be left in continuous form even though they might be categorized when assessing their independent effect on outcome (e.g. child's age). Similarly, for categorical variables, there is no need to collapse categories even when modeling results indicate it would be appropriate since parsimony is not critical (e.g. not combining "multiracial" with "other").

59. 58 Questions and Challenges 6. For stratified analysis, should propensity scores be created first for all observations in a single model (of course not including the stratification variable), or should stratum-specific models be run to create the propensity scores? And, if the scores are generated within strata, should identical pools of variables be used, or might those pools also be stratum-specific ?

60. 59 Resources Software SAS GREEDY MACRO – code and documentation: http://www2.sas.com/proceedings/sugi26/p214-26.pdf http://www2.sas.com/proceedings/sugi26/p214-26.pdf STATA PSMATCH2: http://ideas.repec.org/c/boc/bocode/s432001.htmlhttp://ideas.repec.org/c/boc/bocode/s432001.html Other Matching Programs: http://www.biostat.jhsph.edu/~estuart/propensityscoresoftware.html Select Methods Articles Austin, Peter. Comparing paired vs non-paired statistical methods of analyses when making inferences about absolute risk reductions in propensity-score matched Samples Statist. Med. 2011, 30 1292—1301. (Plus any other recent Austin papers). Caliendo and Kopeinig, 2005 “Some Practical Guidance for the Implementation of Propensity Score Matching” Available at: http://repec.iza.org/dp1588.pdfhttp://repec.iza.org/dp1588.pdf Oakes JM and Johnson P. Propensity Score Matching for Social Epidemiology. Oakes JM, Kaufman JS (Eds.), Methods in Social Epidemiology. San Francisco, CA: Jossey-Bass. Stürmer T, Joshi M, Glynn RJ, Avorn J, Rothman KJ, Schneeweiss S. A Review of Propensity Score Methods Yielded Increasing Use, Advantages in Specific Settings, but not Substantially Different Estimates Compared with Conventional Multivariable Methods. J Clin Epidemiol. 2006 May; 59(5): 437-447. 59

61. 60 Resources Some MCH Applications Bird TM, Bronstein JM, Hall RW, Lowery CL, Nugent R, Mays GP. Late preterm infants: birth outcomes and health care utilization in the first year. Pediatrics (2):e311-9. Epub 2010 Jul 5. Brandt S, Gale S, Tager IB. Estimation of treatment effect of asthma case management using propsensity score methods. Am J Mang Care, 16(4): 257-64, 2010. Cheng YW, Hubbard A, Caughey AB, Tager IB. The association between persistent fetal occiput posterior position and perinatal outcomes: An example of proensity score and covariate distance matching. AJE, 171(6): 656-663, 2010. Johnson P, Oakes JM, Anderton DL. Neighborhood Poverty and American Indian Infant Death: Are the Effects Identifiable? Annals of Epidemiology 18(7), 2008: 552-559. 60