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1 Propensity score matching ..1 Sample Size calculation ..25 ..55 / 2011 (Special Topic) / 2011 ( ) / 2011 (Special Topic)Propensity score matching- 1 -2011 (Special Topic) - (Observational study) bias control2 Pit & score & score 4. , FAQ2 Propensity score matchingPropensity score matching1- 3 - / RCT RCT .. `Confounding bias Regression, restriction, matching, stratification, `Selection bias `Selection bias .matching, stratification, (are not perfect)4 RCT vs Observational studyRCT vs Observational study`Randomized clinical trial Outcome treatment ( ) . Selection bias . - Follow up loss ?

2 Bias . ` (Observational study)Baseline covariate s imbalance . selection bias . 3- 4 -2011 (Special Topic) Adjusting Confoundings WeaknessAdjusting Confoundings -Weakness1. Data - matching, stratification1) 1) . control subject . (substantial case-subject loss)2) Matching (Multi-variate matching) subject . 3) Overmatching (non-confounding variable matching )2. - multivariable analysis (ex: multiple logistic regression)1) (overestimation, underestimation, poor SE)2) bias reduction . Treatment effect or Treatment effect or . 3) Selection bias . 6 Observational study control confounding bias control confounding biasOutcome : Independent variable: Confounding variable: `Regression : multiple logistic regressionCancer = intercept + asbestos + smoking + errorCancer = intercept + asbestos + smoking + errorMhi (Sifii )`Matching (Stratification)1) asbestos with smoking VS non-asbestos with smoking2) b t ith ki VS b t ith ki2) asbestos with non-smoking VS non-asbestos with non-smoking1) 2) dataset stratified analysis5- 5 - / Propensity score ( )definitionPropensity score ( )definition.

3 `T: treatment group`X: covariate`X: covariate`Probability(T=1|X) = a function of X X treatment (0<ps<1) (p) X `The dimension reduction of covariates XN( ( )) P( X ) d iN( (n )) x P( , X ) data matrix N x 1(propensity score) vector8 Propensity score method .7- 6 -2011 (Special Topic) PS PS ` : logistic regression (called PS model) : 2 outcome regression -logistic regression (called PS model) : 2 outcome regression ` : Stent type survival curve (confounding variables )To estimate propensity score Stent type(Cypher vs Taxus) all covariate (confounding variables) subject Stent type = Cypher (PS score) subject Stent type = Cypher (PS score) ( ) 10 Propensity score matching pyg1.

4 - outcome ?- outcome ?- ? 2. PS 2. PS - outcome , logistic regression subject )3. PS . - PS ? PS overlapped ?4. case subject PS control subject Good match ? Bad match ?- . - Case subject loss . ( power ) 6. Matched data analysis for outcome. 9- 7 - / SPSS PS ` ( ) Treatment groupoutcomeSPSS PS `Treatment ( )`Exposed group covariates`Probability(T=1|X) = a function of X-> X treatment = X covariates `estimated by logistic regressionClick!12 SPSS PS ` ( ) Treatment groupoutcomeSPSS PS `Treatment ( )`Exposed group covariates`Probability(T=1|X) = a function of X-> X treatment = X covariates `estimated by logistic regression11- 8 -2011 (Special Topic) PS t hi PS matching ( ).

5 `R(matching package, )`Stata `Stata `SAS macro`SPSS macro( #RandomSampling)14 SPSS PS ` ( ) SPSS PS `Treatment ( )`Exposed group E tit d `Probability(T=1|X) = a function of X-> X treatment = X Estimated propensity score `estimated by logistic regression13- 9 - / M t hi lith i tMatching algorithm using computer`Greedy algorithm`Optimal algorithmpg16 .`PS matching . Matching PS . age ? Age ps , ps matching gp ,pg age matching .15- 10 -2011 (Special Topic) Optimal algorithmcontrolOptimal algorithmcontrolGreedy 11 - / How many of control subject?How many of control subject? Good matching Control !~ therefore the rule of thumb is to choose a control data set at most nine ~ therefore, the rule of thumb is to choose a control data set at most nine times as large as the treatment group, ~ sample size 201:n matching1:n matching`1:1 Matching vs 1:2 Matching case subjets control subjects matching , 1:2 power( ).

6 Case subject ? Case subject ? case subject .`1:5 ? case , , . 19- 12 -2011 (Special Topic) Matching data descriptionb l t t Ci t t t-balance test>>Covariate statusTotal PopulationPropensity-matched PopulationTable 1. Baseline Clinical CharacteristicsTotal PopulationPropensitymatched PopulationPES(n=562)SES(n=1033)p ValuePES(n=407)SES(n=407)p ValueAge, 65246 (43 8)432 (41 8)0 45185 (44 2)163 (38 9)0 12 Age 65246 ( )432 ( ) ( )163 ( ) ( )703 ( ) ( )290 ( ) presentation< angina205 ( )463 ( )159 ( )159 ( )U t bli245 (43 6)398 (38 5)165 (39 4)170 (40 6)Unstable angina245 ( )398 ( )165 ( )170 ( )AMI112 ( )172 ( )95 ( )90 ( )Current smoker144 ( )242 ( ) ( )109 ( ) mellitus190 ( )298 ( ) ( )118 ( ) ()()()()Hypertension333 ( )608 ( ) ( )268 ( ) ( )316 ( ) ( )115 ( ) history of CAD21 ( )41 ( ) ( )18 ( ) vascular disease8 ( )11 ( ) ( )8 ( ) infarction42 ( )86 ( ) ( )34 ( ) cerebrovascular event29 ( )52 ( ) ( )23 ( )> renal failure18 ( )34 ( ) ( )17 ( ) 3 11 959 5 11 40 8058 1 12 059 1 11 80 28fraction*, % <50%68 ( )126 ( ) ( )59 ( )

7 T hi Matching `Stratified analysis . Univariable analysis ( balance )Paired t-test(Wilcoxon signed rank test)Stratified Chi-square test - (ex: Cochran-Mantel- Haenszel method, Mcnemartest)Stratified regression ( )- (ex: mixed model, two-way ANCOVA, Stratified logistic regression GEE)Survival analysis (outcome censored event )Survival analysis (outcome censored event )- Stratified log-rank test (ex: Prentice-Wilcoxon test, etc)- Stratified Cox regression . 21- 13 - / Matching data analysis Example (Cypher vs Taxus)Example (Cypher vs Taxus)` : stent type MACE(major cardiac event) event) . `Log-rank test p-value = (univariate survival analysis for nomatched data)(univariate survival analysis for no-matched data) Incorrect (because of matched data)`tiil t t`prentice-wilcoxon test(univariate survival analysis for paired data)p-value = `Stratfied Cox regression (survival analysis for paired data adjusting for a time-dependent variable)p-value = , hazard ratio = ( ~ )Y[Matching data descriptionb l t t St d di d diff di tibalance test>>Standardized difference description`Recommandation: Balance test Standardized difference.]

8 Propensity score .Total PopulationPropensity-matched PopulationTotal Population Propensitymatched Population PES SES P-value Standardized DifferencePES SES P-value Standardized Difference(n=562) (n=1033) (n=407) (n=407) Age, ( ) 703 ( ) ( ) 290 ( ) presentation< angina205 ( ) 463 ( ) ( ) 159 ( ) 0 Unstable angina245 ( ) 398 ( ) ( ) 170 ( ) ()()()()AMI112 ( ) 172 ( ) ( ) 90 ( ) smoker144 ( ) 242 ( ) ( ) 109 ( ) 14 -2011 (Special Topic) Observational studyexampleObservational study-example-Aim: t-PA(tissue plasminogen activator) treatment and in-hospital mortality from a pyregional stroke registry-Raw data sample sizeTreatment (t-PA) : n = 212 Control : n = 6057 Some observational studies have shown anincreased risk for death associated with t-PAtreatment, while randomized controlled trialsdemonstrated no causal association between t-PA treatment and death.

9 Ref. Kurth et al, , , No. 3Y]Matching data analysis ExampleMatching data analysis ExampleRef: Song et al, Sirolimus-Versus Paclitaxel-Eluting stents for the treatment of coronary bifurcations, JACC, Vol. 55, No, 16, 201025- 15 - / Matching method Matching method ` -False positive error . -Selection bias . ` ` -Subject loss . (rare event outcome small sample size of case group)(rare event outcome, small sample size of case group)-Selection bias . - . 28 Observational studyexampleObservational study-example-Aim: t-PA(tissue plasminogen activator) treatment and in-hospital mortality from a pyregional stroke registry-Raw data sample sizeTreatment (t-PA) : n = 212 Control : n = 6057 Some observational studies have shown anincreased risk for death associated with t-PAtreatment, while (3 of)randomized controlledtrials demonstrated no causal associationbetween t-PA treatment and death.

10 Ref. Kurth et al, , , No. 3Y^- 16 -2011 (Special Topic) Propensity score model descriptionPropensity score model description`C-statistic(Area under the curve) = discriminant power !` stent type !30 Qti & ti i PS titiQuestions & cautions in PS estimation`Too high AUC Is this PS model good?`Variable selection29- 17 - / low AUC of PS model examplelow AUC of PS model exampleROC curve for PS 080y6 080N t b d !True positive bad ! = 002 0 False positive curve for PS po0. 20 . 40 00 20 40 60 81 = positive AUC Propensity score model ? 31- 18 -2011 (Special Topic) Too high AUC to match!Too high AUC to match!` AUC treatment (good logistic model) PS (good logistic model) PS.