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Hester van Eeren Erasmus Medical Centre, Rotterdam Halsteren, August 23, 2010

Propensity score and subgroups: How to find an accurate treatment effect within subgroups when the propensity score is applied to control for selection bias?. Hester van Eeren Erasmus Medical Centre, Rotterdam Halsteren, August 23, 2010. The propensity score (1).

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Hester van Eeren Erasmus Medical Centre, Rotterdam Halsteren, August 23, 2010

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  1. Propensity score and subgroups:How to find an accurate treatment effect within subgroups when the propensity score is applied to control for selection bias? Hester van Eeren Erasmus Medical Centre, Rotterdam Halsteren, August 23, 2010

  2. The propensity score (1) • The propensity score is “…the conditional probability of assignment to a particular treatment given a vector of observed covariates.” (Rosenbaum en Rubin, 1983: 41). • Used in non-randomized studies to control for selection bias • Balance observed pretreatment variables among patient • Find an estimate of the average treatment effect • But, treatment effect can be different within subgroups

  3. The propensity score (2) • Propensity score used in: • Matching • Stratification • Regression • Inverse probabilityweight • Combinations of …

  4. Methods in this study • To find a treatment effect withinsubgroups, if the propensity score is applied: • Method 1: Regressionanalysiswithpropensity score, subgroups and interactionwithtreatmentassignment; • Method 2: Weightedregressionanalysiswithinverse of the propensity score (to weight observations), subgroups and interaction with treatment assignment; • Method 3: Propensity score applied for groups defined on treatment assignment and subgroups; then, regression analysis with propensity score and dummies for groups • Twotreatmentcategories and twosubgroups are used in thisstudy

  5. Variable selection for propensity score • Does the variableforsubgroups has to beincluded? • Discussionaboutvariableselectionforpropensity score; • Only variables related to outcome? • Only variables related to treatmentassignment? • Both variables…? • In thisstudy; 8 different propensity scores (PS) formulated, basedon: • Variables related to outcome, with and without subgroup • Variables related to treatmentassigment, with and without subgroup • Both variables…, with and without subgroup • Only variables related to bothoutcome and treatmentassignment, with and without subgroup

  6. How to test? (1) • Real dataset not useful because effects unknown beforehand; • You cannot test whether the effect found is accurate • Monte Carlo simulation study to test methods and different propensity scores: • Simulate data with known treatment effects • Estimate different propensity scores for this data • Apply different methods for different propensity scores, for this data • Repeat this process 1000 times

  7. How to test? (2) • What do you want to know? • If the treatment effect estimated is (almost) equal to the treatment effect you used to simulate the data • Bias of estimator: difference between estimated treatment effect and the true value of parameter • Want to have an unbiased estimate; • Less bias indicates a more accurate estimate of the treatment effect • Bias is estimated for overall treatment effect and for the treatment effect within subgroups

  8. Results

  9. Results (1) • Whichpropensity score is the most accurate withineachmethodtested (testedwith ANOVA): • But, somevaluesfor bias per propensity score wherenotvery different fromeachother…

  10. Results (2) • Whichmethod is most accurate when the most accurate propensity scores are compared? • Decideonpartial effect size of method in ANOVA* • For generaltreatment effect, the partial effect size is 0,028, wheremethod 1 gives the lowest bias (followedbymethod 3) • For treatment effect withinsubgroups, the partial effect size is 0,051, wheremethod 1 gives the lowest bias too • Although the effect sizesformethod are notverylarge, regressionanalysiswithtreatmentassignment, subgroup, interactionbetween these and the propensity score, which is estimatedwith variables related to outcome, seems to be the most accurate method to findtreatmenteffectswithinsubgroups *Effect size – 0,010 = small; 0,059 = medium; 0,138 = large (Cohen, 1988)

  11. Discussion (1) • Data simulation is donefor different settings: • Sample size, correlationbetweencovariates and correlationwithcovariateforsubgroups are changed over simulations • Resultsfor most accurate propensity score are basedonsum of bias over all these settings; comparisonsbetweenmethodsfor all propensity scores couldgive more in depthresults • The overall bias for different propensity scores was sometimesnotvery different • Model forsimulation of data was simple, linear; the relationbetween variables and outcome in practicecanbe more complicated • ….

  12. Discussion (2) • Questions?

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