Jenn's Propensity Scores summary.pdf

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Harvard University
Epidemiology EPI202-01
Murray Mittleman

Propensity Scores Introduction to the Story  Research Goal: Compare 2 treatments with respect to a health or economic outcome  Counterfactual ideal: what is achievable is “similar” not “same”; the best we can get is comparable treatment groups  Explicit reasons for treatment selection  Indication – confounding by indication can be very strong  Subtype of indication – if indication is very weak, subtype of indication could be strong  Severity of illness, concomitant illnesses, medications, contraindications/sensitivities  Implicit Reasons: Culture of “medicalization,” MD training/experience, regional treatment patterns  Before an “association” can be interpreted as causal, one has to rule out chance, bias, and confounding  Confounding arises when people possess covariate patterns that are preferentially associated with a particular therapy or confer different baseline risks  Propensity adjustment seeks to balance covariate patterns between compared groups, and/or make it so that therapy users have the same baseline risk as non-users  Can adjust for confounding by MEASURED CONFOUNDERS through restriction, stratification, matching, balancing, weighting (through standardization and IPTW) and modeling, which are all amenable to PROPENSITYTECHNIQUES!!!  Can attempt to adjust for UNMEASURED CONFOUNDERS through randomization, proxies (single proxies, multivariate proxies, instruments), and sensitivity analysis  Comparability through randomization  Ethical considerations and lack of equipoise make randomized trials not a viable option  Fortunately, physicians are variable in how they practice, even for drugs with seemingly clear indications  When we can't randomize, we can match on risk factors, but risk factor matching fails when data are rich (i.e., curse of dimensionality)  We could then match on exposure predictors, but still have the same problem with rich data The Propensity Score  Multivariable scoring method that collapses predictors of treatment into a single value  Probability that a subject with observed pretreatment covariates or characteristics will receive a given treatment instead of a specific alternative, conditional on the observed pretreatment variables that are included in the PS model  Removes confounding by components of the score  Avoids the curse of dimensionality  Assumes treatment is non-deterministic  For an individual, it's the conditional probability of his/her treatment given the observed pretreatment covariates  Since it's a probability, it takes values between 0.0 and 1.0  Offers a one-dimensional summary of multidimensional covariates, such that when the propensity score is balanced across the treatment and control groups, the distribution of all the covariates are balanced in expectation across the two groups  Used to create matched pairs or matched sets or strata that balance many observed covariates, on average, in the treated and control groups What's the method for propensity matching?  Identify the candidate predictors of 2 treatments B vs.A  Perform a logistic regression of B vs.A  Obtain from the regression a predicted probability of B vs A  MatchApatients to B patients on their propensity (but you could also stratify, use PS score in a regression model, or use weighted regression adjustments, such as standardization) Definition of Propensity Score  PS i Pr (Z i 1 | X i x i  Rosenbaum and Rubin have shown that Z Ц Y(1), Y(0) | PS  So you can estimate the treatment effect by t(x) = E[((Y(1) – Y(0)) | PS ]  Three properties of a PS  PS’s balance observed covariates.  If it suffices to adjust for covariates X, then it suffices to adjust for their PS.  Akin to assuming no unmeasured confounding  Estimated PS’s are better than true PS’s at removing bias. Regression Model Example:Assuming a dichotomous treatment  PS = logit (Z=1) = β0+ β 1 1 +2X +2· · · + β k k  Predictors must be pre-treatment variables!Adjusting for an effect of treatment is very bad   Also consider potential interactions between predictors of treatment  And then plug the PS into the outcome model…  logit (Y = 1) = 0 + β1I · (Z=1)+β 2S, plus any other variables you want in the outcome model, depending on your study question  Collinearity is not usually an issue because there’s usually enough variability in treatment choice  Assumption: assumes a linear association between the outcome and PS; you could instead use indicators for the PS or a spline function for the PS, and compare the models using LRTs Strengths of Propensity Scores  Advantageous when there
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