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# Jenn's Propensity Scores summary.pdf

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Harvard University

Epidemiology

Epidemiology EPI202-01

Murray Mittleman

Fall

Description

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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Related notes for Epidemiology EPI202-01