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Unformatted text preview: Today Tiny introduction to causal modelling in regression Based on Hernan, et al. “Causal Knowledge as a Prerequisite for Confounding Evaluation: An Application to Birth Defects Epidemiology” Lecture 22 – p. 1/24 Collecting data Have not, to this point, made many statements about how the data were collected in our statistical models All of our inference to this point has been interpreted as associative , rather than causative Question: are there situations where we could interpret the covariates as casually influencing the response? Lecture 22 – p. 2 / 2 Randomized covariates We know that if two covariates of interest are randomly allocated to observations, then they will be uncorrelated (because they will be independent) We know that if two covariates are uncorrelated that, even if both are associated with the response, modelling the mean of the response without one of them will still yield an unbiased estimate of the coefficient for the other Lecture 22 – p. 3/24 Randomized covariates We also know that if two covariates ARE correlated that we will get biased estimation for the coefficients of interest if they are nonzero When we have a binary treatment covariate, in an ideal situation we will randomly allocate it to observations – no need to adjust for other covariates if we are primarily interested in unbiasedness Lecture 22 – p. 4 / 2 Covariates and conditioning In regression, we sometimes forget that our models are conditional probability models In other words, our parameter estimates are defined in terms of conditional probability statements, namely E ( Y  X = x ) , where X = x indicates our set of covariate values Should think carefully about how this conditioning affects our estimates when we are focused on a particular variable For example, if we only care about whether folate intake increases the risk of birth defects, do we actually want to control for low birthweight of the baby? What will that do to our analysis?...
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 Spring '06
 STEELE
 Probability theory, Causality, Hernan, Unbiasedness, treasury secretary

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