Post-Match Analysis After Already Adjusting For Everything

Question

Let's say I am conducting an observational study in which a group that received treatment (T+) is matched to another group (T-) using propensity score analysis where I use the "throw-the-kitchen-sink" methodology and include all risk variables.

My question is when doing post-match analysis with conditional logistic regression, is my categorical variable the outcome variable with only one risk variable (the treatment)?

For example, if I use clogit would it look like:

clogit(outcome ~ treatment, data)

or is it possible I would need to still adjust for additional risk variables which have been shown in the literature to affect the outcome variable (even though when performing matching, I have already adjusted for all these variables):

clogit(outcome ~ treatment + riskVariable1 + riskVariable2, data)

Answer 1

If you have achieved balanced in your pre-treatment variables, it is unnecessary to include those variables in your outcome model with respect to reducing bias. However, if slight imbalances remain in your covariates, including these variables can reduce the bias.

Including covariates in the outcome model is also known as a "doubly robust" method, in that, if either the outcome model is correctly specified or you have achieved balance on the correct variables through preprocessing, you will arrive at an unbiased estimate of the treatment effect. Another benefit of this approach is that the treatment effect estimate will have a smaller standard error.

See Ho, Imai, King, & Stuart (2007) for more about this topic.