5 Finding comparable cases with propensity scores

Let’s get back to a main problem that we have been facing so far: choosing among two alternatives, which is the best option, when no RCTs or A/B tests are available. One example is the kidney stones problem from Chapter 2. We know that the adjustment formula is a good tool to solve this problem. Now we are going to introduce a variation of the adjustment formula. You may wonder, what does this variation bring to the table? Well, it is specially designed to assess whether the positivity assumption holds or not.

5.1 Develop your intuition about the propensity scores

5.1.1 Finding matches for estimating causal effects

5.1.2 But…Is there a match?

5.1.3 How propensity scores can be used to calculate the ATE

5.2 Basic notions of propensity scores

5.2.1 Which cases are we working with?

5.2.2 What are the propensity scores?

5.2.3 Why the positivity assumption is slippery?

5.2.4 In case you want to know more…

5.3 Propensity Scores in practice

5.3.1 Data Preparation

5.3.2 Calculate the propensity scores

5.3.3 Assess the positivity assumption

5.3.4 Calculate ATEs drawn upon the propensity scores

5.4 Calculating Propensity Score Adjustment - an exercise

5.4.1 Exercise Steps

5.5 Summary

5.6 Annexes

5.6.1 Annex: Given a propensity score, the distribution of population characteristics is the same in treated and control groups