5 Finding comparable cases with propensity scores

This chapter covers

Using propensity scores to assess the positivity assumption
Calculating the ATE using propensity-score techniques

Let’s revisit the main point in causal inference: how to choose between two options when we can’t use randomized controlled trials or A/B tests. Remember the kidney-stone example from chapter 2? We’ve used the adjustment formula to tackle problems like this. Now we have a modified version of this formula. Why do we need it? Because it’s specifically made to determine whether the positivity assumption is true.

Remember from chapter 2 that the adjustment formula only works if the positivity assumption is true. Let’s go over what this assumption means. Suppose you have two treatments, A and B. You give treatment A to both young and old people, but treatment B only to young people. If you want to figure out the effect of treatment B on everyone, both young and old, you hit a snag. You can’t know how treatment B affects old people unless some of them also receive this treatment. To determine which treatment is better, you need to apply both treatments, A and B, to both age groups: older and younger.

5.1 Developing 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 Why matching can be hard

5.1.4 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 The positivity assumption is … an assumption

5.3 Propensity scores in practice

5.3.1 Data preparation

5.3.2 Calculating the propensity scores

5.3.3 Assess the positivity assumption

5.3.4 Calculating ATEs drawn from the propensity scores

5.4 Calculating propensity score adjustment: An exercise

5.4.1 Exercise steps

5.5 Further reading

5.6 Chapter quiz