2 First steps: Working with confounders

 

This chapter covers

  • The effects of confounding: Simpson’s paradox
  • Removing confounding bias with the adjustment formula
  • Determining when to apply the adjustment formula

Imagine that you have a causal question, such as wanting to assess the consequences of a past decision, or deciding which of two treatments is better, or determining which of two marketing strategies is more effective. You are comparing two options, called A and B. These may be past decisions, medical treatments, or marketing campaigns, and you want to know their effects on a specific result.

You may think that the best approach is to see what happens when A is used, see what happens with B, and compare the two outcomes to decide if A is better than B. However, as we will explore in this chapter, this intuitive method can often lead to wrong conclusions, especially when dealing with observational data. This is a critical point to consider! Think about how often you or others have made decisions this way.

In chapter 1, we discussed that when dealing with observational data (which isn’t collected from a controlled experiment), we often encounter confounding variables. These confounders are factors that influence both the treatment (or action) and the outcome. This means confounders can cause changes in both the treatment and the outcome, and we may not even know they exist or have any details about them.

2.1 Learning the basic elements of causal inference through Simpson’s paradox

2.1.1 What’s the problem?

2.1.2 Develop your intuition: How to approach the problem

2.1.3 Solving Simpson’s paradox

2.2 Generalizing to other problems

2.2.1 Describing the problem with a graph

2.2.2 Articulating what we would like to know

2.2.3 Finding the way to calculate the causal effect

2.2.4 Articulating what we would like to know: The language of interventions

2.2.5 Finding the way to calculate the causal effect: The adjustment formula

2.2.6 How does the treatment work in each situation? The positivity assumption

2.3 Interventions and RCTs

2.4 First contact with the structural approach

2.4.1 Simulating the kidney stone example

2.4.2 Interventions in the structural approach

2.5 When to apply the adjustment formula

2.5.1 RCT or A/B test

2.5.2 Confounders

2.5.4 Mediators