Introduction

Introduction to Causal Inference

Causal inference is the attempt to draw conclusions that something is being caused by something else. It goes beyond questions of correlation, association, and is distinct from model-based predictive analysis. Questions of robust causal inference are practically unavoidable in health, medicine, or social studies.

Much of the available data in the clinical and social sciences is observational, and we can only observe one outcome per individual. For example, if one individual took pain reliever for a headache and they now feel better, we don’t know what would have happened to that same individual over the same time period, if they had not taken pain reliever. Taking the pain reliever puts them in the treatment group, but since we don’t know what the control outcome of not taking pain reliever would be (without time travel), how can we say pain reliever caused the headache to go away?

Introduction to Matching

When estimating causal effects in an observational setting, one common approach is to match each treatment unit to an identical control unit. Going back to the example, can we find two people sharing every physical attribute, who also had the exact same symptoms, prior to the time when only one of them taking the pain reliever? Secondly, how did their outcomes differ?

In large datasets where we observe many characteristics about individuals, few “identical twins”, (referred to as “exact matches”) exist. What is the best way to match individuals that were treated and controlled? Only once they’re matched are we able to apply common treatment effect estimators to the groups of matched individuals, in order to try to determine the effect of treatment.

Challenges in Matching Methods

“Exact matching” isn’t possible when we a dataset has lots of characteristics about individuals, or is high dimensional. So, matching methods performing the best-possible alternative should be interpretable. Users of matching algorithms need to be able to easily understand which covariates were selected to be most important to their outcome, and need be able to find out why they were selected. This is important so that causal analysis can provide crucial information on who benefits from treatment most, where resources should be spent for future treatments, and why some individuals benefit from treatment while others were not. This can also help researchers determine what type of additional data must be collected.

Secondly, the matches should also be high quality. If an oracle could tell us the exact result of doing treatment on any individual whose treatment we did not observe, then would we find that our estimate of the effect of treatment on that individual is accurate?