Background concepts

Causality and the counterfactual

Here we will review the concepts of causality, the counterfactual, and confounding as they’re related to propensity scores. These concepts are discussed in detail in the module Intro to Study Design if you wish to learn about them in more detail.

Causality is the relationship between a cause and effect. In health research, we use causality to express how exposures and treatments impact health.

The counterfactual model is essential for assessing causality. The counterfactual asks, “How would this person’s outcome be different if they were in the opposite exposure/treatment group?” Now, we cannot observe two different outcomes at the same time, so we do our best to mimic the counterfactual. In study designs where individuals are randomly assigned to different groups (i.e., randomized controlled trials), we can reasonably assume that the observed results at the group level are similar to the counterfactual due to the randomization process. However, we cannot make this assumption in observational studies due to the baseline differences between the exposure/treatment groups.

Confounding

Confounding bias occurs when the relationship between the exposure and outcome is distorted due to an additional variable that is related to both the outcome and exposure. Observational studies are subject to confounding bias due to individuals not being randomly assigned to exposure groups. For example, when looking at the relationship between polypharmacy (i.e., taking multiple prescription medications) and mortality, age is a strong confounder. As people age, they tend to have more prescriptions and have a higher mortality rate. Thus, if you do not account for age, the relationship between polypharmacy and mortality may appear larger than it really is.

Diagram of confounding

ATE vs ATT

When assessing causality there are two possible treatment effects you could be measuring: average treatment effect (ATE) and average treatment effect among the treated (ATT).

Average Treatment Effect: the average effect, at the population level, of moving an entire population from untreated to treated. Propensity score methods such as weighting and stratification can estimate the ATE. ¹

Average Treatment Effect Among the Treated: the average effect of treatment on those subjects who ultimately received the treatment. Propensity score methods such as matching can estimate the ATT. ¹

The choice between ATT and ATE estimation depends on the particular research question. For example, if it is feasible that all the study population can receive the treatment of interest in real life, then ATE is preferred. This is the case when the two treatments being compared are exchangeable in practice (i.e., all the study population are eligible to receive treatment A and all the study population are also eligible to receive treatment B). If it is not feasible that all the study population would receive the treatment of interest in real life, then ATT is preferred. This is the case when the treatment is given to only individuals with certain characteristics. For example, not all pregnant women with depression will receive antidepressants. Treatment decision depends on case severity and weighing the benefits for the expecting mother versus the risk to the infant.

Now that we’ve quickly covered those basic study design concepts, we’ll dive right into propensity scores in the next section. If you feel you need a bit more understanding first, go ahead and read through the references mentioned here.