21.9 Types of Subjects in a Treatment Setting

When conducting causal inference, particularly in randomized experiments or quasi-experimental settings, individuals in the study can be classified into four distinct groups based on their response to treatment assignment. These groups differ in how they react when they are assigned to receive or not receive treatment.

21.9.1 Non-Switchers

Non-switchers are individuals whose treatment status does not change regardless of whether they are assigned to the treatment or control group. These individuals do not provide useful causal information because their behavior remains unchanged. They are further divided into:

• Always-Takers: These individuals will always receive the treatment, even if they are assigned to the control group.
• Never-Takers: These individuals will never receive the treatment, even if they are assigned to the treatment group.

Since their behavior is independent of the assignment, always-takers and never-takers do not contribute to identifying causal effects in standard randomized experiments. Instead, their presence can introduce bias in treatment effect estimation, particularly in intention-to-treat analysis.

21.9.2 Switchers

Switchers are individuals whose treatment status depends on the assignment. These individuals are the primary focus of causal inference because they provide meaningful information about the effect of treatment. They are classified into:

• Compliers: Individuals who follow the assigned treatment protocol.
  • If assigned to the treatment group, they accept and receive the treatment.
  • If assigned to the control group, they do not receive the treatment.
  • Why are compliers important?
    • They are the only group for whom treatment assignment affects actual treatment receipt.
    • Causal effect estimates (such as the local average treatment effect, LATE) are typically identified using compliers.
    • If the dataset only contains compliers, then the intention-to-treat effect (ITT) is equal to the treatment effect.
• Defiers: Individuals who do the opposite of what they are assigned.
  • If assigned to the treatment group, they refuse the treatment.
  • If assigned to the control group, they seek out and receive the treatment anyway.
  • Why are defiers typically ignored?
    • In most studies, defiers are assumed to be a small or negligible group.
    • Standard causal inference frameworks assume monotonicity, meaning no one behaves as a defier.
    • If defiers exist in large numbers, estimating causal effects becomes significantly more complex.

21.9.3 Classification of Individuals Based on Treatment Assignment

The following table summarizes how different types of individuals respond to treatment and control assignments:

	Treatment Assignment	Control Assignment
Compliers	Treated	Not Treated
Always-Takers	Treated	Treated
Never-Takers	Not Treated	Not Treated
Defiers	Not Treated	Treated

Key Takeaways:

1. Compliers are the only group that allows us to estimate causal effects using randomized or quasi-experimental designs.
2. Always-Takers and Never-Takers do not provide meaningful variation in treatment status, making them less useful for causal inference.
3. Defiers typically violate the assumption of monotonicity, and their presence complicates causal estimation.
4. If a dataset consists only of compliers, the intention-to-treat effect will be equal to the treatment effect.

By correctly identifying and accounting for these different subject types, researchers can ensure more accurate causal inference and minimize biases in estimating treatment effects.

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