The CAUSALTRT Procedure

The CAUSALTRT procedure estimates the causal effect of a binary treatment, T, on a continuous or discrete outcome, Y. This section defines causal effects and discusses the assumptions and conditions that enable researchers to establish causal interpretations.

Although the causal effects that PROC CAUSALTRT estimates are called treatment effects, the variable T might represent an intervention or exposure, depending on the problem nature. For example, consider that T is an intervention such as receiving subsidized access to a fitness center, and Y is measure of physical health. The researcher would like to assess the treatment or causal effect of the subsidized fitness program T on the physical health Y. But what exactly is the causal effect? This section uses Neyman-Rubin’s potential outcomes framework (Rubin 1980, 1990) to define causal effects and to discuss their assumptions. Next, it explains the conditions that enable researchers to identify and establish causal effects.

The first important concept for defining a causal effect is potential outcomes. Potential outcomes describe an idealized source of data where you can observe a subject’s response for all possible treatment assignments. For example, if you are estimating the causal effect of a binary variable for which indicates assignment to the control and assignment to treatment, then each subject has two potential outcomes and . The subject-level (also called unit-level) treatment effect is defined as the difference in potential outcomes .

To formally define the potential outcomes as unique and intrinsic values that are associated with a subject, Rubin (1980) states the stable unit treatment value assumption (SUTVA). See also Imbens and Rubin (2015). Two components of the SUTVA are the following:

With a more refined statement, VanderWeele (2009) proposed a less restrictive version to the second component of SUTVA. Essentially, VanderWeele’s version requires that the potential outcomes remain unchanged within certain degree of treatment variation for each treatment level. This version is also known as the treatment variation irrelevance assumption. See also Cole and Frangakis (2009).

Furthermore, Rubin (2005) points out an implicit but important assumption for constructing the potential outcome framework: the potential outcomes are not affected by the treatment assignment mechanism that the researchers use to learn about them. Whether in an observational study or a randomized experiment, potential outcomes remain unique to the subjects given the well-defined causal problem and SUTVA.

To summarize, the potential outcome framework with SUTVA ensures that the causal treatment effect is well defined. However, to actually attempt to estimate causal treatment effects from the data, the consistency assumption that relates an observed outcome to the potential outcome is needed:

This equation states that the observed response Y is equal to the potential outcome with a treatment level that matches the actual assigned treatment level. In this setting, if j is an unobserved treatment condition, the unobserved potential outcome is defined using counterfactual conditionals as the outcome that would occur if, contrary to the observed assignment, the subject received treatment . Because each subject can take part in only one treatment condition, at least half of the potential outcomes would not be observed in the data collection process. Therefore, the unit-level causal effect, as defined by , is seldom the primary interest in research. Instead, average treatment effects in the population are the more common estimands.

The CAUSALTRT procedure estimates two types of treatment effects:

It is important to notice that the preceding discussion of potential outcome framework, the associated assumptions, and the definitions of causal treatment effects apply to both experimental and observational data (Rubin 1990). But for estimating causal treatment effects, statistical methodology for experimental and observational data would be differentiated.

The differentiation is caused by the following important condition (or assumption) for the identification of causal treatment effect: given the pretreatment covariates , the potential outcomes are independent of treatment assignment

This condition states that if all the covariates have been included in the model appropriately (that is, there are no unmeasured covariates), the treatment effect of T on Y conditional on would have a causal interpretation. Consequently, the causal treatment effects can be estimated as some functions of the observed conditional means.

Unfortunately, this condition cannot be 100% established in most applications; hence, this condition is usually referred to as an assumption in causal analysis literature. This assumption is called strong ignorability of treatment assignment or conditional exchangeability. This assumption sheds light on the different statistical methodology between randomized experiments and observational studies.

In experiments where randomization is used to assign subjects to treatment conditions, you can safely assume that the treatment assignment and potential outcomes are independent by design. Hence, for randomized experiments, traditional statistical methods such as t tests and ANOVA can be used without worrying about the confounding that can be caused by covariates .

However, in observational studies, subjects "select" the treatment conditions based on their pretreatment characteristics (covariates), , which could also be associated with the outcome variable. The treatment and outcome association would be confounded by the covariates. In this case, identification of causal effects requires that the strong ignorability or conditional exchangeability assumption be satisfied; that is, only when the estimation of the causal effects can successfully take into account all the confounding that is caused by the covariates .

The CAUSALTRT procedure implements several statistical techniques that enable you to estimate treatment effects when you specify confounding covariates . PROC CAUSALTRT uses the covariates to fit generalized linear models for the treatment T, outcome Y, or both. Predicted values from these models are then incorporated into the estimation of the causal effects. In particular, you can estimate the ATE by the following methods:

Whenever your modeling involves a model for the treatment assignment T or propensity score (that is, when you use either the inverse probability weighting or doubly robust estimation), an additional assumption about positivity is needed: each subject should have a nonzero probability of receiving any treatment condition. This assumption is expressed as follows:

For more information about estimation of the ATE, see the section Estimating the Average Treatment Effect (ATE). For more information about the models that are required for the estimation methods that PROC CAUSALTRT implements and how default estimation methods are determined, see the section Outline of Estimation Method Requirements. You can estimate the ATT by using either inverse probability weights or regression adjustment. For more information about estimation of the ATT, see the section Estimating the Average Treatment Effect for the Treated (ATT).