Identifiability:

• Identifiability:
  • SUTVA: Stable Unit Treatment Value Assumption:
    1. no interference. units do not interfere with each other
    2. one version of treatment.
  • consistency
    • the potential outcome $Y^a$ is equal to the observed outcome of $Y$ if treated $a$.
  • ignorability
    • given pre-treatment covariates $X$, treatment assignment is independent from potential outcomes. $Y^0,Y^1{\perp\!\!\!\!\perp} A|X$ . for example, treatment $Y$ of blood pressure is assigned randomly, regardless of patient $A$’s current blood pressure, given $X$ which is the age of the patient.
  • positivity
    • $P(A=a|X=x)>0, \forall a,x$. this means treatment is not deterministic.

Assumptions: data $Y,A$, and a set of treatment covariates $X$

Stratification

If we want marginal causal effect, we can average over $X$. This gets rid of the X.

$$ E(Y^a)=\sum_x E(Y|A=a,X=x)P(X=x) $$

Example: diabetes treatments. saxagliptin v. sitagliptin.

Marinalize:

In practice, however, there will be many $X$ needed to achieve ignorability.

Incident user and active comparator designs

Cross-sectional look at treatments:

• Also known as new user design, incident user design only follows up the individuals once treatment is assigned.
  • “Cleaner” history of data sets
  • if comparison is no treatment, it is not obvious when follow-up should start for no treatment group.
  • having an active comparator makes this much cleaner. (e.g. zumba fitness v. yoga)