## 8.2 Problem of causal inference

In reality we will only be able to observe part of the values in Table 8.1. This is the *fundamental problem of causal inference* (Rubin 1974; Holland 1986). If Joyce gets the standard treatment, we will observe that she lives for another 4 years, but we will not know that she would have died after one year had she been given the new surgery. We can observe only one of the two outcomes, and hence these outcomes are now known as *potential outcomes*. Of course, we observe no outcome at all if the patient is not yet treated.

At least 50% of the information needed to calculate the ICE is missing, so the quantification of ICE may not be a particularly easy task. Classic linear statistical methods rely on the (mostly implicitly made) simplifying assumption of *unit treatment additivity*, which implies that the treatment has exactly the same effect on each experimental unit. When the assumption is dropped, things become complicated. Neyman (1923) defined individual causal effects for the first time, and he was well aware that these could vary over units. But he also knew that he needed assumptions beyond the data to estimate them. This might have led him to believe that these effects are not interesting or relevant (Neyman 1935, 126):

So long as the

averageyields of any treat are identical, the question as to whether these treats affectseparateyields on asingleplot seems to be uninteresting and academic.

Rubin (1974, 690) said:

… we assume that the average causal effect is the desired typical effect…

and Imbens and Rubin (2015, 18) wrote:

There are many such unit-level causal effects, and we often wish to summarize them for the finite sample or for subpopulations.

These authors also note that estimating the ICE is difficult because the estimates are sensitive to choices for the prior distribution of the dependence structure between the two potential outcomes. Morgan and Harding (2006) wrote

Because it is usually impossible to effectively estimate individual-level causal effects, we typically shift attention to aggregated causal effects.

Weisberg (2010, 36) observed that

Mainstream statistical theory has almost nothing to say about individual causal effects.

For the better or worse, mainstream statistical methodology silently accepted the unit treatment additivity assumption. The assumption is at the heart of the Neyman-Fisher controversy, and curiously Neyman’s argument in 1935 as quoted above may actually have upheld wider use of his own invention. See Sabbaghi and Rubin (2014) for additional historic background.