UCLA

Studies often seek to estimate the causal effect of a treatment on an outcome using a sample that has been drawn from a larger population. Such samples may not be randomly drawn and researcher may not observe all confounding variables that drive selection into treatment. Though researchers may be content to study causal effects averaged over only the sample in hand, selective sampling and unobserved confounding can still bias such effect estimates, threatening their “internal validity” (Campbell, 1957). Sample selection and unobserved confounding are related in how they threaten internal validity and can be examined in conjunction. We develop graphical tools to help evaluate threats from sample selection and unobserved confounding. These tools also allow us to determine when covariate adjustment can overcome these threats. It will not always be possible to solve these problems, however, and we thus generalize sensitivity analyses for unobserved confounding to also address sample selection. We then consider the use of instrumental variables, which in some cases can be biased by these concerns, but in other cases offer a solution to them. Finally, shifting emphasis to unobserved confounding, we discuss the use of placebo variables in partial identification.