A General Algorithm for Deciding Transportability of Experimental Results

Abstract

Generalizing empirical findings to new environments, settings, or populations is essential in most scientific explorations. This article treats a particular problem of generalizability, called "transportability", defined as a license to transfer information learned in experimental studies to a different population, on which only observational studies can be conducted. Given a set of assumptions concerning commonalities and differences between the two populations, Pearl and Bareinboim [1] derived sufficient conditions that permit such transfer to take place. This article summarizes their findings and supplements them with an effective procedure for deciding when and how transportability is feasible. It establishes a necessary and sufficient condition for deciding when causal effects in the target population are estimable from both the statistical information available and the causal information transferred from the experiments. The article further provides a complete algorithm for computing the transport formula, that is, a way of combining observational and experimental information to synthesize bias-free estimate of the desired causal relation. Finally, the article examines the differences between transportability and other variants of generalizability.

Generalizing Experimental Findings

“…I SB on the other hand is characterized by the fact that do-expressions are always conditioned on S, reflecting the fact that we have experimental information only on the selected sample, S ¼ 1. The analysis reported in Pearl and Bareinboim [6] has resulted in an algorithmic criterion for deciding whether transportability is feasible and, when confirmed, the algorithm produces an estimand for the desired effects [7]. The algorithm is complete, in the sense that, when it fails, a consistent estimate of the target effect does not exist (unless one strengthens the assumptions encoded in M).…”

“…A similar change would occur as more individuals become aware of the efficacy of the treatment. The result is an inherent disparity between the target population and the population under study.The problem of generalizing across disparate populations has received a formal treatment in Pearl and Bareinboim [6] where it was labeled "transportability," and where necessary and sufficient conditions for valid generalization were established (see [7]). The problem of selection bias, though it has some unique features, can also be viewed as a nuance of the transportability problem, thus inheriting all the theoretical results established in Pearl and Bareinboim [6] that guarantee valid generalizations.…”

“…(6) is only useful when S-ignorability holds and when Pðy x jzÞ is estimable from the experimental data. Unfortunately, when Z contains post-treatment variables, the former condition will be harder to meet; we shall see that S-ignorability is rarely satisfied in transportability problems by any set Z containing post-treatment variables.In graphical analysis, on the other hand, the problem of generalization has been studied using another assumption, labeled S-admissibility [7], which is defined by:PðyjdoðxÞ; zÞ ¼ PðyjdoðxÞ; z; sÞ ð 7Þ or, using counter factual notation,It states that in every treatment regime X ¼ x, the observed outcome Y is conditionally independent of the selection mechanism S, given Z, all evaluated at that same treatment regime. Clearly, S-admissibility coincides with S-ignorability for pretreatment S and Z; the two notions differ however for treatment-dependent selection and covariates.…”

Generalizing Experimental Findings

“…The problem of generalizing across disparate populations has received a formal treatment in where it was labeled "transportability," and where necessary and sufficient conditions for valid generalization were established (see also Bareinboim and Pearl, 2013). The problem of selection bias, though it has some unique features, can also be viewed as a nuance of the transportability problem, thus inheriting all the theoretical results established in ) that guarantee valid generalizations.…”

“…The analysis reported in has resulted in an algorithmic criterion for deciding whether transportability is feasible and, when confirmed, the algorithm produces an estimand for the desired effects (Bareinboim and Pearl, 2013). The algorithm is complete, in the sense that, when it fails, a consistent estimate of the target effect does not exist (unless one strengthens the assumptions encoded in M ).…”