Negatives about positivity and consistency as conditions for causal inference.

Abstract

Positivity and causal consistency are sometimes presented as general validity requirements. Positivity, however, is not a general requirement for causal inference and does not address the more demanding practical needs for adequate numbers of observations. Common statistical methods in health and medical research depend on large-sample approximations; yet, approximation accuracy is rarely discussed in research reports, even in cases where it has clearly failed. Prioritization by generality and practical importance shifts the emphasis to approximation accuracy over positivity, with the latter better cast as a technical requirement for specific types of methods. Meanwhile, consistency mixes requirements for operationally clear definitions of treatments with more general needs for accurate measurement. All statistical methods depend on conceptual precision and measurement accuracy; hence, those conditions belong among fundamental requirements for valid inferences, alongside control of selection bias and confounding. When measurement problems are addressed in the basic assumptions of formalizations, consistency can be seen as a definition of the targeted outcome variable in a causal model, rather than a central assumption that mixes separate concerns about construct ambiguity and coarsening.