Individual mediating effects and the concept of terminal measures data

Abstract

Researches in the fields in science and statistics often go beyond the two-variable cause-and-effect relationship, and also try to understand what connects the causal relationship and what changes the magnitude or direction of the causal relationship between two variables, predictor(T) and outcome (Y). A mediator (Z) is a third variable that links a cause and an effect, whereby T causes the Z and Z causes Y. In general, a given variable may be said to function as a mediator to the extent that it accounts for the relation between the predictor and the outcome (Baron and Kenny, 1986). The initial question regards the appropriate characterization of a mediation effect. Most studies, when comparing one or more treatments focus on an average mediating effect. This average mediating effect can be misleading when the mediating effects vary from subject to subject in the population. The primary focus of this research is to investigate individual mediating effects in a population, and to define a variance of these individual mediating effects. A concept called subject-mediator (treatment) interaction is presented and its role in evaluating a mediator’s behavior on a population of units is studied. This is done using a framework sometimes called a counterfactual model. Some common experimental designs that provide different knowledge about this interaction term are studied. The subgroup analysis is the most common analytic approach for examining heterogeneity of mediating effects. In mediation analysis, situations can arise where Z and Y cannot both be measured on an individual unit. We refer to such data as terminal measures data. We show a design where a mediating effect cannot be estimated in terminal measures data and another one where it can be, with an assumption. The assumption is linked to the idea of pseudo-replication. These ideas are discussed and a simulation study illustrates the issues involved when analyzing terminal measures data. We know of no methods that are currently available that specifically address terminal measures data.