Causal diagrams, information bias, and thought bias

Abstract

Information bias might be present in any study, including randomized trials, because the values of variables of interest are unknown, and researchers have to rely on substitute variables, the values of which provide information on the unknown true values. We used causal directed acyclic graphs to extend previous work on information bias. First, we show that measurement is a complex causal process that has two components, ie, imprinting and synthesizing. Second, we explain how the unknown values of a variable may be imputed from other variables, and present examples of valid and invalid substitutions for a variable of interest. Finally, and most importantly, we describe a previously unrecognized bias, which may be viewed as antithetical to information bias. This bias arises whenever a variable does not exist in the physical world, yet researchers obtain "information" on its nonexistent values and estimate nonexistent causal parameters. According to our thesis, the scientific literature contains many articles that are affected by such bias.

Keywords: causal diagrams; derived variables; directed acyclic graphs; imputation; information bias; thought bias.

Figure 1

The causal structure of imputation by “measurement alone”.

Figure 2

The causal structure of variable derivation: any derivation (directed acyclic graph A); by any function of two variables (directed acyclic graph B); by a specific function of two variables (directed acyclic graph C).

Figure 3

Theory-based substitution of derived diabetes status (A_S) for unknown, true diabetes status (directed acyclic graph A); causal theories about the effect of diabetes on vital status (directed acyclic graph B).

Figure 4

Examples of invalid and valid substitutions of A_S for A, when A_S is derived from Z.

Figure 5

Thought bias: type 1.

Figure 6

Thought bias: type 2. The arrow from F to G, with conditioning on G, indicates that the universe of all functions is often restricted to some subset.

Figure 7

Alternative structures for the causal relation of V (a natural outcome variable) with X (natural variable), Y (natural variable), F (universe of all functions of X and Y), and D^x,y (a variable derived from X and Y).