Overadjustment bias and unnecessary adjustment in epidemiologic studies

Abstract

Overadjustment is defined inconsistently. This term is meant to describe control (eg, by regression adjustment, stratification, or restriction) for a variable that either increases net bias or decreases precision without affecting bias. We define overadjustment bias as control for an intermediate variable (or a descending proxy for an intermediate variable) on a causal path from exposure to outcome. We define unnecessary adjustment as control for a variable that does not affect bias of the causal relation between exposure and outcome but may affect its precision. We use causal diagrams and an empirical example (the effect of maternal smoking on neonatal mortality) to illustrate and clarify the definition of overadjustment bias, and to distinguish overadjustment bias from unnecessary adjustment. Using simulations, we quantify the amount of bias associated with overadjustment. Moreover, we show that this bias is based on a different causal structure from confounding or selection biases. Overadjustment bias is not a finite sample bias, while inefficiencies due to control for unnecessary variables are a function of sample size.

FIGURE 1

Bias estimating the total effect of exposure of interest E on the outcome D as a function of the direct effect of the unmeasured intermediate (U) variable (β_D) on the outcome D and the direct effect of the unmeasured intermediate (U) variable on another independent descendent (M) of U denoted by β_M.

FIGURE 2

Large and small sample size properties on Monte Carlo relative bias and variance of total effect estimates after adjusting for unnecessary variables.