Quantification of collider-stratification bias and the birthweight paradox

Abstract

The 'birthweight paradox' describes the phenomenon whereby birthweight-specific mortality curves cross when stratified on other exposures, most notably cigarette smoking. The paradox has been noted widely in the literature and numerous explanations and corrections have been suggested. Recently, causal diagrams have been used to illustrate the possibility for collider-stratification bias in models adjusting for birthweight. When two variables share a common effect, stratification on the variable representing that effect induces a statistical relation between otherwise independent factors. This bias has been proposed to explain the birthweight paradox. Causal diagrams may illustrate sources of bias, but are limited to describing qualitative effects. In this paper, we provide causal diagrams that illustrate the birthweight paradox and use a simulation study to quantify the collider-stratification bias under a range of circumstances. Considered circumstances include exposures with and without direct effects on neonatal mortality, as well as with and without indirect effects acting through birthweight on neonatal mortality. The results of these simulations illustrate that when the birthweight-mortality relation is subject to substantial uncontrolled confounding, the bias on estimates of effect adjusted for birthweight may be sufficient to yield opposite causal conclusions, i.e. a factor that poses increased risk appears protective. Effects on stratum-specific birthweight-mortality curves were considered to illustrate the connection between collider-stratification bias and the crossing of the curves. The simulations demonstrate the conditions necessary to give rise to empirical evidence of the paradox.

Figure 1

(a-b) Directed acyclic graphs representing possible causal relations among a risk factor (RF), birthweight (BWT), neonatal mortality and potentially unmeasured factor(s) U.

Figure 2

Effect of a risk factor on mortality as a function of birthweight. Mortality curves as a function of: the effects of an unknown factor U on birthweight (parameter a) and neonatal mortality risk (parameter b); the effects of a risk factor of interest on birthweight (parameter e) and neonatal mortality (parameter c); and the effect of birthweight on neonatal mortality (parameter d). Panel A: a =-1000, b = 0.4, c = 0.6, d =-0.0005, e =-400. Panel B: a =-500, b = 0.8, c = 0.2, d =-0.0005, e =-600. PanelC:a =-500, b = 1.2, c = 0.4, d =-0.0005, e =-400. Panel D: a =-500, b = 1.6, c = 0.2, d = 0, e =-600. Control of the magnitude of the collider-stratification bias through these parameters allows for reversal of effect (higher risk for those with the risk factor in Panel A, higher risk for those without the risk factor in Panel D) or for the crossing of the curves at 2000 g in Panel C.