The birthweight paradox refers to a counter-intuitive observation related to birthweight, neonatal mortality and factors associated with both birthweight and mortality, such as maternal smoking, parity and race, among others; babies that would seem to be at the highest risk (e.g. those of low birthweight and with smoking mothers) appear to do better than those at lower risk (e.g. low birthweight and non-smoking mothers).1-8
Graphically, this is represented as the crossing of birthweight stratum-specific mortality curves, the hallmark of the birthweight paradox.9,10
The interpretation of this observation has long been a subject of debate in the literature.7,8,11-13
In the context of smoking, it has been proposed previously that maternal smoking might somehow modify the risk of low birthweight, although many theories seeking to explain the paradox focus on artifactual, modelling-induced origins.10,14,15
Some have suggested that there is no direct link between birthweight and mortality whatsoever; rather, birthweight has been implied as amarker for some other true link between these factors.16
Recently, directed acyclic graphs (DAG) have been used to illustrate the role of birthweight in the relationship between neonatal mortality and risk factors such as smoking.10
These causal graphs suggest birthweight to be a collider
- a variable in a causal system that is a shared effect of more than one cause. In the case of birthweight, one may easily consider it to be affected by multiple factors including genetic, environmental and behavioural factors.17
Well-established rules show that stratification (via adjustment, restriction, or other approach) on a collider can introduce bias to estimates akin to selection bias.10,14
In the context of birthweight, the result of this collider-stratification bias would be to induce an association between factors affecting birthweight that are unconditionally independent, making them appear correlated within strata of the collider. As a result, neonatal mortality risk estimates may be biased (see Rothman et al
. for an extended discussion of DAGs and colliders).18
Causal diagrams are useful for identifying sources of bias but provide no quantitative information regarding effects.19-21
In order for collider-stratification bias to provide explanation for empirical evidence, the magnitude of causal effects must be considered. While much has been written about confounding bias, there is limited research evaluating collider-stratification bias in applied research, particularly in the context of perinatal epidemiology. Greenland evaluated collider stratification bias and its magnitude, as well as comparing collider-stratification bias with confounding bias when a variable fits both definitions, as in a ‘bowtie’ causal diagram.22
It was shown theoretically that collider-stratification bias tends to be a less substantial source of bias than confounding, with formulas demonstrating how the bias is influenced by the causal associations of factors in the causal system.22
Importantly, the bias induced by adjustment for a collider can result in estimates with opposite direction from true effects under certain circumstances thereby altering conclusions, not just strength of evidence.
As illustrated in , various causal scenarios can be considered where the issue of the birthweight paradox may serve for evaluation of collider-stratification bias; biologically plausible causal models include birthweight as a collider. Many factors are known to affect birthweight, such as maternal smoking, altitude and infant sex. Other determinants of birthweight include processes with specific risk factors as yet unknown. Given assumptions, collider-stratification bias can be quantified and compared against available data used to demonstrate the paradoxical ‘crossing of the curves’.
(a-b) Directed acyclic graphs representing possible causal relations among a risk factor (RF), birthweight (BWT), neonatal mortality and potentially unmeasured factor(s) U.
In this paper, we first consider causal diagrams to describe the role of birthweight in assessment of the relation between risk factors like smoking and neonatal mortality, to formalise the question of interest and to introduce the counterfactual notions of total, direct and indirect effects. Subsequently, we describe a simulation study to quantify collider-stratification bias using smoking as the risk factor of interest along with birthweight, and neonatal mortality. Finally, we describe the conditions necessary to give rise to the crossing of curves in the birthweight paradox when stratifying on birthweight.