Assortative mating and within-spouse pair comparisons

Abstract

Spousal comparisons have been proposed as a design that can both reduce confounding and estimate effects of the shared adulthood environment. However, assortative mating, the process by which individuals select phenotypically (dis)similar mates, could distort associations when comparing spouses. We evaluated the use of spousal comparisons, as in the within-spouse pair (WSP) model, for aetiological research such as genetic association studies. We demonstrated that the WSP model can reduce confounding but may be susceptible to collider bias arising from conditioning on assorted spouse pairs. Analyses using UK Biobank spouse pairs found that WSP genetic association estimates were smaller than estimates from random pairs for height, educational attainment, and BMI variants. Within-sibling pair estimates, robust to demographic and parental effects, were also smaller than random pair estimates for height and educational attainment, but not for BMI. WSP models, like other within-family models, may reduce confounding from demographic factors in genetic association estimates, and so could be useful for triangulating evidence across study designs to assess the robustness of findings. However, WSP estimates should be interpreted with caution due to potential collider bias.

Fig 1. Causal diagram illustrating collider bias in within-spouse pair and within-sibship models.

A) To illustrate collider bias in the context of spouses, consider a model with age and educational attainment (E) which are assumed here to be independent. Assuming that spouses assort on similarities for age and education, it follows that spousal assortment (A) is a common effect of age and education similarities. In a within-spouse pair model, adjusting or accounting for A would induce associations between age and education similarities. For example, if a spouse-pair have a large difference in age, then they must be similar for education. B) Contrastingly, for a within-sibship model, it is less plausible that age and education influence the sibling’s family F, as age and education are post-birth phenotypes. Therefore, adjusting for F is unlikely to induce an association between age and education.

Fig 2. Causal diagrams of simulated models for assortative mating, spousal correlations, and collider bias.

The WSP design uses pairwise spousal differences (e.g. X_M1−X_F1 & Y_M1−Y_F1) in regression models, fitting each spouse pair as a single observation. A) Within-spouse pair: spousal correlations for confounders. Exposure X; Outcome Y; Unmeasured confounder E; Spousal assortment A; WSP exposure X* (X* = X_M−X_F); WSP outcome Y* (Y* = Y_M−Y_F); WSP environmental confounder (the non-shared portion of the set of confounders) E* (E* = E_M−E_F). This figure illustrates the effect of an exposure on an outcome in the presence of an unmeasured confounder. Here, spousal pairing is determined by an assortment variable correlated with the confounder (indicated by A, a child of the confounder E). It follows that the value of spouses’ confounders will be correlated. In this example, a WSP model will reduce simulated bias in the estimate of the effect of X on Y (S1 Fig). Here we assume that spousal correlations for the confounder reflect assortment but in practice they could also relate to the shared spousal environment. B) Within-spouse pair: assortative mating and collider bias. Exposures X₁ X₂; Outcome Y; Spousal assortment A; WSP exposures $X_1^{*}$, $X_2^{*}(X_i^{*}=X_{iM}-X_{iF})$; WSP outcome Y* (Y* = Y_M−Y_F). This figure illustrates the effect of an exposure on an outcome when two, otherwise independent exposures influence both the outcome and spousal assortment. It follows that associations will be present in the WSP model between the two exposures, which will distort the WSP estimated effect of the exposure on the outcome. We quantify the effect of potential collider bias in the WSP model at different levels of assortment on the two exposures. Dashed lines indicate associations induced by spousal assortment.