Estimating sibling spillover effects with unobserved confounding using gain-scores

Abstract

Purpose: A growing area of research in epidemiology is the identification of health-related sibling spillover effects, or the effect of one individual's exposure on their sibling's outcome. The health within families may be confounded by unobserved factors, rendering identification of sibling spillovers challenging.

Methods: We demonstrate a gain-score (fixed effects) regression method for identifying exposure-to-outcome spillover effects within sibling pairs in linear models. The method identifies the exposure-to-outcome spillover effect if only one sibling's exposure affects the other's outcome, and it identifies the difference between the spillover effects if both siblings' exposures affect the others' outcomes. The method fails with outcome-to-exposure spillover or with outcome-to-outcome spillover. Analytic results, Monte Carlo simulations, and a brief application demonstrate the method and its limitations.

Results: We estimate the spillover effect of a child's preterm birth on an older sibling's literacy skills, measured by the Phonological Awareness Literacy Screening-Kindergarten test. We analyze 20,010 sibling pairs from a population-wide, Wisconsin-based (United States) birth cohort. Without covariate adjustment, we estimate that preterm birth modestly decreases an older sibling's test score.

Conclusions: Gain-scores are a promising strategy for identifying exposure-to-outcome spillover effects in sibling pairs while controlling for sibling-invariant unobserved confounding.

Keywords: Causality; Epidemiologic methods; Family; Siblings.

Figure 1.

Causal directed acyclic graphs for linear data-generating models with one-sided exposure-to-outcome sibling spillover. Subscripts i and j denote family and sibling, respectively. T_ij is the exposure, Y_ij is the outcome, D_i is the gain-score, and U_i is an unobserved family-level confounder. Greek letters denote effects. (1A) does not have exposure-to-exposure spillover, whereas (1B) and (1C) have exposure-to-exposure spillovers. The gain-score method precisely identifies the spillover effect θ (T_i1 → Y_i2) in all three models.

Figure 2.

Causal directed acyclic graphs for linear data-generating models with two-sided exposure-to-outcome sibling spillover. Subscripts i and j denote family and sibling, respectively. T_ij is the exposure, Y_ij is the outcome, D_i is the gain-score, and U_i is an unobserved family-level confounder. Greek letters denote effects. (2A) does not have exposure-to-exposure spillover, whereas (2B) and (2C) have exposure-to-exposure spillover. The gain-score method identifies the differences between the spillover effects θ (T_i1 → Y_i2) and κ (T_i2 → Y_i1) in all three models.

Figure 3.

Causal directed acyclic graphs for linear data-generating models with one-sided exposure-to-outcome sibling spillover and spillover from outcomes. Subscripts i and j denote family and sibling, respectively. T_ij is the exposure, Y_ij is the outcome, D_i is the gain-score, and U_i is an unobserved family-level confounder. Greek letters denote effects. (3A) has outcome-to-exposure spillover, and (3B) and (3C) have outcome-to-outcome spillover. The gain-score method does not identify the spillover effect θ (T_i1 → Y_i2) in any of the three models.

Figure 4.

Results (average spillover coefficients and empirical 95% confidence intervals [CI]) from simulations of the nine sibling spillover models in Figures 1-3. Each simulation consisted of 1000 runs of 5000 observations, where each observation represented a sibling pair (i.e., family). Subscripts i and j indicate family and sibling, respectively. T_ij is the exposure and Y_ij is the outcome. The target quantity is the spillover effect (T_i1 → Y_i2), set to θ = 0.5 in all models. Other spillover effects include κ (T_i2 → Y_i1), τ (T_i2 → T_i1), φ (T_i1 → T_i2), ψ (Y_i1 → T_i2), η (Y_i1 → Y_i2), and λ (Y_i2 → Y_i1). Except for θ, all spillover parameters were set to zero except in the following cases: κ = 0.3 in Figures 2A-C; τ = 0.3 in Figures 1B and 2B; φ = 0.3 in Figures 1C and 2C; ω = 0.3 in Figure 3A; η = 0.3 in Figure 3B; and λ = 0.3 in Figure 3C. The spillover coefficient identifies (i.e., is unbiased) for θ in all models of one-sided spillover (Figure 1); identifies the difference between the two exposure-to-outcome spillover effects with two-sided spillover (Figure 2); and is biased in the presence of spillovers originating from outcomes (Figure 3).

Figure 5.

A directed acyclic graph of the relationship between siblings’ preterm birth (gestational age <37 weeks) and their score on the Phonological Awareness Literacy Assessment-Kindergarten test with overlaid estimates. Subscripts i and j denote family and sibling, respectively, where j = 1 is the younger sibling and j = 2 is the older sibling. PTB_ij is a preterm birth indicator, PALSK_ij the test score, D_i is a gain-score, and U_i is an unobserved confounder. Greek letters denote effects, and θ and δ are estimated using gain-score regression.