Bounding the average causal effect in Mendelian randomisation studies with multiple proposed instruments:An application to prenatal alcohol exposure and attention deficit hyperactivity disorder

Background: As large-scale observational data become more available, caution regarding causal assumptions remains critically important. This may be especially true for Mendelian randomisation (MR), an increasingly popular approach. Point estimation in MR usually requires strong, often implausible homogeneity assumptions beyond the core instrumental conditions. Bounding, which does not require homogeneity assumptions, is infrequently applied in MR. Objectives: We aimed to demonstrate computing nonparametric bounds for the causal risk difference derived from multiple proposed instruments in an MR study where effect heterogeneity is expected. Methods: Using data from the Norwegian Mother, Father and Child Cohort Study (n = 2056) and Avon Longitudinal Study of Parents and Children (n = 6216) to study the average causal effect of maternal pregnancy alcohol use on offspring attention deficit hyperactivity disorder symptoms, we proposed 11 maternal SNPs as instruments. We computed bounds assuming subsets of SNPs were jointly valid instruments, for all combinations of SNPs where the MR model was not falsified. Results: The MR assumptions were violated for all sets with more than 4 SNPs in one cohort and for all sets with more than 2 SNPs in the other. Bounds assuming one SNP was an individually valid instrument barely improved on assumption-free bounds. Bounds tightened as more SNPs were assumed to be jointly valid instruments, and occasionally identified directions of effect, though bounds from different sets varied. Conclusions: Our results suggest that, when proposing multiple instruments, bounds can contextualise plausible magnitudes and directions of effects. Computing bounds over multiple assumption sets, particularly in large, high-dimensional data, offers a means of triangulating results across different potential sources of bias within a study and may help researchers to better evaluate and emphasise which estimates are compatible with the most plausible assumpt