{'fraction_non_alphanumeric': 0.01932633903920486, 'fraction_numerical': 0.006626173384870237, 'mean_word_length': 5.81203007518797, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Bounding the average causal effect in Mendelian randomization studies with multiple proposed instruments: An application to prenatal alcohol exposure and attention deficit hyperactivity disorder

Background: Point estimation in Mendelian randomization (MR), an instrumental variable model, usually requires strong homogeneity assumptions beyond the core instrumental conditions. Bounding, which does not require homogeneity assumptions, is infrequently applied in MR. Objective: 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 and Avon Longitudinal Study of Parents and Children (n=4457, 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 contextualize plausible magnitudes and directions of effects. Computing bounds over multiple assumption sets underscores the importance of evaluating the assumptions of MR models.