  Mendelian randomization (MR) is a natural experimental design based on the
random transmission of genes from parents to offspring. However, this
inferential basis is typically only implicit or used as an informal
justification. As parent-offspring data becomes more widely available, we
advocate a different approach to MR that is exactly based on this natural
randomization, thereby formalizing the analogy between MR and randomized
controlled trials. We begin by developing a causal graphical model for MR which
represents several biological processes and phenomena, including population
structure, gamete formation, fertilization, genetic linkage, and pleiotropy.
This causal graph is then used to detect biases in population-based MR studies
and identify sufficient confounder adjustment sets to correct these biases. We
then propose a randomization test in the within-family MR design using the
exogenous randomness in meiosis and fertilization, which is extensively studied
in genetics. Besides its transparency and conceptual appeals, our approach also
offers some practical advantages, including robustness to misspecified
phenotype models, robustness to weak instruments, and elimination of bias
arising from population structure, assortative mating, dynastic effects, and
horizontal pleiotropy. We conclude with an analysis of a pair of negative and
positive controls in the Avon Longitudinal Study of Parents and Children. The
accompanying R package can be found at
https://github.com/matt-tudball/almostexactmr.
