A generalized test of genotype–phenotype causality in population-sampled nuclear families

We recently developed a causal inference framework and test—the Transmission Mean Test (TMT)—to identify causal genotype–phenotype relationships in population-sampled parent–child trios, where one child per family is observed. Here, we establish the generalized TMT (gTMT) for population-sampled nuclear families, allowing multiple offspring per family. This extension focuses on detecting genetic loci with non-zero average causal effects (ACE) on child phenotypes, taking into account that siblings share similar random family-specific effects. We construct a potential outcomes trait model that considers both individual-level and family-level heterogeneity, captures additive and non-additive genetic effects, and accommodates both quantitative (continuous or count) and dichotomous traits. We design an unbiased estimate dgTMT of the ACE and develop a sampling variance estimate σ^gTMT2 to form a statistic testing the null hypothesis of no causal effect. We provide both theory and empirical evidence demonstrating that gTMT is robust to confounding factors such as the population structure and family-specific effects. We analyze nuclear families in the UK Biobank as an illustrative example of the gTMT in action. When parental genotypes are missing, we propose to further extend gTMT by using Bayesian calculations on child genotypes to model parental genotypes as intermediate random variables.Author summary: There has been a recent resurgence of interest in family designs, as genome-wide association studies have reached sizes at which subtle biases can overcome statistical control in population-based studies. At the same time, methodological advances in causal inference have created new opportunities for causal discoveries. In this work, we develop the generalized Transmission Mean Test (gTMT), a causal inference framework for identifying causal genotype–phenotype relationships in population-sampled nuclear families with multiple offspring per family. Building on our previous work on the Transmission Mean Test that focuses on parent–child trio data, this extension allows for shared family-specific effects among siblings and accommodates both quantitative and dichotomous traits. We formulate a potential outcomes model that captures individual- and family-level heterogeneity, construct unbiased estimators of average causal effects, and derive valid inference procedures. Through theoretical analysis and empirical studies, including an application to nuclear families in the UK Biobank, we demonstrate that gTMT is robust to a broad class of confounding effects, including population structure and family-level confounding. We further propose a Bayesian extension to address missing parental genotypes.