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Pregnancy is a fascinating biological process in which the best theory and evidence suggest that the mother and newborn form two divergent processes which are themselves integrated into the surrounding environment. Thus, the early life health profile of a newborn depends closely on that of their mother as well as environmental factors during pregnancy. While many previous studies have provided evidence for such associations, they either tend to have small sample sizes and hence limited statistical power, or only have studied a few of the factors in isolation. In this study, we systematically probed the associations by means of principled Bayesian data analysis on a very large commercial insurance claims dataset based in the United States. After a brief exposition of the prerequisite of the statistical models employed in our study, we first identified newborns in the dataset with potential mothers using appropriate diagnostic codes, which served as the foundation of our subsequent work. Using this matched newborn--mother cohort, we first re-examined more than a hundred previously reported associations between the sex ratio at birth, also known as the secondary sex ratio, with environmental, socioeconomic and other stress factors. By showing that these association did not form discernible patterns that popular adaptive theories of sexual selection predict, we provided further evidence against these theories and call for a reformulation of this particular area of evolutionary theory for humans. To demonstrate further use of the matched cohort, we performed a large cohort study on the associations between early-life neurodevelopmental disorders and maternal immune activation, use of anti-infective prescription and various adverse birth conditions. Echoing recent results suggesting a common aetiology of early life immune system diseases and neurodevelopmental disorders as disruptions to modules of the microbiota--gut--brain axis, our results demonstrated that many risk factors that may be effects of dysbiosis were indeed associated with elevated risks of neurodevelopmental disorders. Finally, we included a preliminary study on using Morgan fingerprints as an efficient method of attaining state-of-the-art predictive performance on a commonly used drug--drug interactions dataset.