Non-interventional studies can provide meaningful insights on important questions of drug safety and effectiveness. However, these studies can be vulnerable to residual biases, which threaten the validity of results. In this thesis I outline and apply methods to reduce, diagnose, and quantify bias due to unmeasured confounding in non-interventional studies. I apply these methods to two drug safety areas where unmeasured confounding may have affected published findings: (1) the association between proton pump inhibitor prescribing and mortality (2) the associations of fluoroquinolone prescribing with incidence of uveitis, retinal detachment, aortic aneurysm or aortic dissection hospitalisation, and peripheral neuropathy. The methods applied include active comparators and self-controlled designs to reduce confounding; secondary comparator groups, negative control outcomes, and the high-dimensional propensity score to diagnose residual confounding; and quantitative bias analysis to quantify the potential effect of unmeasured confounders. In a cohort study I find evidence of an association between proton pump inhibitor prescribing and increased all-cause and cause-specific mortality. However, the findings of methods to diagnose and quantify residual confounding, including the high-dimensional propensity score and secondary comparator groups, bring into question the causality of the association. I do not find strong evidence for an association between fluoroquinolone prescribing and aortic aneurysm or dissection, uveitis, or retinal detachment in cohort or self-controlled studies with active comparators. I do find some evidence for an association between fluoroquinolone prescribing and peripheral neuropathy. However, the association is small and could possibly be explained by residual confounding as highlighted by quantitative bias analysis. In conclusion, while unmeasured confounding can threaten the validity of pharmacoepidemiological studies, there are valuable approaches available to reduce, diagnose, and quantify this bias. In this thesis these approaches have been outlined and employed in order to demonstrate their value, and to provide more robust insight on two important drug safety topics.