The cardiovascular risks of exogenous testosterone have been a subject of controversy. In this study, our objective was to examine the association between testosterone (versus glaucoma treatments as an active comparator, with no assumed effect) and the new onset of cardiovascular, cerebrovascular and thromboembolic adverse events, in a US commercial insurance database. Data was analyzed by three complementary designs: inverse propensity score weighting (IPSW), calendar time instrumental variable (IV) and instrumented difference-in-differences (iDiD). Results of these analyses suggest that there is no difference between testosterone and glaucoma treatments regarding the risk of the composite primary endpoint of acute myocardial infarction, ischemic stroke and sudden cardiac arrest / ventricular arrhythmia. In contrast, IPSW analysis identified a negative association between testosterone and the secondary endpoint of venous thromboembolism. However, this association was attenuated towards the null in the calendar time IV and iDiD analysis, which suggests that there might be unmeasured confounding in the IPSW analysis. Because there is no uniquely suitable method that offers a universally optimal solution for evaluating causal relationships between exposures and outcomes from observational data, using multiple state-of-the-art methods to answer the question of interest can help in assessing the robustness of findings to various forms of unmeasured confounding, thereby aiding in causal inference.