In this paper we review the methodological underpinnings of the general pharmacogenetic approach for uncovering genetically-driven treatment effect heterogeneity. This typically utilises only individuals who are treated and relies on fairly strong baseline assumptions to estimate what we term the 'genetically moderated treatment effect' (GMTE). When these assumptions are seriously violated, we show that a robust but less efficient estimate of the GMTE that incorporates information on the population of untreated individuals can instead be used. In cases of partial violation, we clarify when Mendelian randomization and a modified confounder adjustment method can also yield consistent estimates for the GMTE. A decision framework is then described to decide when a particular estimation strategy is most appropriate and how specific estimators can be combined to further improve efficiency. Triangulation of evidence from different data sources, each with their inherent biases and limitations, is becoming a well established principle for strengthening causal analysis. We call our framework 'Triangulation WIthin a STudy' (TWIST)' in order to emphasise that an analysis in this spirit is also possible within a single data set, using causal estimates that are approximately uncorrelated, but reliant on different sets of assumptions. We illustrate these approaches by re-analysing primary-care-linked UK Biobank data relating to CYP2C19 genetic variants, Clopidogrel use and stroke risk, and data relating to APOE genetic variants, statin use and Coronary Artery Disease.