In large clinical trials designed to determine efficacy of an experimental treatment, patients are enrolled with presence or absence of various risk factors, such as diabetes or history of atrial fibrillation. A treatment-by-risk factor interaction indicates that the treatment effect may depend on the risk factor presence or absence. It is important to identify such interaction, since a treatment may fail or cause adverse events in the presence of the risk. Although statistical methods exist to identify such interaction, they are underutilized in clinical stroke research. This paper reviews the notion of treatment-by-risk factor interaction and identifies two types of interaction, quantitative and qualitative, using a graphical technique and statistical testing. We illustrate how to avoid drawing the erroneous conclusions regarding the treatment effect on subgroups when failing to detect an interaction, and provide rigorous tools to estimate the treatment effect on subgroups when an interaction is observed. Applications are presented using the data collected from the NINDS t-PA stroke studies. In stroke clinical trials, a treatment-by-risk factor interaction must be considered if the data permit. The graphical approach provides a heuristic illustration of interactions. Qualitative interactions are more important than quantitative interactions on therapeutic conclusion. Results of NINDS t-PA stroke studies confirmed our previous conclusions on the treatment t-PA benefit within 3-h therapeutic window. No subgroup of patients would lead a physician to withhold the t-PA treatment.