As engineering educators and practitioners, we must broaden the participation of students from racially minoritized populations to meet engineering education's social and ethical responsibilities to address problems and design solutions relevant to our diverse communities. However, the engineering profession in the United States has historically and continues to exclude certain racial and ethnic populations, including Black, Latinx, and Native people. As a result, engineering remains a predominantly white discipline despite national calls to broaden participation. There have been interventions to help historically excluded students navigate the exclusionary engineering culture, including institution-driven and student-driven interventions. Affinity engineering student organizations, such as the National Society of Black Engineers (NSBE), are student-driven and serve as effective interventions to help improve persistence and graduation rates for historically excluded undergraduate engineering students. In this study, we explore different quantitative methodological approaches (logistic regression and survival analysis) to examine how various dimensions of involvement influence persistence. We consider a local chapter of NSBE at a large, Midwestern historically and predominantly white institution as a model student-driven intervention using a sample of 348 students. To understand how involvement in NSBE influences persistence, we define two dimensions of involvement within NSBE for our analysis: "time as a member" and "first-semester membership" as initial proxies for time invested and energy expended by Black engineering student members. We found a significant association between the length of time spent as a member of NSBE and the likelihood of graduation with an Engineering degree, highlighting the need for a depth of involvement. Interestingly, early involvement with NSBE was not associated with persistence to graduation in this study. The results provide less explored insights into the impact of different dimensions of a student-driven intervention on Black engineering student success and point to new quantitative methodological approaches that may be used for any intervention to understand its impact on student success. Next steps to expand on this work include adding more academic history control variables, increasing sample size, and examining institution-driven interventions as variables. This paper would be of interest to engineering educators, student support practitioners, institutional leaders, and all engineering stakeholders invested in understanding the broader ecosystem of student support, especially for interventions that serve historically marginalized students.