Imagine we want to know how long it takes students to pass a key qualifying exam, but we never observe the exact term they pass. Instead, for each of our 60 students we only know an interval: the last term we checked and they had not yet passed (left_censor_term) and the term by which we confirmed they had passed (survival_censor_term). This kind of inexact, interval- bounded timing is common when assessments are only given periodically. We also recorded each student’s department: engineering, social, or health. We use Interval-Censored Survival Analysis because the event time is only known to fall within an interval, and standard methods that assume exact times would be inappropriate.

In educational monitoring we rarely know the exact time of an event: we check students at term ends, find them successful one term and over a threshold at the next check — the event happened somewhere between. Interval- censored survival (Turnbull algorithm) handles exactly this uncertainty, avoiding fixing the event to an arbitrary date. Median survival is 8 terms. By the nature of periodic assessment (term exams, annual checks), event times are always within an interval; forcing this data to a single point biases the result. The interval-censored method matches the reality of monitoring data.