Tumor recurrence due to acquired resistance to anti-cancer treatments poses a major clinical problem in treating cancer. One major cause of drug-resistance is the acquisition of random point mutations in the genomic sequence of cancer cells which confer resistant phenotypes. Despite an initial response to treatment, emergent drug-resistant subpopulations often eventually drive the recurrence and regrowth of the tumor. The timing of such cancer recurrence is highly variable in patient populations, and is governed by a balance between several factors such as initial tumor size, mutation rates, and growth kinetics of drug-sensitive and resistant cells. To better understand patterns of cancer progression in patient populations, we are interested in the mechanisms driving early or late cancer recurrences. In previous work, we modeled the dynamics of recurrence by considering escape from a subcritical branching process, where the establishment of a clone of escape mutants can lead to total population growth after the initial decline. Here, we study and characterize the rare events leading to early or late crossover time, defined as the time at which the total cancer population first becomes dominated by the emerging resistant cell population. In particular, using this model we investigate algorithms for estimating the probability of early crossover events, which are correlated with early tumor recurrence.