Relapses arising from dormant liver-stage Plasmodium vivax parasites (hypnozoites) are a major cause of vivax malaria. However, in endemic areas, a recurrent blood-stage infection following treatment can be hypnozoite-derived (relapse), a blood-stage treatment failure (recrudescence), or a newly acquired infection (reinfection). Each of these requires a different prevention strategy, but it was not previously possible to distinguish between them reliably. We show that individual vivax malaria recurrences can be characterised probabilistically by combined modelling of time-to-event and genetic data within a framework incorporating identity-by-descent. Analysis of pooled patient data on 1441 recurrent P. vivax infections in 1299 patients on the Thailand-Myanmar border observed over 1000 patient follow-up years shows that, without primaquine radical curative treatment, 3 in 4 patients relapse. In contrast, after supervised high-dose primaquine only 1 in 40 relapse. In this region of frequent relapsing P. vivax, failure rates after supervised high-dose primaquine are significantly lower (∼3%) than estimated previously.