Many investigations have shown that artemisinin-based combination therapies are effective in the treatment of uncomplicated malaria and that they do not increase parasite resistance to treatment as much as treatment with single substance. We study the relation between some biological covariates and the time to first recurrence of malaria for children treated for malaria in a clinical trial. One group received artesunate plus sulfadoxine-pyrimethamine and the other only sulfadoxine-pyrimethamine. We consider the event malaria-free for the first 42 (and 84) days. We use logistic regression models for the analyses. The main results show that the probability of no recurrence is higher if the parasite density in the blood is high. The results are inconclusive for other explanatory biological variables. The infecting parasites having genes that indicate resistance, gave different results at the two different treatment centres. There was no appreciable difference in the effects of treatment over the two follow-up periods and these treatments do not have any effect on the probability of a recurrence.