A statistical model for interval censored data is described. Assuming a piecewise constant incidence enables us to analyse very unbalanced data in a generalized linear model. The distribution of age at first appearance of P. falciparum parasites in infants in Liberia has been estimated. A new graphical method for presentation of test results on all children was developed. In an illness--death model it is described how the proportion of undetected and detected malaria parasitemias depends on parasite rates and testing frequency. The incidence of detectable malaria parasitemia was 0.14 per month in infants under 4 months of age, and 0.60 per month in children over 4 months (p < 0.001). The congenital resistance to malaria in African infants living in a highly endemic area had largely disappeared by the age of 4 months; before this age children were partly protected.