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Back‐calculation is a widely used method to estimate HIV incidence rates, and is commonly based on times of AIDS diagnosis. Following up earlier work, we extend this method to also incorporate knowledge of times of HIV diagnosis (first positive test). This is achieved through the use of a Markov model which describes the progress of an HIV infected person through various stages, and which allows causal connections between events to be explicitly modelled. Estimation is based on maximum likelihood, the likelihood being calculated within a discretized version of the Markov model. The effect of sampling uncertainty and model uncertainty (sensitivity) is evaluated simultaneously by means of a combined bootstrap and simulation procedure. At each replication we resample both the data and the model (from a set of possible models described by randomizing one or more parameters). For instance, uncertain …