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Introduction: In a previous paper on acceleration of failure time we highlighted the difficulties of the application to the case of mesothelioma of the methodology proposed by Berry. In this contribution we elaborate further on the concept of anticipation/acceleration, taking into account the content of the III Italian Consensus Document. Methods: We analyzed the ways in which the concept of anticipation/acceleration has been proposed and interpreted in the III Consensus Document. Results: We show that the concept of anticipation of the III Consensus Document has to do with incidence (frequency) in a population (and not with acceleration of the pathological process in an individual case), and is a measure which is alternative to other measures of frequency effects. In addition, we show that the same epidemiological result is compatible with causal models where no cases, all the cases, or some of the cases are anticipated. Discussion: This paper suggests that the concept of anticipation measurable through epidemiologic data has to do exclusively with the anticipation of a frequency indicator (more occurrencies and anticipated occurrencies are indistinguishable and alternative concepts) but not with the acceleration of the biological process in individual cases. In causal terms, without a biological support it is not possible to infer from the epidemiologic results if a causal model is in action with no, all, or some of cases anticipated.