There is interest in estimating and attributing temporal changes in incidence of breast cancer in relation to the initiation of screening programmes, in particular to estimation of overdiagnosis of breast cancer as a result of screening. In this paper, we show how screening introduces complexities of analysis and interpretation of incidence data. For example, lead time brings forward time- and age-related increases in incidence. In addition, risk factors such as hormone replacement therapy use have been changing contemporaneously with the introduction of screening. Although we do not indicate exactly how such complexities should be corrected for, we use some simple informal adjustments to show how they may account for a substantial proportion of increased incidence, which might otherwise erroneously have been attributed to overdiagnosis. We illustrate this using an example of analysis of breast cancer incidence data from Sweden.