The population attributable fraction (PAF) is a useful measure for describing the expected change in an outcome if its risk factors are modified. Cohort studies allow researchers to assess the predictive value of the risk factor modification on the incidence of the outcome during a certain follow-up. Estimation of PAF for both mortality and morbidity in cohort studies with censored survival data has been developed in the recent years. So far, however, censoring due to death in the estimation of PAF for morbidity has been ignored, resulting in estimation of a quantity which is not relevant in practice as some people are likely to die during the follow-up. The risk factors related to the disease incidence may also be related to mortality, and modification of these risk factors is likely to delay the occurrence of both events. Thus, censoring due to death and the impact of risk factor modification must be considered when estimating PAF for disease incidence. We consider both and introduce two measures of disease burden: PAF for the incidence of disease during lifetime and PAF for the prevalence of disease in the population at a certain time. We demonstrate how consideration of censoring due to death changes the estimated PAF for disease incidence and its confidence interval. This underlines the importance of choosing a correct PAF measure depending on the outcome of interest and the risk factors of interest to obtain accurate and interpretable results.