Delay of the diagnosis of hepatitis C virus (HCV), and its treatment to avert cirrhosis, is often present since the early stage of HCV progression is latent. Current methods to determine the incubation time to HCV-related cirrhosis and the duration time from cirrhosis to subsequent events (e.g. complications or death) used to be based on the time of liver biopsy diagnosis and ignore this delay which led to an interval censoring for the first event time and a double censoring for the subsequent event time. To investigate the impact of this delay in estimating HCV progression rates and relevant estimating bias, we present a correlated two-stage progression model for delayed diagnosis time and fit the developed model to the previously studied hepatitis C cohort data from Edinburgh. Our analysis shows that taking the delayed diagnosis into account gives a mildly different estimate of progression rate to cirrhosis and significantly lower estimated progression rate to HCV-related death in comparison with conventional modelling. We also find that when the delay increases, the bias in estimating progression increases significantly.