Impact of delayed diagnosis time in estimating progression rates to hepatitis C virus-related cirrhosis and death

Bo Fu, Wenbin Wang and Xin Shi have a new paper in Statistical Methods in Medical Research. The paper is interested in the estimation of rates of progression from hepatitis C infection to cirrhosis and from cirrhosis to death. The primary complication in the model is that the time of cirrhosis development is interval censored, since it is only diagnosed at clinic examination times.

The model consists of a simple unidirectional 3-state model. A parametric Weibull approach is taken, where the time to cirrhosis from infection has a standard Weibull distribution and the time from cirrhosis to death has a Weibull distribution where the scale parameter is a function of the time between infection and cirrhosis.

Unsurprisingly, they show that a full likelihood approach which takes into account the interval censoring is much less biased than an approach that ignores the problem of interval censoring.

A criticism of the model, which the authors acknowledge, is that the possibility of death before cirrhosis is not accommodated. Potentially, even under their current model there might also be cases where death occurs after cirrhosis but before diagnosis of cirrhosis - a scenario which isn't accommodated in the three cases listed in their likelihood development. The rate of increase of the hazard of cirrhosis from infection is observed to increase after 30 years since infection. It is not clear whether this is a real effect, whether it is due to a small number of people at risk or whether it is an artifact of not accommodating the possibility of death without cirrhosis. Given the long follow-up time in the study it might have been more sensible to consider age rather than either time since cirrhosis or time to infection as the primary timescale, at least for time to death.

Finally, whilst the approach might be novel for HPV patients, the 3-state approach is clearly widely used in other contexts, most specifically in HIV/AIDS studies. For instance the penalised likelihood approach of Joly and Commenges would be highly applicable.