A multistate modelling approach for pancreatic cancer development in genetically high risk families

Kolamunnage-Dona, Vitone, Greenhalf, Henderson and Williamson have a new paper in Applied Statistics. This uses a competing risks model with shared frailties to model data on the progression of pancreatic cancer in the presence of clustering and informative censoring. Clustering is present due to data being available on patients from the same family groups. A patient having a resection causes censoring of the main event, time to pancreatic cancer, but is likely to be informative. This is dealt with by allowing the cause-specific hazards to depend on the same frailty term. The methodology in the paper is very similar to that of Huang and Wolfe (Biometrics, 2002), the only extension being that the current formulation allows for the possibility of time dependent covariates. It isn't clear what if any complication this adds to the original procedure in Huang and Wolfe. An MCEM algorithm is used where the E-step is approximated by using Metropolis-Hastings in order to calculate the required expected quantities. It's not clear what the authors mean when they say the Metropolis-Hastings step use "a vague prior for the frailty variance." Hopefully they mean an improper uniform prior as otherwise they would be pointlessly adding Bayesian features to an otherwise frequentist estimating procedure. On a related computational point, since the random effect for each cluster is one dimensional, I suspect using a Laplace approximation to compute the required integrals at each step would perform quite well and be a lot faster than using Metropolis-Hastings

In the analysis there does seem evidence for a shared frailty within clusters, but it appears that the parameter which links the frailty in the time to pancreatic cancer to the time to resection intensity is hard to identify having a very wide 95% confidence interval encompassing strong negative dependence through independence to strong positive dependence. The typical cluster size in the data is quite small (e.g. median is 3) and this is probably insufficient as you would ideally need some subjects to fail and some to be informatively censored in each cluster to assess their association. The point estimate is negative implying a counter intuitive negative association between resection and pancreatic cancer. The authors suggest as a model extension to allow a specific bivariate frailty linking competing risks (presumably within individuals?) - which is unlikely to be helpful.