Uncovering the natural history of cancer from post-mortem cross-sectional diameters of hepatic metastases

Abstract

We develop a mathematical and statistical methodology for estimation of important unobservable characteristics of the individual natural history of cancer from a sample of cross-sectional diameters of liver metastases measured at autopsy. Estimation of the natural history of cancer is based on a previously proposed stochastic model of cancer progression tailored to this type of observations. The model accounts for primary tumour growth, shedding of metastases, their selection, latency and growth in a given secondary site. The model was applied to the aforementioned data on 428 liver metastases detected in one untreated small cell lung cancer patient. Identifiable model parameters were estimated by the method of maximum likelihood and through minimizing the $L^{2}$ distance between theoretical and empirical cumulative distribution functions. The model with optimal parameters provided an excellent fit to the data. Results of data analysis support, if only indirectly, the hypothesis of the existence of stem-like cancer cells in the case of small cell lung carcinoma and point to the possibility of suppression of metastatic growth by a large primary tumour. They also lead to determination of the lower and upper bounds for the age of cancer onset and expected duration of metastatic latency. Finally, model-based inference on the patient's natural history of cancer allowed us to conclude that resection of the primary tumour would most likely not have had a curative effect.