Nonparametric estimation of transitions in cancer
Go, Kerry W.
Doctor of Philosophy
This research is concerned with estimating the relationship between the occurrence of metastases and the size of primary cancers. We are interested in finding the distribution functions of tumor sizes at the points of nodal metastatic and distant metastatic transitions. Understanding the sequential order and timing of events in cancer is essential for measuring the impact of various surveillance and treatment strategies. Since the tumor size at the points of metastatic transitions is usually not observable, estimation of these distributions requires the use of the Expectation-Maximization Algorithm. Nonparametric methods of estimation are explored, with attention to the fact that tumors often fail to be measured, particularly those that are known to be metastatic. The methods are applied to the estimation of primary tumor sizes at the points of nodal and distant metastases in lung cancer (epidermoid and adenocarcinoma) and colorectal cancer. Extensive numerical and simulation studies have been carried out to assess the applicability of the procedure. Also, for comparison, a fully parametric algorithm, based on exponentiality assumption, has been derived and tested. The nonparametric procedure performed best on data sets which are "balanced," i.e., include meaningful proportions of both nonmetastatic and metastatic cases. The parametric version performs very well for data simulated from the exponential distribution. The algorithm developed is applied to data on cancer of colon, lung, and breast, collected by investigators at the Memorial Sloan-Kettering Cancer Center. The results yielded by the nonparametric and parametric algorithms are consistent with each other. They are consistent also with the previous estimates obtained using a simpler model. This allows interesting comparisons of metastatic potential of different cancers. Further research includes extension of the algorithm to multiple transitions and further exploration of biomedical data.
Biostatistics; Statistics; Public health