Comparison of multi-state Markov models for cancer progression with different procedures for parameters estimation. An application to breast cancer

Abstract

Background: the knowledge of sojourn time (the duration of the preclinical screen-detectable period) and screening test sensitivity is crucial for understanding the disease progression and the effectiveness of screening programmes. For this purpose a model of the natural history of the disease is needed. The aim of this work is to provide an illustration of the application of multistate Markov models for breast cancer progression to the data of the Florentine screening programme, in order to estimate the sojourn time and sensitivity for breast cancer screening. Methods: three different multi-state Markov models of increasing complexity were used with three different estimation procedures based on non-linear least squares, maximum likelihood, and on a Bayesian approach. All the models produced estimates for screening sensitivity and mean sojourn time. The data used in our application seem to lead to a non-identifiability problem, since the estimation procedures for both the Maximum Likelihood and Non-Linear Least Squares gave estimates that changed with the parameters’ initial values or difficultly converged. In order to take this problem into account we used the Bayesian Approach by incorporating prior information on all the parameters. Results: the mean sojourn time varied between 2-7 years and 3-5 years for women aged 50-59 and 60-69, respectively. When the model complexity was increased a higher variability in estimates was observed among the estimation procedures. The results of the screening sensitivity estimates were highly variable, both among estimation techniques and models - varying between 63% and 100%, and between 77% and 100% for women aged 50-59 and 60-69, respectively. Conclusions: results are in accord with the literature; those obtained through the Bayesian Approach seem to be more reliable.