Bayesian Estimation of Partial Functional Tobit Censored Quantile Regression Model

The information extracted from imaging data has become increasingly important in disease diagnosis as it uncovers associations between imaging features and diseases of interest. This study proposes a partial functional Tobit censored quantile regression (PFTCQR) model to investigate the quantile-specific relationships between the time of incidence of laryngeal cancer and a set of imaging and clinical predictors based on the data collected from a laryngeal cancer study in the Otolaryngology Department of a tertiary hospital in Jilin Province, China. The functional principal component analysis and moment method are employed to estimate the slope and covariance functions of the functional predictors. An efficient Markov chain Monte Carlo (MCMC) algorithm is developed, leveraging the location-scale mixture representation of the asymmetric Laplace distribution (ALD) to perform the estimation. Furthermore, we extend the PFTCQR model to the composite quantile regression framework and incorporate variable selection for scalar covariates, further enhancing the robustness and efficiency of parameter estimation and improving model fitting. The proposed method is demonstrated through simulation studies and applied to the laryngeal carcinoma data. Results provide new insights into potential risk factors for laryngeal carcinoma and their effects varying across quantiles. Specific laryngeal regions are identified as significantly associated with the progression of the disease.