A Censored Semicontinuous Regression for Modeling Clustered/Longitudinal Zero-Inflated Rates and Proportions: An Application to Colorectal Cancer

Zero-inflated rate/proportions/ratio models are commonly used in biomedical data where the response variable takes its values over the interval (0,1). When proportion data include many zeroes in addition to the values in the interval and are correlated among study units, fitting a marginal model using generalized estimating equations (GEE) that can incorporate subject-to-subject correlations is a natural choice. In the present study a GEE based zero-inflated censored Beta (GEE.ZICBETA) model is proposed to fit clustered rate data with zeroes that allows for some proportions to be left-censored. The model combines elements of logistic regression for the Bernoulli success probability, the Beta distribution for the rate observations, and left censoring. A corresponding sandwich variance estimator as well as a clustered resampling (bootstrap)-based procedure are used to estimate the variance. Using a simulation study, the asymptotical properties of the estimators are shown. The resulting inference procedure is applied to investigate the association between several potential climatic risk factors and colorectal cancer rate in Iran. Several risk factors clinically relevant are identified using the proposed model.