In conventional survival analysis there is an underlying assumption that all study subjects are susceptible to the event. In general, this assumption does not adequately hold when investigating the time to an event other than death. Owing to genetic and/or environmental etiology, study subjects may not be susceptible to the disease. Analyzing nonsusceptibility has become an important topic in biomedical, epidemiological, and sociological research, with recent statistical studies proposing several mixture models for right-censored data in regression analysis. 　　In longitudinal studies, we often encounter left, interval, and right-censored data because of incomplete observations of the time endpoint, as well as possibly left-truncated data arising from the dissimilar entry ages of recruited healthy subjects. In practice, survival curves over different strata may have multiple crossing points, and their tails frequently become flat after different time points. In this presentation, we report the logistic-AFT location-scale regression models to tackle these kinds of incomplete data (Chen, Tsay, Wu and Horng, 2013). Relative times of the conditional event time distribution for susceptible subjects are extended in the accelerated failure time location-scale submodel. We also constructed graphical goodness-of-fit procedures on the basis of the Turnbull-Frydman estimator (1976, 1994) and newly proposed residuals. Using the web-based statistical software system entitled “EHA-RiskFree” for facilitating data analysis via our proposed models, we recently studied genetics of alcoholism dependence from the COGA, metabolic diseases from the CVDFACTS and hepatocellular carcinoma from the REVEAL-HBV study conducted in Taiwan. These statistical methods will be useful for researches in molecularly targeted clinical trials and biobank studies.