Problems encountered in multiple regression due to multicolinearity or missing data can be overcome by using PLS regression. Several versions of the PLS regression algorithm exist. In this paper, we present a new version of this algorithm which can be extended to generalized linear regression models such as ordinal or multinomial logistic regression, generalized linear models, and Cox regression models. An application with discrete censored data concerning the occurrence of prematurely graying hair in more than 4000 adult males is presented. The Cox regression model has been used. For discrete data summarizing a continuous time process, this model is equivalent to a generalized linear model using a complementary log-log link function.