The extreme values in biomarker indicate abnormal status. Identifying characteristics of the subgroups with abnormally high/low values in biomarker is important for risk management. Furthermore, nearly all biomarkers are subject to measurement error. To address these issues, we use Gumbel-Normal mixture distributions by assuming that the true biomarker follows a Gumbel distribution given covariates and employing an additive measurement error model. We propose semiparametric Gumbel-Normal mixture models, which adjust parametrically for covariates and non-parametrically for time effect on biomarker values. In this paper, we focus on finding sub-population trends rather than individual variations over time. For longitudinal biomarker values, we use pseudo-likelihood by multiplying the marginal distributions and obtain maximum likelihood estimates via implementing the EM algorithm. We approximate the time effect in the models by using Bernstein splines so that flexible modeling for time effect is allowed. We compare the proposed models to generalized linear models in analyzing blood glucose data from a diabetes ancillary study to the Atherosclerosis Risk in Communities (ARIC) Study.