Introduction:Conventional Z-scores are generated by subtracting the mean and dividing by the standard deviation. More recent methods linearly correct for age, sex, and education, so that these "adjusted" Z-scores better represent whether an individual's cognitive performance is abnormal. Extreme negative Z-scores for individuals relative to this normative distribution are considered indicative of cognitive deficiency. Methods:In this article, we consider nonlinear shape constrained additive models accounting for age, sex, and education (correcting for nonlinearity). Additional shape constrained additive models account for varying standard deviation of the cognitive scores with age (correcting for heterogeneity of variance). Results:Corrected Z-scores based on nonlinear shape constrained additive models provide improved adjustment for age, sex, and education, as indicated by higher adjusted-R2. Discussion:Nonlinearly corrected Z-scores with respect to age, sex, and education with age-varying residual standard deviation allow for improved detection of non-normative extreme cognitive scores.