Background Norming neuropsychological tests and standardizing their raw scores are needed to draw objective clinical judgments on clients’ neuropsychological profile. The Equivalent Score (ES) method is a regression-based normative/standardization technique that relies on the non-parametric identification of the observations corresponding to the outer and inner tolerance limits (oTL; iTL) — to derive a cut-off, as well as to between-ES thresholds — to mark the passage across different levels of ability. However, identifying these observations is still a time-consuming, “manual” procedure. This work aimed at providing practitioners with a user-friendly code that helps compute TLs and ES thresholds. Methods R language and RStudio environment were adopted. A function for identifying the observations corresponding to both TLs by exploiting Beta distribution features was implemented. A code for identifying the observations corresponding to ES thresholds according to a z-deviate-based approach is also provided. Results An exhaustive paradigm of usage of both the aforementioned function and script has been carried out. A user-friendly, online applet is provided for the calculation of both TLs and ESs thresholds. A brief summary of the regression-based procedure preceding the identification of TLs and ESs threshold is also given (along with an R script implementing these steps). Discussion The present work provides with a software solution to the calculation of TLs and ES thresholds for norming/standardizing neuropsychological tests. These software can help reduce both the subjectivity and the error rate when applying the ES method, as well as simplify and expedite its implementation.

Multivariate functional data that are cross-sectionally compositional data are attracting increasing interest in the statistical modeling literature, a major example being trajectories over time of compositions derived from causespecific mortality rates. In this work, we develop a novel functional concurrent regression model in which independent variables are functional compositions. This allows us to investigate the relationship over time between life expectancy at birth and compositions derived from cause-specific mortality rates of four distinct age classes, namely 0-4, 5-39, 40-64 and 65+. A penalized approach is developed to estimate the regression coefficients and select the relevant variables. Then an efficient computational strategy based on an augmented Lagrangian algorithm is derived to solve the resulting optimization problem. The good performances of the model in predicting the response function and estimating the unknown functional coefficients are shown in a simulation study. The results on real data confirm the important role of neoplasms and cardiovascular diseases in determining life expectancy emerged in other studies and reveal several other contributions not yet observed.

The above article was published online with errors. The Methods and Results sections contained minor calculation errors -which, however, did not invalidate the proposed method/software. Accordingly, Figure 2 has also been revised.The original article has been corrected.