Computational protocol: The nonlinear relationship between cerebrospinal fluid Aβ42 and tau in preclinical Alzheimer’s disease

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[…] Demographic differences between cohorts and Outcome Group were assessed using ANOVA with Tukey post hoc correction for pairwise comparisons for continuous variables. Chi-square tests with Bonferroni correction for pairwise comparisons were used to test nominal variables for group differences. The standard confounds of age, sex and ApoE4 status were added to all statistical models as covariates with the exception of models with demographically matched outcome groups.We observed in the individual cohort scatterplots that both high and low levels Aβ42 were associated high Tau levels. From this observation we hypothesized that a quadratic fit of Aβ42 would explain more of the variance in the Tau measures than the linear fit of Aβ42 alone. Linear regression models, with the T-Tau and P-Tau181 measures as dependent variables, were used to test this hypothesis. The linear Aβ42 term followed by the quadratic Aβ42 term (Aβ2) were added consecutively to test the incremental change in the model with the standard confounds. To account for possible heteroscedasticity of the estimators, robust (Huber-White) sandwich estimators were used to estimate the standard errors. Sensitivity analysis was performed using all available subjects with normal cognition at their baseline LP (no exclusions) from each cohort.To have sufficient power to investigate possible interaction effects and the relationship of Aβ2 with future cognitive decline, subjects with follow-up clinical data from the three cohorts were combined and analyzed using Generalized Estimating Equations (GEE). The GEE allowed us to account for possible clustering of subjects within cohorts. We assumed an unstructured correlation matrix in all GEE models with cohort included as a within-subjects effect. The GEE models were analyzed first on the raw biomarker values. However, since the cohorts used different assays, the scale of the raw values were different for each cohort making graphing and the interpretation of model coefficients problematic. For this reason, z scores for each cohort were calculated using the mean and standard deviation from the raw biomarker values. The results are reported and graphed using the z scores.The X-Tau measures were examined as the dependent variables with the identity link function in the GEE, with the standard covariates, Aβ42, Aβ2, and the interactions of the standard confounds with Aβ42 and Aβ2. In the presence of significant interaction terms, the data was subdivided and reanalyzed to explore the interaction.We hypothesized that both high and low Aβ42 were associated with future cognitive decline and that this effect would be stronger in younger subjects. To test this hypothesis we used the GEE with the logit link and Outcome group as a binary dependent variable. Aβ42 was added to the standard confounds as an independent variable to test a linear association with Future MCI/AD. Subsequently, we added Aβ2 and its interaction with age. Observing a significant interaction with age, the sample was divided at the median age of the Future MCI/AD group (75y) and the GEE models including the standard confounds, Aβ42 and Aβ2 were evaluated separately in young (45-75y) and old age groups (75.1-86y). This analysis was replicated in the matched outcome groups.In the subset of 233 NYU subjects who additionally had Aβ38, Aβ40, and Aβ42 measured with MSD, we hypothesized that Aβ42 would show quadratic relationships with X-Tau measures, whereas Aβ38 and Aβ40 would show linear relationships. To test this hypothesis we used linear regression models with the X-Tau measures as the dependent variables and the linear and quadratic terms for Aβ38, Aβ40 and Aβ42 as independent variables.All analyses were checked for violations of the model assumptions and any conflicts are reported. The Box Cox transformation procedure [] was used to determine the most appropriate power transformation to reconfigure values to a normal distribution. Differences in variances were tested using Levene's Test for Equality of Variances. All variables were centered for the calculation of higher order terms to avoid multicollinearity with the main effects. For all results, statistical significance was defined as a two-sided p-value of less than 5%. Statistical analyses were performed using IBM SPSS (Version 23.0) and figures were rendered in Adobe Illustrator (CC 2015). […]

Pipeline specifications

Software tools SPSS, Adobe Illustrator
Application Miscellaneous
Diseases Alzheimer Disease, Tauopathies