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Table 1 Relationship of residuals with cognitive decline, with and without adjusting for baseline cognition

From: Issues and recommendations for the residual approach to quantifying cognitive resilience and reserve

  β (residual*time) CI p-value
Model 1: Cognition ~ Residuals*Time 0.05 0.03–0.08 <0.001
Model 2: Cognition ~ Residuals*Time + BaselineCognition*Time −0.10 −0.14 to −0.06 <0.001
Model 3: Cognition ~ ResidualsCor*Time −0.11 −0.14 to −0.07 <0.001
  1. All models are linear mixed effects models with random intercepts and slopes per participant, and cognitive score at each timepoint as dependent variable. Cognition was assessed using ADNI-MEM, the standardized composite ADNI memory score
  2. Model 1: Cognition ~ Residuals*Time. This model represents the usual case scenario in which the (cognition) residual is used as a predictor in a subsequent analysis (e.g., here to predict decline)
  3. Model 2: Cognition ~ Residuals*Time + BaselineCognition*Time. This model represents the first proposed alternative solution, i.e., adding baseline cognition, on which the residual is based, as a covariate alongside the residual to assess the effect of “resilience independent of cognitive performance”
  4. Model 3: Cognition ~ ResidualsCor*Time. This model represents the second proposed alternative solution, i.e., regressing the cognition variable out of the residual to obtain a “corrected” residual (“ResidualsCor”) in a subsequent analysis
  5. Abbreviations: β unstandardized regression coefficient from linear mixed effects models, CI 95% confidence interval