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Descriptive summaries were computed for the entire cohort and by diagnosis (CS and AD). Continuous variables were summarized as the median and IQR (interquartile range; 25–75 percentiles) and categorical variables as frequencies (proportions). Differences in the distributions of categorical and continuous variables by diagnosis were assessed using either the chi-square test/Fisher’s exact test or the Mann–Whitney test, respectively.

Separate linear regression models were constructed to quantify the association between the age of AD onset and each autoimmune condition, history of gout, and ApoE-ε4 status. Parameter estimates from these models, and their 95% confidence intervals, were computed to summarize expected differences of the age of AD onset by autoimmune condition (e.g., alopecia vs. no alopecia), history of gout, and ApoE ε4 status. Due to the rarity of many of the autoimmune conditions, simultaneous adjustments for ApoE ε4 status were not performed when characterizing the relationship between the age of onset and the presence of each autoimmune condition. Given that these variables were unrelated to autoimmune diseases, the resultant parameter estimates remain unbiased [26].

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