## 2 Materials and Methods  
**ADNI genotype data**. The data used in this study were obtained from the ADNI public dataset; more specifically, from the ADNI-1 study ([[https://adni.loni.usc.edu/about/adni1/](https://adni.loni.usc.edu/about/adni1/)]([https://adni.loni.usc.edu/about/adni1/](https://adni.loni.usc.edu/about/adni1/)), accessed on 1 February 2023). The individuals in this dataset underwent genotyping via the Illumina Human610-Quad BeadChip. The dataset contains the genotypic information of 599,011 SNPs from 757 individuals; 344 individuals had been diagnosedwith Alzheimer's disease (IAD), 210 individuals were perceived as cognitively normal (ICN), and 203 individuals had mild cognitive impairment (IMCI). The data were submitted to quality control and population stratification, which were carried out in accordance with the procedure described by [PERSON] and others (2010) [14], and was conducted using the PLINK software [15] (version 1.9). To perform our study, we considered genotypic data from IAD and ICN individuals with western European ancestry, and information regarding probes that were dedicated to copy number variation was excluded. During the quality control procedure, a total of 103 samples were excluded. The exclusions were made as follows: 2 samples due to gender discrepancies; 96 samples due to divergent ancestry; 16 samples with a heterozygosity rate higher than expected; 2 samples due to non-reported relatedness to another participant of the study; and 4 samples with more than 5% missing genotypes. Additionally, for the initial 599,011 genotyped SNPs, we used filters to allow for the exclusion of SNPs with a missing rate higher than 5% (19,406), deviation from the Hardy-Weinberg equilibrium (130), and for having a minor allele frequency lower than 5% (61,218). The criteria used in data filtering and variable selection aligned with the guidelines for GWAS [16]. Also, the missing rate of genotyped SNPs was compared between cases (IAD) and controls (ICN), and no significant differences were detected [14]. An imputation was made to fill in missing genotypes using the _bigsnpr_ R package, namely the _smp_fastlmpute_ method with the default parameters. Therefore, the final database was composed of 451 individuals, with 163 ICN (36.1%), 288 IAD (63.9%), and 518,257 SNPs. **Dataset handling. ** The data were divided into the two following datasets: a training set and a test set. The training set included 70% of the initial sample (116 ICN--36.7%; 200 IAD--63.3%), and was used to perform variable selection, as well as to build the prediction models. The test set included the remaining 30% (47 ICN--34.8%; 88 IAD--65.2%), and was used to assess the performance of the prediction models. This division was made randomly, and was stratified by the attributes of the dependent variable (IAD and ICN) in order to maintain the correct proportion of cases and controls. **Stable variable selection method with shrinkage regression. ** The proposed method analyzes and combines the results of the repeated applications of a penalized regression model on the training dataset. The main objective of our procedure is to identify the most important variables and to define the corresponding regression coefficient using a measure of the relative quality of fit of each model. Variables that are selected more often in higher quality models will have greater potential to be selected for the final model. In fact, the \"variable weight\" (defined below) depends not only on the frequency of the selection of the variable in all models, but also on the inherent quality of the fit of each model. Therefore, the proposed variable selection procedure is more restrictive than the usual correspondent penalized regression approach. The final regression coefficient of the relevant variables is calculated based on the coefficients obtained in each repetition of the penalized regression model.