# The Iterative Exclusion of Compatible Samples Workflow for Multi-SNP Analysis in Complex Diseases
## 2 Materials and Methods
### Iterative Exclusion of Compatible Samples Workflow
MDR performs the permutation test on generated multiple new datasets by randomly shuffling the outcome of the original samples and then carries out MDR analysis on these new datasets, which is very computationally intensive, resulting in its having the lowest speed among IECS, MDR, and BOOST. BOOST employs an approximate approach to evaluate all pairs of loci by calculating the approximate likelihood ratio in a non-iterative way, which reduces the runtime by simplifying the calculation. With increasing noise ratio, the runtime remains almost constant. Figure 3: (**a**) The power levels of IECS, MDR, and BOOST for simulated data with different noise levels. When the noise was less than or equal to 60%, the power of IECS was greatest; when the noise was 70%, the power of IECS was slightly less than MDR, but greater than BOOST. (**b**) The power levels of the three algorithms with different numbers of samples. With the increase in the number of samples, the power of MDR and BOOST increase slowly and IECS remains constant; the more samples, the more information about the pathogenic model obtained by the MDR and BOOST algorithms and the greater the power. However, in IECS, the QCA calculation engine becomes insensitive to the number of samples beyond a certain amount. For Collection II, the power levels of IECS, MDR, and BOOST for simulated data with different numbers of samples are presented in Figure 3b. With an increasing number of samples, the power of MDR and BOOST increases slowly, while that of IECS remains almost constant. With more samples, more information about the pathogenic model could be obtained by MDR and BOOST, which would contribute to a greater power. However, in IECS, the QCA calculation engine becomes insensitive to the number of samples beyond a certain amount. When the noise is constant, the number of excluded samples will be adjusted proportionally, and then the extracted pattern is almost unchanged, resulting in the constant power of IECS. The runtimes of IECS, MDR, and BOOST for simulated data with different numbers of samples are presented in Table 1. With an increasing number of samples, the runtime of MDR and IECS will increase, because more information needs to be calculated for more samples, and therefore more runtime is consumed. BOOST employs an approximate approach to evaluate all pairs of loci by calculating the approximate likelihood ratio in a non-iterative way, which is not sensitive to the number of samples, resulting in an almost constant runtime. Based on the above results of simulated datasets with a comprehensive comparison of power and runtime, IECS has a stronger recognition ability for pathogenic models with an acceptable runtime. ### Alzheimer's Disease Data Experiment

The dominant model was adopted to code homozygous wild-type alleles as 0 and heterozygous wild-type and mutant alleles or homozygous mutant alleles as 1. Four iterations were completed in the IECS workflow. The pattern of the simultaneous mutation of SNP (IV S22 + 36 C > A) and SNP (3'UT R159 C > T) was extracted in the first round; the IV S17 \(-\) 294 C > T mutation pattern was extracted in the second round; the simultaneous mutation pattern of IV S3 + 106 T >G, IV S10 \(-\) 5 C > T, and 3 'UT R159 C > T was extracted in the third round; and the IV S22 + 36 C > A mutation pattern was extracted in the fourth round. Please refer to Table 2 for the results of the QCA analysis. The chi-square test was employed to analyze the predictive power of the four patterns in the source dataset, and the \(p\)-value of the pattern with simultaneous mutation of IV S3 + 106 T > G, IV S10 \(-\) 5 C > T, and 3'UT R159 C > T was 0.909, which was greater than 0.05, and therefore this pattern was excluded from the pathogenic model. The relationship between SNPs and Alzheimer's disease was obtained by IECS. If IV S22 + 36 C > A and 3'UT R159 C > T are simultaneously mutated, or IV S17 \(-\) 294 C > T or IV S22 + 36 C > A is mutated, the individual might get Alzheimer's disease.