# The Iterative Exclusion of Compatible Samples Workflow for Multi-SNP Analysis in Complex Diseases
## 1 Introduction
GPQMDR, proposed in 2018, is a method to detect interactions between genes for complex quantitative traits via generalized fuzzy classification, which can calculate multiple SNP interactions with a heavy computational burden [32]. The screening methods can effectively screen SNPs, delete a large number of noise sites, and effectively retain the genetic correlation of data, thereby improving the calculation efficiency and recognition ability. In 2008, a two-stage method for epistasis analysis was reported. In this method, significant SNPs are first screened out and single SNPs with marginal effects significantly exceeding the threshold are retained, and then epistasis is identified based on the retained SNPs [33]. INTERSNP, proposed in 2009, can screen SNPs by combining SNP association, genomic location, and pathway information, and logistic regression (LR) is then used to identify higher-order epistasis based on the screened SNPs [34]. The efficient detection of all pairwise interactions in genome-wide case-control studies can be achieved through the application of the BOolean operation-based screening and testing (BOOST) approach [35]. BOOST introduces a Boolean expression of genotype, establishes a 3 \(\times\) 3 contingency table, and adopts a two-stage searching approach. To evaluate all SNP pairs, a non-iterative method is utilized in the filtering stage to calculate the approximate likelihood statistical ratio [36], and the interactive impact of the chosen SNP pairs is evaluated using both the classical likelihood ratio test and the chi-square test during the testing stage [37; 38]. Machine learning methods judge the phenotype of new data by learning the training data and select the SNP combinations with the strongest association with diseases by converting epistasis detection into a classification problem. Random forest (RF) [39], support vector machines (SVM) [40], neural networks (NNs) [41], and LR [42] are machine learning methods commonly used in epistasis analysis. Usually, machine learning models are difficult to interpret due to their complexity. Some of the aforementioned algorithms can only analyze two-order SNP interactions, and some have a heavy computational workload or difficulty in interpretation. Boolean algebra is a rigorous logical calculation system that can obtain the combination of conditional variables for a specific result which has the potential to be used to study the association between SNPs and complex diseases. Qualitative comparative analysis (QCA) [43], a configurational analysis method grounded in set theory and Boolean algebra, has been extensively applied in sociology [44; 45] to examine the interplay between conditional variables and outcome variables. For an SNP dataset, there are generally many conditional variables and relatively few samples. Boolean minimization and simplification can only eliminate a small number of conditional variables, and therefore the complex solution of QCA usually has no simple prime implicants. Since complex diseases are often caused by mutated SNPs, the mutated SNPs can be extracted from the prime implicants screened according to the coverage and then combined into pathogenic patterns, followed by the chi-square test on the pathogenic pattern in the source data to check the association between the pathogenic pattern and complex diseases. To further mine the information, the samples compatible with the pathogenic pattern are excluded, and the remaining samples will be subjected to the next round of calculation. The four steps (QCA, pattern extraction, the chi-square test, and compatible sample exclusion) are iterated and form the IECS workflow.