# The Iterative Exclusion of Compatible Samples Workflow for Multi-SNP Analysis in Complex Diseases
## 2 Materials and Methods
### Iterative Exclusion of Compatible Samples Workflow
During the iterations, if the solution of QCA is empty or the extracted pathogenic pattern is empty, the items obtained in previous rounds of iteration are output, and the IECS workflow is ended. datasets identified by the algorithm to that of all datasets [35]. Power is calculated as follows:

\[\text{Power}=N_{T}/N_{D} \tag{3}\]

where \(N_{T}\) denotes the number of identified datasets determined by whether the whole solution has at least one item that is the same as the item in the logical expression of the pathogenic model [46], and \(N_{D}\) denotes the total number of datasets, which was set to 1000 in this experiment. Runtime is obtained by calculating the average time that the program runs in each dataset of each dataset group. ### Simulated Data

Suppose the S disease is caused by the simultaneous mutation of SNP-A and SNP-B or SNP-C and SNP-D, and E is added to stand for any other SNP. The configuration table of all logical combinations of the S disease is expressed as A \(\times\) B \(\times\) C \(\times\) D \(\times\) E \(\times\) S, and the pathogenic model is recorded as A \(\times\) B + C \(\times\) D = S.

Collection I comprises seven dataset groups introduced with 10%, 20%, 30%, 40%, 50%, 60%, and 70% noise, respectively, and each group contains 1000 datasets, with each dataset including 100 samples. Collection II comprises seven dataset groups respectively containing 200, 400, 600, 800, 1000, 1200, and 1400 samples, and each dataset group includes 1000 datasets introduced with 30% noise. ### Alzheimer's Disease Data

The etiology of [PERSON]'s disease (a neurodegenerative disorder) remains unknown [47]. The performance of IECS was further tested in a real dataset of Alzheimer's disease downloaded from the Kaggle website. This dataset encompasses 257 Chinese individuals diagnosed with sporadic Alzheimer's disease along with 242 control subjects exhibiting normal cognitive function. The average age of the patients at examination was 76.7 years, and the average age of the controls was 80.0 years. ## 3 Results and Discussion

All calculations were executed on the same computer with the configuration as follows: CPU, Intel(R) Core(TM) i7-8700 CPU @ 3.20 GHz; RAM, 16.0 GB; OS, Windows 10 64 Bit. ### Simulated Data Experiment

For Collection I, the power levels of IECS, MDR, and BOOST are presented in Figure 3a. The results revealed that when the noise was lower than or equal to 60%, IECS exhibited a greater power compared to both the MDR and BOOST methods; when the noise level reached 70%, the power of IECS was slightly smaller than that of MDR, but greater than that of BOOST. IECS utilizes QCA for calculation and then extracts the pattern for the chi-square test, which can minimize the negative impact caused by noise and then more accurately identify SNP interactions. Noise showed a great influence on the power: the power of IECS, MDR, and BOOST was close to 1 when the noise was 10% and gradually decreased with increasing noise. A greater noise ratio represents more interfered samples. For MDR, a greater noise ratio means a greater error probability to define different combinations of SNP pairs and accordingly a higher probability of incorrect results in the cross-validation, thereby leading to the smaller power of the algorithm; for BOOST, it means a lower probability that the distribution of the contingency table is consistent with the pathogenic model, so the power is smaller; and for IECS, it means a greater reduction in the consistency and coverage during QCA, which has a greater impact on the identification process and then leads to smaller power. The runtimes of IECS, MDR, and BOOST for simulated data with different noise ratios are shown in Table 1. In general, BOOST is the fastest, followed by IECS and then MDR.