Scale Transformation Analysis Method For Binary Traits Based On Mixed Model

In the genome-wide association analysis for quantitative traits,the linear mixed model(LMM)and generalized linear mixed model(GLMM)of the micro-effect multigene effect can well correct the statistical expansion caused by population stratification and the analysis of the implicit kinship between individuals,so that the false positive of the correlation statistical test results can be controlled,and then effective screening of genetic marker SNPs can be realized.However,the complete LMM and GLMM involve complex iterations in the estimation of variance components,and a large amount of computing resources need to be mobilized to limit the efficiency of the correlation test to a very low level.Based on that,the researchers have developed a variety of optimization algorithms based on LMM and GLMM.In the association analysis for binary traits composed of case and control,researchers usually use GLMM-based optimization algorithms to achieve the purpose of analysis.In terms of statistical test efficiency,compared with the complete GLMM,although the existing GLMM optimization algorithm has been improved,when the proportion of case in phenotypic traits is extreme and the genetic relationship among population samples is very complex,the difficulty of variance component estimation is increased,and even the iteration does not converge,which reduces the reliability of correlation test results.As a special quantitative trait,binary traits can be analyzed quickly and efficiently through LMM-based optimization algorithms such as EMMAX.However,binary traits obey binomial distribution and the scale of normal distribution required by LMM is different,solution based on the LMM method is not convincing and has fuzzy biological significance.Given various phenomena in binary trait analysis,this study uses the specialty that binomial distribution can be transformed into standard normal distribution under certain conditions,and introduce the correlation analysis method of scale transformation for mixed model(the following refers to the method of scale transformation).The method of scale transformation method first adopts the idea of EMMAX to perform an association test based on LMM by considering the binary trait as a continuous trait,screening and testing the significant genetic markers,and then bringing the genotype indicator variables of the significant genetic markers in LMM into the constructed GLMM to calculate its effect value again,after that the QTN effect under LMM scale was transformed to interpretable GLMM scale.Using the advantages of high statistical efficiency and strong ability to control false positives of LMM,the filtering for invalid SNP loci is realized,which saves the time for scanning a large number of invalid markers in GLMM.According to the above reason,the accuracy under GLMM is obtained based on the test efficiency of LMM,which greatly elevates the speed of binary trait association analysis.We used six genomic datasets including human,maize,mouse,catfish,tilapia,and rainbow trout,which were genetically different in complexity,so as to simulate the binary trait of different QTN numbers and incidence rate(case ratio).The performance of the scale transformation method is evaluated from three aspects: the detection effectiveness of QTN,the false positive control of results,and the running time.The summary of the results of the simulation experiments shows as follows:(1)In terms of efficiency for QTN detection: the performance about the QTN detection efficiency of the scale transformation method is similar to methods of GMMAT and SAIGE when tested populations with low genetic complexity.In the population with the high complexity of genetic relationships,the detection efficiency of QTN by scale transformation method is significantly higher than that of GMMAT and SAIGE methods.(2)In terms of false-positive control of results: the method of scale transformation maintains a high false-positive control ability during the six animals with different complexity of kinship,that is,the fitting curve obtained from the scale transformation method is more closely fitted with the theoretical line in the Q-Q diagram,and the GC value calculated by the method is stable around 1.00.In addition,the accuracy of the QTN effect estimated by the scale transformation method is comparable to the method of SAIGE when the tested population with low genetic complexity but higher than those methods of GMMAT and SAIGE when the tested population perform high genetic complexity.(3)In terms of running time: the efficiency of correlation analysis by scale transformation method can be comparable with the method of GMMAT and much higher than the method of SAIGE.In the correlation analysis for resistance to Rickettsia in rainbow trout,two QTN loci were detected by those methods of scale transformation and SAIGE,but only one QTN locus was detected from the method of GMMAT.At the same time,the running time of the scale transformation method was similar to the method of GMMAT but much lower than the SAIGE method;During the association analysis for sex traits in Macrobrachium nipponense,the results show that 16 QTNs were detected by the scale conversion method,12 QTNs were obtained from the SAIGE method and the method of GMMAT only discover 9 QTNs.It confirms that the scale transformation method can improve the detection efficiency of QTN and promote the efficiency of the correlation test.