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Background: There is growing concern of health effects of exposure to pollutant mixtures. We initially proposed an Environmental Risk Score (ERS) as a summary measure to examine the risk of exposure to multi-pollutants in epidemiologic research considering only pollutant main effects. We expand the ERS by consideration of pollutantpollutant interactions using modern machine learning methods. We illustrate the multi-pollutant approaches to predicting a marker of oxidative stress (gamma-glutamyl transferase (GGT)), a common disease pathway linking environmental exposure and numerous health endpoints. Methods: We examined 20 metal biomarkers measured in urine or whole blood from 6 cycles of the National Health and Nutrition Examination Survey (NHANES 2003(NHANES -2004(NHANES to 2013(NHANES -2014. We randomly split the data evenly into training and testing sets and constructed ERS's of metal mixtures for GGT using adaptive elastic-net with main effects and pairwise interactions (AENET-I), Bayesian additive regression tree (BART), Bayesian kernel machine regression (BKMR), and Super Learner in the training set and evaluated their performances in the testing set. We also evaluated the associations between GGT-ERS and cardiovascular endpoints. Results: ERS based on AENET-I performed better than other approaches in terms of prediction errors in the testing set. Important metals identified in relation to GGT include cadmium (urine), dimethylarsonic acid, monomethylarsonic acid, cobalt, and barium. All ERS's showed significant associations with systolic and diastolic blood pressure and hypertension. For hypertension, one SD increase in each ERS from AENET-I, BART and SuperLearner were associated with odds ratios of 1.26 (95% CI, 1.15, 1.38), 1.17 (1.09, 1.25), and 1.30 (1.20, 1.40), respectively. ERS's showed non-significant positive associations with mortality outcomes. Conclusions: ERS is a useful tool for characterizing cumulative risk from pollutant mixtures, with accounting for statistical challenges such as high degrees of correlations and pollutant-pollutant interactions. ERS constructed for an intermediate marker like GGT is predictive of related disease endpoints.

In wheat breeding, improved quality traits, including grain quality and dough rheological properties, have long been a critical goal. To understand the genetic basis of key quality traits of wheat, two single-locus and five multi-locus GWAS models were performed for six grain quality traits and three dough rheological properties based on 19, 254 SNPs in 267 bread wheat accessions. As a result, 299 quantitative trait nucleotides (QTNs) within 105 regions were identified to be associated with these quality traits in four environments. Of which, 40 core QTN regions were stably detected in at least three environments, 19 of which were novel. Compared with the previous studies, these novel QTN regions explained smaller phenotypic variation, which verified the advantages of the multi-locus GWAS models in detecting important small effect QTNs associated with complex traits. After characterization of the function and expression in-depth, 67 core candidate genes involved in protein/sugar synthesis, histone modification and the regulation of transcription factor were observed to be associated with the formation of grain quality, which showed that multi-level regulations influenced wheat grain quality. Finally, a preliminary network of gene regulation that may affect wheat quality formation was inferred. This study verified the power and reliability of multi-locus GWAS methods in wheat quality trait research, and increased the understanding of wheat quality formation mechanisms. The detected QTN regions and candidate genes in this study could be further used for gene cloning and marker-assisted selection in highquality breeding of bread wheat.

In biobank data analysis, most binary phenotypes have unbalanced case-control ratios, and this can cause inflation of type I error rates. Recently, a saddle point approximation (SPA) based single-variant test has been developed to provide an accurate and scalable method to test for associations of such phenotypes. For gene-or region-based multiple-variant tests, a few methods exist that can adjust for unbalanced case-control ratios; however, these methods are either less accurate when case-control ratios are extremely unbalanced or not scalable for large data analyses. To address these problems, we propose SKAT-and SKAT-O-type region-based tests; in these tests, the singlevariant score statistic is calibrated based on SPA and efficient resampling (ER). Through simulation studies, we show that the proposed method provides well-calibrated p values. In contrast, when the case-control ratio is 1:99, the unadjusted approach has greatly inflated type I error rates (90 times that of exome-wide sequencing a ¼ 2.5 3 10 À6 ). Additionally, the proposed method has similar computation time to the unadjusted approaches and is scalable for large sample data. In our application, the UK Biobank whole-exome sequence data analysis of 45,596 unrelated European samples and 791 PheCode phenotypes identified 10 rare-variant associations with p value < 10 À7 , including the associations between JAK2 and myeloproliferative disease, HOXB13 and cancer of prostate, and F11 and congenital coagulation defects. All analysis summary results are publicly available through a web-based visual server, and this availability can help facilitate the identification of the genetic basis of complex diseases.

Several biobanks, including UK Biobank (UKBB), are generating large-scale sequencing data. An existing method, SAIGE-GENE, performs well when testing variants with minor allele frequency (MAF) ≤ 1%, but inflation is observed in variance component set-based tests when restricting to variants with MAF ≤ 0.1% or 0.01%. Here, we propose SAIGE-GENE+ with greatly improved type I error control and computational efficiency to facilitate rare variant tests in large-scale data. We further show that incorporating multiple MAF cutoffs and functional annotations can improve power and thus uncover new gene–phenotype associations. In the analysis of UKBB whole exome sequencing data for 30 quantitative and 141 binary traits, SAIGE-GENE+ identified 551 gene–phenotype associations.

In biobank data analysis, most binary phenotypes have unbalanced case-control ratios, which can cause inflation of type I error rates. Recently, a saddlepoint approximation (SPA) based single variant test has been developed to provide an accurate and scalable method to test for associations of such phenotypes. For gene-or region-based multiple variant tests, a few methods exist which adjust for unbalanced case-control ratios; however, these methods are either less accurate when case-control ratios are extremely unbalanced or not scalable for large data analyses. To address these problems, we propose SKAT/SKAT-O type region-based tests, where the single-variant score statistic is calibrated based on SPA and Efficient Resampling (ER).Through simulation studies, we show that the proposed method provides well-calibrated pvalues. In contrast, the unadjusted approach has greatly inflated type I error rates (90 times of exome-wide =2.5×10 -6 ) when the case-control ratio is 1:99. Additionally, the proposed method has similar computation time as the unadjusted approaches and is scalable for large sample data.Our UK Biobank whole exome sequence data analysis of 45,596 unrelated European samples and 791 PheCode phenotypes identified 10 rare variant associations with p-value < 10 -7 , including the associations between JAK2 and myeloproliferative disease, TNC and large cell lymphoma and F11 and congenital coagulation defects. All analysis summary results are publicly available through a web-based visual server.

Latent class models have become a popular means of summarizing survey questionnaires and other large sets of categorical variables. Often these classes are of primary interest to better understand complex patterns in data. Increasingly, these latent classes are reified into predictors of other outcomes of interests, treating the most likely class as the true class to which an individual belongs even though there is uncertainty in class membership. This uncertainty can be viewed as a form of measurement error in predictors, leading to bias in the estimates of the regression parameters associated with the latent classes. Despite this fact, there is very limited literature treating latent class predictors as measurement error models. Most applications ignore this issue and fit a two-stage model that treats the modal class prediction as truth. Here, we develop two approaches—one likelihood-based, the other Bayesian—to implement a joint model for latent class analysis and outcome prediction. We apply these methods to an analysis of how acculturation behaviors predict depression in South Asian immigrants to the United States. A simulation study gives guidance for when a two-stage model can be safely implemented and when the joint model may be required.

The etiology of most complex diseases involves genetic variants, environmental factors, and gene-environment interaction (G 3 E) effects. Compared with marginal genetic association studies, G 3 E analysis requires more samples and detailed measure of environmental exposures, and this limits the possible discoveries. Large-scale population-based biobanks with detailed phenotypic and environmental information, such as UK-Biobank, can be ideal resources for identifying G 3 E effects. However, due to the large computation cost and the presence of case-control imbalance, existing methods often fail. Here we propose a scalable and accurate method, SPAGE (Sad-dlePoint Approximation implementation of G 3 E analysis), that is applicable for genome-wide scale phenome-wide G 3 E studies. SPAGE fits a genotype-independent logistic model only once across the genome-wide analysis in order to reduce computation cost, and SPAGE uses a saddlepoint approximation (SPA) to calibrate the test statistics for analysis of phenotypes with unbalanced case-control ratios. Simulation studies show that SPAGE is 33-79 times faster than the Wald test and 72-439 times faster than the Firth's test, and SPAGE can control type I error rates at the genome-wide significance level even when case-control ratios are extremely unbalanced. Through the analysis of UK-Biobank data of 344,341 white British European-ancestry samples, we show that SPAGE can efficiently analyze large samples while controlling for unbalanced case-control ratios.