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1.  Modeling relationships between calving traits: a comparison between standard and recursive mixed models 
Background
The use of structural equation models for the analysis of recursive and simultaneous relationships between phenotypes has become more popular recently. The aim of this paper is to illustrate how these models can be applied in animal breeding to achieve parameterizations of different levels of complexity and, more specifically, to model phenotypic recursion between three calving traits: gestation length (GL), calving difficulty (CD) and stillbirth (SB). All recursive models considered here postulate heterogeneous recursive relationships between GL and liabilities to CD and SB, and between liability to CD and liability to SB, depending on categories of GL phenotype.
Methods
Four models were compared in terms of goodness of fit and predictive ability: 1) standard mixed model (SMM), a model with unstructured (co)variance matrices; 2) recursive mixed model 1 (RMM1), assuming that residual correlations are due to the recursive relationships between phenotypes; 3) RMM2, assuming that correlations between residuals and contemporary groups are due to recursive relationships between phenotypes; and 4) RMM3, postulating that the correlations between genetic effects, contemporary groups and residuals are due to recursive relationships between phenotypes.
Results
For all the RMM considered, the estimates of the structural coefficients were similar. Results revealed a nonlinear relationship between GL and the liabilities both to CD and to SB, and a linear relationship between the liabilities to CD and SB.
Differences in terms of goodness of fit and predictive ability of the models considered were negligible, suggesting that RMM3 is plausible.
Conclusions
The applications examined in this study suggest the plausibility of a nonlinear recursive effect from GL onto CD and SB. Also, the fact that the most restrictive model RMM3, which assumes that the only cause of correlation is phenotypic recursion, performs as well as the others indicates that the phenotypic recursion may be an important cause of the observed patterns of genetic and environmental correlations.
doi:10.1186/1297-9686-42-1
PMCID: PMC2830933  PMID: 20100345
2.  Detecting single-nucleotide polymorphism by single-nucleotide polymorphism interactions in rheumatoid arthritis using a two-step approach with machine learning and a Bayesian threshold least absolute shrinkage and selection operator (LASSO) model 
BMC Proceedings  2009;3(Suppl 7):S63.
The objective of this study was to detect interactions between relevant single-nucleotide polymorphisms (SNPs) associated with rheumatoid arthritis (RA). Data from Problem 1 of the Genetic Analysis Workshop 16 were used. These data consisted of 868 cases and 1,194 controls genotyped with the 500 k Illumina chip. First, machine learning methods were applied for preselecting SNPs. One hundred SNPs outside the HLA region and 1,500 SNPs in the HLA region were preselected using information-gain theory. The software weka was used to reduce colinearity and redundancy in the HLA region, resulting in a subset of 6 SNPs out of 1,500. In a second step, a parametric approach to account for interactions between SNPs in the HLA region, as well as HLA-nonHLA interactions was conducted using a Bayesian threshold least absolute shrinkage and selection operator (LASSO) model incorporating 2,560 covariates. This approach detected some main and interaction effects for SNPs in genes that have previously been associated with RA (e.g., rs2395175, rs660895, rs10484560, and rs2476601). Further, some other SNPs detected in this study may be considered in candidate gene studies.
PMCID: PMC2795964  PMID: 20018057
3.  Application of Multi-SNP Approaches Bayesian LASSO and AUC-RF to Detect Main Effects of Inflammatory-Gene Variants Associated with Bladder Cancer Risk 
PLoS ONE  2013;8(12):e83745.
The relationship between inflammation and cancer is well established in several tumor types, including bladder cancer. We performed an association study between 886 inflammatory-gene variants and bladder cancer risk in 1,047 cases and 988 controls from the Spanish Bladder Cancer (SBC)/EPICURO Study. A preliminary exploration with the widely used univariate logistic regression approach did not identify any significant SNP after correcting for multiple testing. We further applied two more comprehensive methods to capture the complexity of bladder cancer genetic susceptibility: Bayesian Threshold LASSO (BTL), a regularized regression method, and AUC-Random Forest, a machine-learning algorithm. Both approaches explore the joint effect of markers. BTL analysis identified a signature of 37 SNPs in 34 genes showing an association with bladder cancer. AUC-RF detected an optimal predictive subset of 56 SNPs. 13 SNPs were identified by both methods in the total population. Using resources from the Texas Bladder Cancer study we were able to replicate 30% of the SNPs assessed. The associations between inflammatory SNPs and bladder cancer were reexamined among non-smokers to eliminate the effect of tobacco, one of the strongest and most prevalent environmental risk factor for this tumor. A 9 SNP-signature was detected by BTL. Here we report, for the first time, a set of SNP in inflammatory genes jointly associated with bladder cancer risk. These results highlight the importance of the complex structure of genetic susceptibility associated with cancer risk.
doi:10.1371/journal.pone.0083745
PMCID: PMC3877090  PMID: 24391818

Results 1-3 (3)