Estimation and Testing for the Effect of a Genetic Pathway on a Disease Outcome Using Logistic Kernel Machine Regression Via Logistic Mixed Models
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Summary of Literature14: Estimation and testing for the effect of a genetic pathway on a disease outcome using logistic kernel machine regression via logistic mixed modelsAs technology advanced for the last decade, there is a growing interest in biological pathways which explores the genes within a pathway and their interactions. However, due to the complexity, it is not easy to model the pathway. Previously, linear model was an approach to model pathway but with limitations. This paper has proposed a nonparametric approach to model the pathway which is kernel machine regression model, specifically, logistic kernel machine regression model for binary outcome. By using this model, this paper has tested prostate cancer to study how a genetic pathway is related to the prostate cancer risk while controlling for the covariates. As it is logistic kernel machine regression, the outcome is binary which resembles the prostate cancer state. Also, this paper has utilized simulation study for parameter estimation and score test for the pathway effect. For parameter estimation, the authors have taken the logistic mixed model formulation. For the mixed model, the Gaussian kernel scale parameter is defined as 5 and using the independent uniform defined as (-0.5, 0.5). The result of mixed model shows that the model has small bias even when the sample size is small. When sample size increases, even though there is still bias, but it is getting smaller. For the score test for the pathway effect, nonlinear and linear functions are both considered. When it is nonlinear, the size is very close to nominal which representing a higher power than Goeman. When it is linear, the model also works well for moderate size which also represents a high power. For modeling pathway data, the nonparametric approach proposed by this paper has few strengths over linear models. First, it is able to handle more complicated data and capture the relationship between genes, which is not addressed in linear models. Also, it can detect the interactions within genes which is not feasible in linear models. Comparing to nonparametric pathway-based regression model proposed by Wei and Li, and Bayesian belief network approach proposed by Michalowski et al, the model proposed in this study also has some strengths. As this model is based on penalized likelihood, parameter estimation and inference can be conducted systematically within likelihood framework, therefore, it is not difficult to estimate and quantify the pathway effect. Also, it proposes a formal statistical test for the significance of pathway effect.