Penalized Logistic Regression And Multifactor Dimensionality Reduction For Detecting Interactions

Objective: We propose using a variant of logistic regression (LR) with L2-regularization to fit high-order interaction models that the standard logistic regression can't do this. We compare the Penalized logistic regression with Multifactor dimensionality reduction that is a popular technique for detecting and characterizing gene–gene/gene–environment interactions and illustrate the advantages and defects of their own. Then it provided some references for the study of interactions in the complicated biomedical research.Methods: Introduce the basic principles and the analysis step for identify interactions of MDR. Introduce the basic principles of the Penalized logistic regression model. We discussed theoretic and did simulation study for the simple size and the ability to identify the low-order or high-order interactions. The procedures of penalized logistic regression were accomplished in R software. In the paper we put forward a proposal for the applications and the advantages or the flaws of PLR and MDR in the clinic study.Result: The simulation and clinic study indicates that different adjustment parameterλhave significant effects on the result of simulation. If the adjustment parameterλ, which make the score of the cost-complexity statistic C minimum, then, the deviance is minimum, the simulation results more close to the true values, the coefficients are more steady, and the model is the best model. Comparing with the LR, the deviance is smaller and the coefficients are more steady using PLR to estimate. Especially, when the sample size is small(less than 3 hundreds), PLR is better. The simulation study of the ability to identify interactions indicates that when charactering low-order interactions, PLR does better than MDR. When identifying high-order interactions PLR and MDR both do well. Even if when we added noise to the data the ability to identify interactions of the two methods do well either. MDR is sensitive to high-order interactions, it is able to identify all kinds of interactions, but PLR is more fit for synergistic interactions. Conclusions: Comparing with other methods, PLR and MDR do well in identifying high-order interactions. In this paper by simulation study and a real data example we draw some conclusions that when the simple size is small, using LR the results isn't so steady, when the simple size is less than 3 hundred, PLR do much better than LR. Charactering low-order interactions MDR do not so good, PLR is more fit for synergistic interactions. When there are other nature of interactions, we propose using general relative risk models and combining with other methods.