Some Issues On Interaction Analysis And Control Of Type Ⅰ Error

In the first two parts of chapter 1,we provided a broad review to the topic of interaction between the effects of exposures and then we focused on the details of additive interaction and multiplicative interaction,including study design,statistical models,analysis program,and presentation of statistical results.Relationship between additive interaction and multiplicative interaction,choice of measures of additive interaction,and choice of methods of calculating 95%confidence interval were also discussed.Then an example was followed to show the process of analysis and exhibition of results.This paper aimed to strengthen us the understanding of interaction in medical research and provide some recommendations for choosing proper model and method of interaction analysis.In the third part of chapter 1,we provided a broad review to the topic of issues and techniques related to interaction analysis.Techniques included data transformation and common methods of exhibiting interaction.Whereas issues during interaction analysis involved multiplicity,proper calculation of standardized regression coefficient,distinction between interaction and non-linear effect,and imputation for missing data.In the last part of chapterl,we discussed the topic on methods for interaction selection.Additionally,formulas for sample size calculation in generalized linear models with interaction effect based on Wald test were derived in the appendixIn the first part of chapter 2,we gave definitions of basic indices for error control in one hypotheses testing and discuss their relationships in view of diagnostic test.Then we generalized these indices for error control to multiple hypotheses testings,then reviewed the history of conception development of family-wise error rate and false discovery rate,and their connections and distinctions.Furthermore,we comprehensively reviewed common formulas,common indices and common soft-wares and their realization in type I error control.In the second part of chapter 2,we introduced one special type of method for type I error control,including closed testing procedures and hierarchical testing procedures,and illustrated common family-wise error control methods combined with closed testing.In the last part of chapter 2,we reviewed the papers on control of the false discovery rate in multiple testing under dependency,and these involved methods were classified into three categories.The methods in the first category were conservative to dependency,the second categorical approaches built models to approximate the dependency structure,and the last kind of methods create some dummy variables.One of the most famous and ingenious methods was model-X knockoffs framework for false discovery rate control in general high dimensional regression based on Lasso penalty introduced by Candes et al.(2018)In the chapter 3,we combined the model-X knockoffs framework with SCAD penalty,MCP penalty and SIS,and compared them to model-X knockoffs based on Lasso,corresponding penalty.Simulation results showed that combination of model-X knockoffs framework with Lasso,SCAD,MCP and SIS could control FDP near the prespecified level,lower the number of selected variables,and they also lowered the power,compared with corresponding penalty method used only.Four methods had similar number of selected variables,FNR,FPR,and power except for special cases where Lasso combined with knockoffs got slightly higher power.Model-X knockoffs framework with Lasso further was applied in the two-stage interaction selection to control the FDR of main effect variables.Simulation results showed that number of selected main effect variables and interaction decreased together keeping high power and high probability of selecting correct interactionIn a summary,we concluded the main results in the former two chapters,and discussed the issues during the simulation.Further more,we discussed the possible research directions.