# Predicting outcomes using non-parametric Inverse-Probability bagging This method trains classifiers by correcting them for sample selection bias via non-parametric inverse-probability bagging. This method fits classifiers from different resampled data whose observations are increased per stratum to correct for the bias in the original sample. The so attained ensemble of predictors is aggregated by averaging. ```r IPbag(..., learner, list.train.learner, list.predict.learner, n.bs) ``` ## Arguments - `...`: see the parameter ipOversampling() of package sambia. - `learner`: a character indicating which classifier is used to train. Note: set learner='rangerTree' if random forest should be applied as in Krautenbacher et al. (2017), i.e. the correction step is incorporated in the inherent random forest resampling procedure. - `list.train.learner`: a list of parameters specific to the classifier that will be trained. Note that the parameter 'data' need not to be provided in this list since the training data which the model will learn on is already attained by new sampled data produced by the method genSample(). - `list.predict.learner`: a list of parameters specifiying how to predict new data given the learned model. (This learned model is uniquely determined by parameters 'learner' and 'list.train.learner'). - `n.bs`: number of bootstramp samples. ## Examples ```r ## simulate data for a population require(pROC) set.seed(1342334) N = 100000 x1 <- rnorm(N, mean=0, sd=1) x2 <- rt(N, df=25) x3 <- x1 + rnorm(N, mean=0, sd=.6) x4 <- x2 + rnorm(N, mean=0, sd=1.3) x5 <- rbinom(N, 1, prob=.6) x6 <- rnorm(N, 0, sd = 1) # noise not known as variable x7 <- x1*x5 # interaction x <- cbind(x1, x2, x3, x4, x5, x6, x7) ## stratum variable (covariate) xs <- c(rep(1,0.1*N), rep(0,(1-0.1)*N)) ## effects beta <- c(-1, 0.2, 0.4, 0.4, 0.5, 0.5, 0.6) beta0 <- -2 ## generate binary outcome linpred.slopes <- log(0.5)*xs + c(x %*% beta) eta <- beta0 + linpred.slopes p <- 1/(1+exp(-eta)) # this is the probability P(Y=1|X), we want the binary outcome however: y<-rbinom(n=N, size=1, prob=p) # population <- data.frame(y,xs,x) #### draw "given" data set for training sel.prob <- rep(1,N) sel.prob[population$xs == 1] <- 9 sel.prob[population$y == 1] <- 8 sel.prob[population$y == 1 & population$xs == 1] <- 150 ind <- sample(1:N, 200, prob = sel.prob) data = population[ind, ] ## calculate weights from original numbers for xs and y w.matrix <- table(population$y, population$xs)/table(data$y, data$xs) w <- rep(NA, nrow(data)) w[data$y==0 & data$xs ==0] <- w.matrix[1,1] w[data$y==1 & data$xs ==0] <- w.matrix[2,1] w[data$y==0 & data$xs ==1] <- w.matrix[1,2] w[data$y==1 & data$xs ==1] <- w.matrix[2,2] ### draw a test data set newdata = population[sample(1:N, size=200 ), ] n.bs = 5 pred_nb <- sambia::IPbag(data = data, weights = w, learner='naiveBayes', list.train.learner = list(formula=formula(y~.)), list.predict.learner = list(newdata=newdata, type="raw"), n.bs = n.bs) roc(newdata$y, pred_nb, direction="<") ``` ## References Krautenbacher, N., Theis, F. J., & Fuchs, C. (2017). Correcting Classifiers for Sample Selection Bias in Two-Phase Case-Control Studies. Computational and mathematical methods in medicine, 2017. ## Author(s) Norbert Krautenbacher, Kevin Strauss, Maximilian Mandl, Christiane Fuchs

IPbag function