costing {sambia}

Predicting outcomes using Costing.

Description

This method trains classifiers by correcting them for sample selection bias via Costing, a method proposed in Zadrozny et al. (2003) . This method is similar to sambia's IP bagging function in terms of resampling from the learning data and aggregation of the learned algorithms. It differs in the implementation of resampling. Observations from the original data enters a resampled data set only once at most.

Usage

costing(..., learner, list.train.learner, list.predict.learner, n.bs,
  mod = FALSE)

Arguments

...

see the parameter rejSamp() 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 rejSamp().

list.predict.learner

a list of parameters specifiying how to predict new data given the trained model. (This trained model is uniquely determined by parameters 'learner' and 'list.train.learner'

n.bs

number of bootstramp samples.

mod

If mod = TRUE: strategy for always having (at least) two outcome classes in subsets.

Author(s)

Norbert Krautenbacher, Kevin Strauss, Maximilian Mandl, Christiane Fuchs

References

Zadrozny, B., Langford, J., & Abe, N. (2003, November). Cost-sensitive learning by cost-proportionate example weighting. In Data Mining, 2003. ICDM 2003. Third IEEE International Conference on (pp. 435-442). IEEE.

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.

Examples

## 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 = 20
pred_nb <- sambia::costing(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, mod=TRUE)
roc(newdata$y, pred_nb, direction="<")