synthIPbag {sambia}

Train a classifier via synthetic observations using inverse-probability weights

Description

This method trains classifiers by correcting them for sample selection bias via stochastic inverse-probability oversampling or parametric inverse-probability bagging (Krautenbacher et al 2017). Classifiers are trained from differently resampled data whose observations are weighted by inverse-probability weights per stratum to correct for the bias in the original sample. The so attained ensemble of predictors is aggregated by averaging.

Usage

synthIPbag(..., learner, list.train.learner, list.predict.learner, n.bs)

Arguments

...

see the parameter genSample() 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 trained model.

n.bs

number of bootstramp samples. This trained model is uniquely determined by parameters 'learner' and 'list.train.learner'.

Author(s)

Norbert Krautenbacher, Kevin Strauss, Maximilian Mandl, Christiane Fuchs

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.

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 = 10
## glm
pred_glm <- sambia::synthIPbag(data = data, weights = w, type='parIP',
                              strata.variables = c('y', 'xs'), learner='glm', 
                              list.train.learner = list(formula=formula(y~.),family="binomial"),
                              list.predict.learner = list(newdata=newdata, type="response"),
                              n.bs = n.bs)
roc(newdata$y, pred_glm, direction = "<")

## random forest
pred_rf <- sambia::synthIPbag(data = data, weights = w, type='parIP',
                             strata.variables = c('y','xs'), learner='rangerTree', 
                             list.train.learner = list(formula=formula(as.factor(y)~.)),
                             list.predict.learner = list(data=newdata),
                             n.bs = n.bs)
roc(newdata$y, pred_rf, direction = "<")