Imputation in MICE using Random Forest

Description

Multivariate Imputation by Chained Equations (MICE) is commonly used to impute missing values in analysis datasets using full conditional specifications. However, it requires that the predictor models are specified correctly, including interactions and nonlinearities. Random Forest is a regression and classification method which can accommodate interactions and non-linearities without requiring a particular statistical model to be specified.

The mice package provides the mice.impute.rf function for imputation using Random Forest, as of version 2.20. The CALIBERrfimpute package provides different, independently developed imputation functions using Random Forest in MICE.

This package contains reports of two simulation studies:

Simulation study is a comparison of Random Forest and parametric MICE in a linear regression example.

Vignette for survival analysis with interactions - large sample compares the Random Forest MICE algorithm for continuous variables (mice.impute.rfcont) with parametric MICE and the algorithm of Doove et al. in the mice package (mice.impute.cart and mice.impute.rf).

Vignette for survival analysis with interactions - small sample is a small sample example of the above, created during compilation of the package.

Details

Author(s)

Anoop Shah

Maintainer: anoop@doctors.org.uk

References

Shah AD, Bartlett JW, Carpenter J, Nicholas O, Hemingway H. Comparison of Random Forest and parametric imputation models for imputing missing data using MICE: a CALIBER study. American Journal of Epidemiology 2014; 179(6): 764–774. doi:10.1093/aje/kwt312 https://academic.oup.com/aje/article/179/6/764/107562

Doove LL, van Buuren S, Dusseldorp E. Recursive partitioning for missing data imputation in the presence of interaction effects. Computational Statistics and Data Analysis 2014; 72: 92–104. doi:10.1016/j.csda.2013.10.025 https://www.sciencedirect.com/science/article/abs/pii/S0167947313003939

See Also

mice, randomForest, mice.impute.rfcont, mice.impute.rfcat, mice.impute.rf

Creates artificial missing at random missingness

Description

Introduces missingness into x1 and x2 into a data.frame of the format produced by simdata, for use in the simulation study. The probability of missingness depends on the logistic of the fully observed variables y and x3; hence it is missing at random but not missing completely at random.

Usage

makemar(simdata, prop = 0.2)

Arguments

Details

This function is used for simulation and testing.

Value

A data.frame with columns:

See Also

simdata

Examples

set.seed(1)
mydata <- simdata(n=100)
mymardata <- makemar(mydata, prop=0.1)
# Count the number of missing values
sapply(mymardata, function(x){sum(is.na(x))})
# y x1 x2 x3 x4 
# 0 11 10  0  0 

Impute categorical variables using Random Forest within MICE

Description

This method can be used to impute logical or factor variables (binary or >2 levels) in MICE by specifying method = 'rfcat'. It was developed independently from the mice.impute.rf algorithm of Doove et al., and differs from it in some respects.

Usage

mice.impute.rfcat(y, ry, x, ntree_cat = NULL,
    nodesize_cat = NULL, maxnodes_cat = NULL, ntree = NULL, ...)

Arguments

Details

This Random Forest imputation algorithm has been developed as an alternative to logistic or polytomous regression, and can accommodate non-linear relations and interactions among the predictor variables without requiring them to be specified in the model. The algorithm takes a bootstrap sample of the data to simulate sampling variability, fits a set of classification trees, and chooses each imputed value as the prediction of a randomly chosen tree.

Value

A vector of imputed values of y.

Note

This algorithm has been tested on simulated data and in survival analysis of real data with artificially introduced missingness completely at random. There was slight bias in hazard ratios compared to polytomous regression, but coverage of confidence intervals was correct.

Author(s)

Anoop Shah

References

Shah AD, Bartlett JW, Carpenter J, Nicholas O, Hemingway H. Comparison of Random Forest and parametric imputation models for imputing missing data using MICE: a CALIBER study. American Journal of Epidemiology 2014; 179(6): 764–774. doi:10.1093/aje/kwt312 https://academic.oup.com/aje/article/179/6/764/107562

See Also

setRFoptions, mice.impute.rfcont, mice, mice.impute.rf, mice.impute.cart, randomForest

Examples

set.seed(1)

# A small sample dataset 
mydata <- data.frame(
    x1 = as.factor(c('this', 'this', NA, 'that', 'this')),
    x2 = 1:5,
    x3 = c(TRUE, FALSE, TRUE, NA, FALSE))
mice(mydata, method = c('logreg', 'norm', 'logreg'), m = 2, maxit = 2)
mice(mydata[, 1:2], method = c('rfcat', 'rfcont'), m = 2, maxit = 2)
mice(mydata, method = c('rfcat', 'rfcont', 'rfcat'), m = 2, maxit = 2)

# A larger simulated dataset
mydata <- simdata(100, x2binary = TRUE)
mymardata <- makemar(mydata)

cat('\nNumber of missing values:\n')
print(sapply(mymardata, function(x){sum(is.na(x))}))

# Test imputation of a single column in a two-column dataset
cat('\nTest imputation of a simple dataset')
print(mice(mymardata[, c('y', 'x2')], method = 'rfcat', m = 2, maxit = 2))

# Analyse data
cat('\nFull data analysis:\n')
print(summary(lm(y ~ x1 + x2 + x3, data = mydata)))

cat('\nMICE normal and logistic:\n')
print(summary(pool(with(mice(mymardata,
    method = c('', 'norm', 'logreg', '', ''), m = 2, maxit = 2),
    lm(y ~ x1 + x2 + x3)))))

# Set options for Random Forest
setRFoptions(ntree_cat = 10)

cat('\nMICE using Random Forest:\n')
print(summary(pool(with(mice(mymardata,
    method = c('', 'rfcont', 'rfcat', '', ''), m = 2, maxit = 2),
    lm(y ~ x1 + x2 + x3)))))

cat('\nDataset with unobserved levels of a factor\n')
data3 <- data.frame(x1 = 1:100, x2 = factor(c(rep('A', 25),
    rep('B', 25), rep('C', 25), rep('D', 25))))
data3$x2[data3$x2 == 'D'] <- NA
mice(data3, method = c('', 'rfcat'), m = 2, maxit = 2)

Impute continuous variables using Random Forest within MICE

Description

This method can be used to impute continuous variables in MICE by specifying method = 'rfcont'. It was developed independently from the mice.impute.rf algorithm of Doove et al., and differs from it in drawing imputed values from a normal distribution.

Usage

mice.impute.rfcont(y, ry, x, ntree_cont = NULL,
    nodesize_cont = NULL, maxnodes_cont = NULL, ntree = NULL, ...)

Arguments

Details

This Random Forest imputation algorithm has been developed as an alternative to normal-based linear regression, and can accommodate non-linear relations and interactions among the predictor variables without requiring them to be specified in the model. The algorithm takes a bootstrap sample of the data to simulate sampling variability, fits a regression forest trees and calculates the out-of-bag mean squared error. Each value is imputed as a random draw from a normal distribution with mean defined by the Random Forest prediction and variance equal to the out-of-bag mean squared error.

If only one tree is used (not recommended), a bootstrap sample is not taken in the first stage because the Random Forest algorithm performs an internal bootstrap sample before fitting the tree.

Value

A vector of imputed values of y.

Note

This algorithm has been tested on simulated data with linear regression, and in survival analysis of real data with artificially introduced missingness at random. On the simulated data there was slight bias if the distribution of missing values was very different from observed values, because imputed values were closer to the centre of the data than the missing values. However in the survival analysis the hazard ratios were unbiased and coverage of confidence intervals more conservative than normal-based MICE, but the mean length of confidence intervals was shorter with mice.impute.rfcont.

Author(s)

Anoop Shah

References

Shah AD, Bartlett JW, Carpenter J, Nicholas O, Hemingway H. Comparison of Random Forest and parametric imputation models for imputing missing data using MICE: a CALIBER study. American Journal of Epidemiology 2014; 179(6): 764–774. doi:10.1093/aje/kwt312 https://academic.oup.com/aje/article/179/6/764/107562

See Also

setRFoptions, mice.impute.rfcat, mice, mice.impute.rf, mice.impute.cart, randomForest

Examples

set.seed(1)

# A small dataset with a single row to be imputed
mydata <- data.frame(x1 = c(2, 3, NA, 4, 5, 1, 6, 8, 7, 9), x2 = 1:10,
    x3 = c(1, 3, NA, 4, 2, 8, 7, 9, 6, 5))
mice(mydata, method = c('norm', 'norm', 'norm'), m = 2, maxit = 2)
mice(mydata[, 1:2], method = c('rfcont', 'rfcont'), m = 2, maxit = 2)
mice(mydata, method = c('rfcont', 'rfcont', 'rfcont'), m = 2, maxit = 2)

# A larger simulated dataset
mydata <- simdata(100)
cat('\nSimulated multivariate normal data:\n')
print(data.frame(mean = colMeans(mydata), sd = sapply(mydata, sd)))

# Apply missingness pattern
mymardata <- makemar(mydata)
cat('\nNumber of missing values:\n')
print(sapply(mymardata, function(x){sum(is.na(x))}))

# Test imputation of a single column in a two-column dataset
cat('\nTest imputation of a simple dataset')
print(mice(mymardata[, c('y', 'x1')], method = 'rfcont'))

# Analyse data
cat('\nFull data analysis:\n')
print(summary(lm(y ~ x1 + x2 + x3, data=mydata)))

cat('\nMICE using normal-based linear regression:\n')
print(summary(pool(with(mice(mymardata,
    method = 'norm'), lm(y ~ x1 + x2 + x3)))))

# Set options for Random Forest
setRFoptions(ntree_cont = 10)

cat('\nMICE using Random Forest:\n')
print(summary(pool(with(mice(mymardata,
    method = 'rfcont'), lm(y ~ x1 + x2 + x3)))))

Set Random Forest options for imputation using MICE

Description

A convenience function to set global options for number of trees or number of nodes.

Usage

setRFoptions(ntree_cat = NULL, ntree_cont = NULL,
    nodesize_cat = NULL, nodesize_cont = NULL,
    maxnodes_cat = NULL, maxnodes_cont = NULL)

Arguments

Details

This function sets the global options which have the prefix 'CALIBERrfimpute_'.

Value

No return value. The function prints a message stating the new option setting.

See Also

mice.impute.rfcat, mice.impute.rfcont

Examples

# Set option using setRFoptions
setRFoptions(ntree_cat=15)
options()$CALIBERrfimpute_ntree_cat

# Set option directly
options(CALIBERrfimpute_ntree_cat=20)
options()$CALIBERrfimpute_ntree_cat

Simulate multivariate data for testing

Description

Creates multivariate normal or normal and binary data, as used in the simulation study.

Usage

simdata(n = 2000, mymean = rep(0, 4), mysigma = matrix(
	c( 1,   0.2, 0.1, -0.7,
	   0.2, 1,   0.3,  0.1,
	   0.1, 0.3, 1,    0.2,
	  -0.7, 0.1, 0.2,  1), byrow = TRUE, nrow = 4, ncol = 4),
	residsd = 1, x2binary = FALSE)

Arguments

Value

Data frame with 5 columns:

See Also

makemar

Examples

set.seed(1)
simdata(n=4, x2binary=TRUE)
#             y          x1 x2         x3        x4
# 1 -0.06399616 -1.23307320  2 -0.6521442 1.6141842
# 2  1.00822173 -0.05167026  1  0.4659907 0.5421826
# 3  2.87886825  0.43816687  1  1.5217240 0.2808691
# 4  0.79129101 -0.72510640  1  0.7342611 0.1820001