varImpact - variable importance through causal inference

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Introduction

varImpact uses causal inference statistics to generate variable importance estimates for a given dataset and outcome. It answers the question: which of my Xs are most related to my Y? Each variable's influence on the outcome is estimated semiparametrically, without assuming a linear relationship or other functional form, and the covariate list is ranked by order of importance. This can be used for exploratory data analysis, for dimensionality reduction, for experimental design (e.g. to determine blocking and re-randomization), to reduce variance in an estimation procedure, etc. See Hubbard & van der Laan (2016) for more details.

Each covariate is analyzed using targeted minimum loss-based estimation (TMLE) as though it were a treatment, with all other variables serving as adjustment variables via SuperLearner. Then the statistical significance of the estimated treatment effect for each covariate determines the variable importance ranking. This formulation allows the asymptotics of TMLE to provide valid standard errors and p-values, unlike other variable importance algorithms.

The results provide raw p-values as well as p-values adjusted for false discovery rate using the Benjamini-Hochberg (1995) procedure. Adjustment variables are automatically clustered hierarchically using HOPACH (van der Laan & Pollard 2003) in order to reduce dimensionality. The package supports multi-core and multi-node parallelization, which are detected and used automatically when a parallel backend is registered. Missing values are automatically imputed using K-nearest neighbors and missingness indicator variables are incorporated into the analysis.

varImpact is under active development so please submit any bug reports or feature requests to the issue queue, or email Alan & Chris directly.

Installation

Install varImpact from Github

# Install devtools if necessary:
if (!require("devtools")) install.packages("devtools")
devtools::install_github("ck37/varImpact")

Examples

####################################
# Create test dataset.
set.seed(1)
N <- 200
num_normal <- 7
X <- as.data.frame(matrix(rnorm(N * num_normal), N, num_normal))
Y <- rbinom(N, 1, plogis(.2*X[, 1] + .1*X[, 2] - .2*X[, 3] + .1*X[, 3]*X[, 4] - .2*abs(X[, 4])))
# Add some missing data to X so we can test imputation.
for (i in 1:10) X[sample(nrow(X), 1), sample(ncol(X), 1)] <- NA

####################################
# Basic example
vim <- varImpact(Y = Y, data = X)
vim
vim$results_all
exportLatex(vim)

# Impute by median rather than knn.
vim <- varImpact(Y = Y, data = X, impute = "median")

# Customize Q and g libraries for TMLE estimation.
Q_lib <- c("SL.gam","SL.glmnet", "SL.stepAIC", "SL.randomForest", "SL.rpartPrune", "SL.bayesglm")
g_lib <- c("SL.stepAIC", "SL.glmnet")
vim <- varImpact(Y = Y, data = X, Q.library = Q_lib, g.library = g_lib)

####################################
# doMC parallel (multicore) example.
library(doMC)
registerDoMC()
vim <- varImpact(Y = Y, data = X)

####################################
# doSNOW parallel example.
library(doSNOW)
library(RhpcBLASctl)
# Detect the number of physical cores on this computer using RhpcBLASctl.
cluster <- makeCluster(get_num_cores())
registerDoSNOW(cluster)
vim <- varImpact(Y = Y, data = X)
stopCluster(cluster)

####################################
# mlbench BreastCancer example.
data(BreastCancer, package="mlbench")
data <- BreastCancer

# Create a numeric outcome variable.
data$Y <- as.numeric(data$Class == "malignant")

# Use multicore parallelization to speed up processing.
doMC::registerDoMC()
vim <- varImpact(Y = data$Y, data = subset(data, select=-c(Y, Class, Id)))

Authors

Alan E. Hubbard and Chris J. Kennedy, University of California, Berkeley

References

Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the royal statistical society. Series B (Methodological), 289-300.

Gruber, S., & van der Laan, M. J. (2012). tmle: An R Package for Targeted Maximum Likelihood Estimation. Journal of Statistical Software, 51(i13).

Hubbard, A., Munoz, I. D., Decker, A., Holcomb, J. B., Schreiber, M. A., Bulger, E. M., ... & Rahbar, M. H. (2013). Time-Dependent Prediction and Evaluation of Variable Importance Using SuperLearning in High Dimensional Clinical Data. The journal of trauma and acute care surgery, 75(1 0 1), S53.

Hubbard, A. E., & van der Laan, M. J. (2016). Mining with inference: data-adaptive target parameters (pp. 439-452). In P. Bühlmann et al. (Ed.), Handbook of Big Data. CRC Press, Taylor & Francis Group, LLC: Boca Raton, FL.

van der Laan, M. J. (2006). Statistical inference for variable importance. The International Journal of Biostatistics, 2(1).

van der Laan, M. J., & Pollard, K. S. (2003). A new algorithm for hybrid hierarchical clustering with visualization and the bootstrap. Journal of Statistical Planning and Inference, 117(2), 275-303.

van der Laan, M. J., Polley, E. C., & Hubbard, A. E. (2007). Super learner. Statistical applications in genetics and molecular biology, 6(1).

van der Laan, M. J., & Rose, S. (2011). Targeted learning: causal inference for observational and experimental data. Springer Science & Business Media.