Machine learning-based summary of association with multivariate outcomes
Authors: David Benkeser and Ivana Malenica
This package provides a method for summarizing the strength of association between a set of variables and a multivariate outcome. In particular, cross-validation is combined with stacked regression (aka super learning) to estimate the convex combination of a multivariate outcome that maximizes cross-validated R-squared of a super learner-based prediction. The method is particularly well suited for situations with high-dimensional covariates and/or complex relationships between covariates and outcomes.
You can install a stable release of cvma from GitHub via
devtools with:
devtools::install_github("benkeser/cvma")In the future, the package will be available from CRAN via
install.packages("cvma")If you encounter any bugs or have any specific feature requests, please file an issue.
This minimal example shows how to use cvma with very simple, simulated data set. For more examples and detailed explanations, we refer the user to the vignette. To start with, we use the nonparametric R^2 to evaluate the strength of association between a set of variables and a multivariate outcome:
suppressMessages(library(cvma))
set.seed(1234)
#Simulate data:
X <- data.frame(x1=runif(n=100,0,5), x2=runif(n=100,0,5))
Y1 <- rnorm(100, X$x1 + X$x2, 1)
Y2 <- rnorm(100, X$x1 + X$x2, 3)
Y <- data.frame(Y1 = Y1, Y2 = Y2)
#cvma with nonparametric R^2:
fit <- cvma(Y = Y, X = X, V = 10,
learners = c("SL.glm","SL.mean"))
fit
#> cv_measure ci_low ci_high p_value
#> 1 0.7648338 0.6616586 0.8365464 3.120828e-15The following example evaluates the strength of association using AUC:
#Simulate data:
X <- data.frame(x1=runif(n=100,0,5), x2=runif(n=100,0,5))
Y1 <- rbinom(100, 1, plogis(-2 + 0.1*X$x1 + 0.2*X$x2))
Y2 <- rbinom(100, 1, plogis(-2 + 0.1*X$x1))
Y <- data.frame(Y1 = Y1, Y2 = Y2)
#cvma with AUC:
fit <- cvma(Y = Y, X = X, V = 5,
learners = c("SL.glm","SL.mean"),
sl_control = list(ensemble_fn = "ensemble_linear",
optim_risk_fn = "optim_risk_sl_nloglik",
weight_fn = "weight_sl_convex",
cv_risk_fn = "cv_risk_sl_auc",
family = binomial(),
alpha = 0.05),
y_weight_control = list(ensemble_fn = "ensemble_linear",
weight_fn = "weight_y_01",
optim_risk_fn = "optim_risk_y_auc",
cv_risk_fn = "cv_risk_y_auc",
alpha = 0.05))
fit
#> cv_measure ci_low ci_high p_value
#> 1 0.3379673 0.1823169 0.4936178 0.9793412The cross-validated performance of two fits can be compared using the compare_cvma function. This can be used to define a variable importance measure for a set of variables.
#Simulate data:
X <- data.frame(x1=runif(n=100,0,5), x2=runif(n=100,0,5))
Y1 <- rnorm(100, X$x1 + X$x2, 1)
Y2 <- rnorm(100, X$x1 + X$x2, 3)
Y <- data.frame(Y1 = Y1, Y2 = Y2)
# fit data with full X
fit1 <- cvma(Y = Y, X = X, V = 10,
learners = c("SL.glm","SL.mean"))
# fit data with only x1
fit2 <- cvma(Y = Y, X = X[, -2, drop = FALSE], V = 10,
learners = c("SL.glm","SL.mean"))
# difference in cross-validated R^2 for the two fits
compare_cvma(fit1, fit2)
#> contrast ci_low ci_high p_value
#> 1 0.4587962 0.3195792 0.5980131 1.052884e-10© 2017 David C. Benkeser
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