Fig 1.
Schematic plot of an example binary decision tree with exposures
. Note: The predicted values of the leaf nodes are
, with the branch splitting rules as
,
, and
.
Table 1.
Simulation results for 15 exposures and a continuous outcome, with hierarchical variable selection for modified BART and BKMR.
Table 2.
Average PIPs for 15 exposures and a continuous outcome, with both component-wise and hierarchical variable selection for modified BART and BKMR. The true relationship is a non-linear main effect only model , with
.
Fig 2.
Average marginal effects for exposures ,
and
, in simulations with 15 exposures and a continuous outcome, using hierarchical variable selection for modified BART with 20 trees and BKMR. The true relationship is a non-linear main effects only model
, with
. Note: All simulations were replicated 500 times. The reference lines are true effects of each exposure by fixing all other exposures at their quartiles.
Table 3.
Simulation results for 15 exposures and a binary outcome, with hierarchical variable selection for modified probit BART and probit BKMR.
Table 4.
Average PIPs for 15 exposures and a binary outcome, with both component-wise and hierarchical variable selection for modified probit BART and probit BKMR. The true relationship is a non-linear main effect only model , with
.
Fig 3.
Average marginal effects for exposures ,
and
, in simulations with 15 exposures and a binary outcome, using hierarchical variable selection for modified probit BART with 20 trees and probit BKMR. The true relationship is a non-linear main effects only model
, with
. Note: All simulations were replicated 500 times. The reference lines are true effects of each exposure by fixing all other exposures at their quartiles.
Table 5.
PIPs for 18 POPs and log-LTL from the NHANES 2001-2002 data, with both component-wise and hierarchical variable selection for modified BART and BKMR.
Fig 4.
Marginal effects of 18 POPs on log-LTL from the NHANES 2001-2002 data, using hierarchical variable selection for modified BART with 20 trees and BKMR.
Note: All chemicals were log-transformed and scaled. The reference lines are partial dependency curves from BKMR by fixing all other exposures at their quartiles.