mcma_PCA: Principal component analysis based multiple mediation...

In zhaoyi1026/spcma: Sparse Principal Component based High-Dimensional Mediation Analysis

Description

This function performs marginal causal mediation analysis under the linear structural equation modeling framework. The new mediators are linear projections of the original ones, such that they are causally independent.

Usage

mcma_PCA(X, M, Y, adaptive = FALSE, var.per = 0.8, n.pc = NULL, boot = TRUE, 
  sims = 1000, boot.ci.type = c("bca", "perc"), conf.level = 0.95, 
  p.adj.method = c("BH", "bonferroni", "BY"))

Arguments

X	a vector of length n, the randomized treatment assignment.
M	a n\times p data matrix, the mediators.
Y	a vector of length n, the outcome of interest.
adaptive	a logic variable, if adaptive = TRUE, the number of principal components (PCs) is determined based on the percentage of variance explained. Default is FALSE.
var.per	a numeric variable, the designated percentage of variance explained, which determines the number of PCs. Will be ignored if adaptive = FALSE.
n.pc	an integer variable, the number of PCs considered. Will be ignored if adpative = TRUE. Default is NULL. If n.pc = NULL, will set adaptive to TRUE.
boot	a logic variable, if FALSE a quasi-Bayesian approximation is used for confidence intervals; if TRUE nonparametric bootstrap will be used. Default is TRUE.
sims	a numeric value, the number of bootstrap replications. Default is 1000.
boot.ci.type	a character of the way of calculating bootstrap confidence interval. If boot.ci.type = "bca", the bias corrected confidence interval is returned; if boot.ci.type = "perc", the percentile confidence interval is returned.
conf.level	a numeric value, the designated significance level. Default is 0.05, i.e., return 95\% confidence interval.
p.adj.method	a character of the method implemented for multiple testing adjustment. See p.adjust.

Details

Consider the case of multiple mediators, and there is a linear projection of the original mediators \tilde{M}^{(j)}=Mφ_{j}, where Φ=(φ_{1},…,φ_{p}) is an orthonormal matrix, such that for j\neq k,

\tilde{M}^{(j)}~\perp~\tilde{M}^{(k)}~|~X.

We can perform a series of marginal mediation analysis on the new projected mediators, i.e.,

\tilde{M}_{i}^{(j)}=α_{0j}+α_{j}X_{i}+ξ_{ij},

Y_{i}=β_{0j}+γ_{j}X_{i}+β_{j}\tilde{M}_{i}^{(j)}+η_{ij},

where ξ_{ij} and η_{ij} are model errors with mean zero and independent of each other.

Value

IE	an outcome matrix, the estimate, p-value, lower and upper bound of the confidence interval, and the adjusted p-value of the indirect effect for each mediator.
DE	an outcome matrix, for each mediator, this provides the estimate of the direct effect, as well as the p-value, lower and upper bound of the confidence interval.
alpha	an outcome matrix, the estimate of the treatment effect on each mediator, as well as the p-value, lower and upper bound of the confidence interval and the adjusted p-value.
beta	an outcome matrix, the estimate of the mediator effect on the outcome with a one-unit increment, as well as the p-value, lower and upper bound of the confidence interval and the adjusted p-value.
gamma	an outcome matrix, th estimate, p-value, lower and upper bound of the confidence interval, and the adjusted p-value of γ_{j} in the model. For each mediator, this is the effect not explained by the mediator.
IE.total	an outcome matrix, the estimate, p-value, lower and upper bound of the total indirect effect.
U	the estimated loading matrix.
var.per	the cumulative proportion of variance explained by the PCs.

Author(s)

Yi Zhao, Johns Hopkins University, [e-mail];

Martin A. Lindquist, Johns Hopkins University, [e-mail];

Brian S. Caffo, Johns Hopkins University, [e-mail].

References

Huang and Pan (2016). “Hypothesis test of mediation effect in causal mediation model with high-dimensional continuous mediators”. Biometrics, 72(2):402-413.

Examples

#############################################
data(env.example)
X<-get("X",env.example)
M<-get("M",env.example)
Y<-get("Y",env.example)

# principal component based mediation analysis
mcma_PCA(X,M,Y,adaptive=TRUE,var.per=0.75,boot=FALSE)
#############################################

zhaoyi1026/spcma documentation built on May 4, 2019, 1:23 p.m.