rsisVIVE

The goal of rsisVIVE (robustified some invalid some valid instrumental variable estimator) is to estimate the causal relationship between an outcome and an exposure in the presence of invalid instruments while tolerating large proportions of contamination in the exposure and/or outcome values. The algorithm follows closely with the sisVIVE method of Kang et. al. (2016). The rsisVIVE replaces the two step algorithm of the sisVIVE with robust counterparts.

More details of the method can be seen in the master’s thesis submission by Jana Osea at the University of British Columbia as a partial fulfillment of the requirements for Master’s of Science, Department of Statistics under the supervision of Dr. Gabriela Cohen-Freue.

Installation

You can install the development version of rsisVIVE like so:

devtools::install_github("jfosea/rsisVIVE")
library(rsisVIVE)

Example

This is a basic example which shows you how to solve a common problem:

library(rsisVIVE)
#> Warning: replacing previous import 'MASS::select' by 'dplyr::select' when
#> loading 'rsisVIVE'

n <- 100
L <- 10
s <- 3
m <- floor(0.2*n)
Sigma <- diag(1, nrow = L)

a0 <- 1
a1 <- rep(0.05, L)

b0 <- 1
b1 <- c(rep(1,s), rep(0, L-s)) # alpha
b2 <- 1                        # beta (parameter of interest)

error <- MASS::mvrnorm(n, c(0, 0), matrix(c(1, 0.9, 0.9, 1), 2, 2))

Z <- MASS::mvrnorm(n, mu = rep(0, L), Sigma)
D <- a0 + Z %*% a1 + error[, 1]
Y <- b0 + Z %*% b1 + D * b2 + error[, 2]

Y[sample(1:n, m)] <- rnorm(m, 70, 1) # add contamination
rsisVIVE(Y, D, Z, method = 'PE_SE', ncores = 1)
#> $alpha
#>          x1          x2          x3          x4          x5          x6 
#>  0.00000000  0.00000000 -0.09379886  0.00000000  0.00000000 -0.25057890 
#>          x7          x8          x9         x10 
#> -1.94291405  0.32676347  0.00000000  1.31882800 
#> 
#> $beta
#> [1] 1.920595

We compare with the results of sisVIVE.

# compare with sisVIVE
sisVIVE::cv.sisVIVE(Y, D, Z)
#> $lambda
#> [1] 160.7302
#> 
#> $estCVError
#> [1] 7155.194
#> 
#> $alpha
#>  [1] 0 0 0 0 0 0 0 0 0 0
#> 
#> $beta
#> [1] 8.768325
#> 
#> $whichInvalid
#> [1] ""

References

Kang, H., Zhang, A., Cai, T. T., and Small, D. S. (2016). Instrumental Variables EStiamtion with Some Invalid Instruments and its Application to Mendelian Randomization. Journal of the American Statistical Association , 111, 132-144.