Efficiently compute a multivariate, penalized image-based linear regression model (milr)

This function simplifies calculating image-wide multivariate beta maps from linear models. Image-based variables are stored in the input matrix list. They should be named consistently in the input formula and in the image list. If they are not, an error will be thrown. All input matrices should have the same number of rows and columns. The model will minimize a matrix energy similar to norm( X - UVt - UranVrant ) where the U are standard design and random effect (intercept) design matrices. The random intercept matrix is only included if repeated measures are indicated.

milr(
  dataFrame,
  voxmats,
  myFormula,
  smoothingMatrix,
  iterations = 10,
  gamma = 1e-06,
  sparsenessQuantile,
  positivity = c("positive", "negative", "either"),
  repeatedMeasures = NA,
  orthogonalize = FALSE,
  verbose = FALSE
)

Arguments

dataFrame

This data frame contains all relevant predictors except for the matrices associated with the image variables.

voxmats

The named list of matrices that contains the changing predictors.

myFormula

This is a character string that defines a valid regression formula.

smoothingMatrix

allows parameter smoothing, should be square and same size as input matrix

iterations

number of gradient descent iterations

gamma

step size for gradient descent

sparsenessQuantile

quantile to control sparseness - higher is sparser

positivity

restrict to positive or negative solution (beta) weights. choices are positive, negative or either as expressed as a string.

repeatedMeasures

list of repeated measurement identifiers. this will allow estimates of per identifier intercept.

orthogonalize

boolean to control whether we orthogonalize the v

verbose

boolean to control verbosity of output

Value

A list of different matrices that contain names derived from the formula and the coefficients of the regression model.

Author

BB Avants.

Examples

set.seed(1500)
nsub <- 12
npix <- 100
outcome <- rnorm(nsub)
covar <- rnorm(nsub)
mat <- replicate(npix, rnorm(nsub))
mat2 <- replicate(npix, rnorm(nsub))
myform <- " vox2 ~ covar + vox "
df <- data.frame(outcome = outcome, covar = covar)
result <- milr(df, list(vox = mat, vox2 = mat2), myform)

if (FALSE) { # \dontrun{
# a 2nd example with 3 modalities
imageIDs <- c("r16", "r27", "r30", "r62", "r64", "r85")
images <- list()
feature1Images <- list()
feature2Images <- list()
feature3Images <- list()
ref <- antsImageRead(getANTsRData("r16"))
mask <- ref * 0
for (i in 1:length(imageIDs)) {
  cat("Processing image", imageIDs[i], "\n")
  tar <- antsImageRead(getANTsRData(imageIDs[i]))
  images[[i]] <- tar
  mask <- mask + tar
  feature1Images[[i]] <- iMath(images[[i]], "Grad", 1.0)
  feature2Images[[i]] <- iMath(images[[i]], "Laplacian", 1.0)
  feature3Images[[i]] <- reflectImage(tar, axis = 0, tx = "Affine")$warpedmovout
}
i <- 1
mask <- getMask(mask)
spatmat <- t(imageDomainToSpatialMatrix(mask, mask))
smoomat <- knnSmoothingMatrix(spatmat, k = 23, sigma = 100.0)
mat <- imageListToMatrix(images, mask)
mat2 <- imageListToMatrix(feature1Images, mask)
mat3 <- imageListToMatrix(feature3Images, mask)
myscale <- function(x) {
  return(scale(x, center = TRUE, scale = T))
}
x <- list(x1 = myscale(mat[-5, ]), x2 = myscale(mat2[-5, ]), x3 = myscale(mat3[-5, ]))
df <- data.frame(m1 = rowMeans(x$x1), m2 = rowMeans(x$x2), m3 = rowMeans(x$x3))
myform <- " x1 ~ x2 + x3 + m2 + m3 "
result <- milr(df, x, myform,
  iterations = 32, smoothingMatrix = smoomat,
  gamma = 1e-1, verbose = T
)
k <- 1
mm <- makeImage(mask, (result$prediction[k, ])) %>% iMath("Normalize")
tar <- makeImage(mask, x$x1[k, ])
plot(mm, doCropping = FALSE)
plot(tar, doCropping = FALSE)
cor.test(result$prediction[k, ], x$x1[k, ])
myol <- makeImage(mask, abs(result$v[, "x2"])) %>% iMath("Normalize")
plot(tar, myol, doCropping = FALSE)
myol <- makeImage(mask, abs(result$v[, "m3"])) %>% iMath("Normalize")
plot(tar, myol, doCropping = FALSE)
result <- milr(df, x, myform,
  iterations = 11, smoothingMatrix = smoomat,
  sparsenessQuantile = 0.5, positivity = "positive",
  gamma = 1e-2, verbose = T
)
myol <- makeImage(mask, abs(result$v[, "x2"])) %>% iMath("Normalize")
plot(tar, myol, doCropping = FALSE, window.overlay = c(0.1, 1))
mm <- makeImage(mask, (result$prediction[k, ])) %>% iMath("Normalize")
tar <- makeImage(mask, x$x1[k, ])
plot(mm, doCropping = FALSE)
plot(tar, doCropping = FALSE)
cor.test(result$prediction[k, ], x$x1[k, ])
# univariate outcome
myform <- " m1 ~ x2 + x3 + m2 + m3 "
result <- milr(df, x, myform,
  iterations = 11, smoothingMatrix = smoomat,
  gamma = 1e-2, verbose = T
)
} # }