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hyprcoloc.R
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hyprcoloc.R
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##########################################################
##### Prior #####
##########################################################
#' prior
#'
#' @param p.1 probability of one trait having a causal variant in the genetic region
#' @param gamma step probability
#' @param k number of traits
#' @noRd
prior <- function(p.1, gamma, k) {
if (k == 1) {
p.1
} else {
i <- c(2:k)
G <- (1 - gamma^(i - 1))
p.1 * prod(G)
}
}
##########################################################
##### SNP scores #####
##########################################################
#' p.0
#'
#' @param j number of traits
#' @param Q number of SNPs
#' @noRd
p.0 <- function(j, Q) {
(j - 1) * Q - j * (j - 1) / 2 + 1
}
#' ind.snp.score
#'
#' @param Q the number of traits
#' @param snp.scores vector of per snp contributions to the posterior probability of colocalization
#' @noRd
ind.snp.score <- function(Q, snp.scores) {
loc <- vector("numeric", Q - 1)
res <- vector("numeric", Q)
for (j in 1:Q) {
i <- 1
while (i < j) {
loc[i] <- p.0(i, Q) + j - (i + 1)
i <- i + 1
}
if (j <= Q - 1) {
loc[i:(Q - 1)] <- (p.0(j, Q)):(p.0(j + 1, Q) - 1)
}
res[j] <- sum(snp.scores[loc])
}
return(res)
}
##########################################################
##### Reduce dimensions of datasets #####
##########################################################
#' samp.reduc
#'
#' @param Z matrix of Z-scores
#' @param W ratio matrix of prior standard deviation and observed standard errors
#' @param ld.matrix LD matrix
#' @param trait.cor correlation matrix between traits
#' @param sample.overlap matrix of sample overlap between traits
#' @param trts vector of traits
#' @param window.size size of window for 2CV testing
#' @param sentinel sentinel variant
#' @param Zsq matrix of Z-scores squared
#' @param Wsq matrix of W squared
#' @noRd
samp.reduc <- function(Z, W, ld.matrix, trait.cor, sample.overlap, trts, window.size = dim(Z)[1], sentinel = 0, Zsq, Wsq) {
q <- dim(Z)[1]
Z <- Z[, trts]
W <- W[, trts]
Zsq <- Zsq[, trts]
Wsq <- Wsq[, trts]
trait.cor <- trait.cor[trts, trts]
sample.overlap <- sample.overlap[trts, trts]
if (window.size < q) {
if (sentinel == 0) {
max.Z <- which(abs(Z) == max(abs(Z)))
if (length(max.Z) > 1) {
max.Z <- sample(max.Z, 1)
}
row.Z <- max.Z %% dim(Z)[1]
if (row.Z == 0) {
row.Z <- dim(Z)[1]
}
} else {
row.Z <- sentinel
}
Q <- window.size
if (Q %% 2 == 1) {
Q <- Q - 1
}
if (max(row.Z - Q / 2, 1) == 1) {
row.col <- 1:(Q + 1)
Z <- Z[row.col, ]
W <- W[row.col, ]
Zsq <- Zsq[row.col, ]
Wsq <- Wsq[row.col, ]
ld.matrix <- ld.matrix[row.col, row.col]
} else if (min(row.Z + Q / 2, q) == q) {
row.col <- (q - Q):q
Z <- Z[row.col, ]
W <- W[row.col, ]
Zsq <- Zsq[row.col, ]
Wsq <- Wsq[row.col, ]
ld.matrix <- ld.matrix[row.col, row.col]
} else {
row.col <- (row.Z - Q / 2):(row.Z + Q / 2)
Z <- Z[row.col, ]
W <- W[row.col, ]
Zsq <- Zsq[row.col, ]
Wsq <- Wsq[row.col, ]
ld.matrix <- ld.matrix[row.col, row.col]
}
} else {
row.col <- 1:q
}
return(list(Z, W, ld.matrix, trait.cor, sample.overlap, row.col, Zsq, Wsq))
}
#' colMax
#'
#' @param x data.frame or matrix
#' @noRd
colMax <- function(x) {
apply(x, MARGIN = c(2), max)
}
################################################################################
##### Compute credible sets of snps for each cluster of colocalized traits #####
################################################################################
#' Credible sets
#'
#' `cred.sets` computes credible sets of SNPs for each cluster of colocalized traits
#' @name cred.sets
#' @param res list of results from hyprcoloc when setting "snpscores = TRUE"
#' @param value the sum of the probabilities of the snps included in the credible set
#' @author Christopher Foley <chris.neal.foley@gmail.com> & James Staley <jrstaley95@gmail.com>
#' @export
#' @md
cred.sets <- function(res, value = 0.95) {
clusters <- which(!is.na(res[[1]]$traits))
results <- vector("list", length(clusters))
if (length(clusters) > 0) {
count <- 1
for (i in clusters) {
snp.scores <- res[[2]][[i]]
snp.scores <- snp.scores[order(-snp.scores)]
tmp.rmv <- which(snp.scores < (1 - value) / length(snp.scores))
tmp.lgt <- length(snp.scores) - length(tmp.rmv)
snp.scores <- snp.scores[-tmp.rmv]
if (tmp.lgt > 1) {
row.col <- combn(tmp.lgt, 2)
row <- c(1:tmp.lgt, row.col[1, ])
col <- c(1:tmp.lgt, row.col[2, ])
snp.cols <- sparseMatrix(i = row, j = col, x = 1, dims = c(tmp.lgt, tmp.lgt))
wch.snps <- snp.cols[, min(which(colSums(snp.scores * snp.cols) >= value))] == 1
results[[count]] <- snp.scores[wch.snps]
} else {
results[[count]] <- snp.scores[tmp.lgt]
}
count <- count + 1
}
}
return(results)
}
###########################################################################################################################################
##### Perform a sensitivity analysis by varying the algorithm (regional and alignment) thresholds and coloclaization prior (prior.c) #####
###########################################################################################################################################
#' Sensitivity plot
#'
#' `sensitivity.plot` is a function which repeatedly calls the hyprcoloc function to compute a similarity matrix which illustrates how strongly clustered/colocalized pairs of traits are across different input thresholds and priors
#' @name sensitivity.plot
#' @param effect.est matrix of snp regression coefficients (i.e. regression beta values) in the genomic region
#' @param effect.se matrix of standard errors associated with the beta values
#' @param binary.outcomes a binary vector of dimension the number of traits: 1 represents a binary trait 0 otherwise
#' @param trait.subset vector of trait names (or number) from the full trait list: used for trageted colocalization analysis in a region
#' @param trait.names vector of trait names corresponding to the columns in the effect.est matrix
#' @param snp.id vector of SNP IDs
#' @param ld.matrix LD matrix
#' @param trait.cor matrix of pairwise correlations between traits
#' @param sample.overlap matrix of pairwise sample overlap between traits
#' @param bb.alg branch and bound algorithm: TRUE, employ BB algorithm; FALSE, do not
#' @param bb.selection branch and bound algorithm type, e.g. regional or alignment selection
#' @param reg.steps regional step paramter
#' @param reg.thresh a vector of regional probability thresholds
#' @param align.thresh a vector of alignment probability thresholds
#' @param prior.1 prior probability of a SNP being associated with one trait
#' @param prior.c vector of conditional colocalization priors: where prior.c is the probability of a SNP being associated with an additional trait given that the SNP is associated with at least 1 other trait
#' @param prior.12 COLOC prior p12: prior probability of a SNP being associated with any two traits
#' @param uniform.priors uniform priors
#' @param ind.traits are the traits independent or to be treated as independent
#' @param equal.thresholds fix the regional and alignment thresholds to be equal
#' @param similarity.matrix To be viewed as a similarity matrix. Default FALSE.
#' @import pheatmap RColorBrewer
#' @author Christopher Foley <chris.neal.foley@gmail.com> & James Staley <jrstaley95@gmail.com>
#' @export
#' @md
sensitivity.plot <- function(effect.est, effect.se, binary.outcomes = rep(0, dim(effect.est)[2]),
trait.subset = c(1:dim(effect.est)[2]), trait.names = c(1:dim(effect.est)[2]),
snp.id = c(1:dim(effect.est)[1]), ld.matrix = diag(1, dim(effect.est)[1], dim(effect.est)[1]),
trait.cor = diag(1, dim(effect.est)[2], dim(effect.est)[2]),
sample.overlap = matrix(rep(1, dim(effect.est)[2]^2), nrow = dim(effect.est)[2]),
bb.alg = TRUE, bb.selection = "regional",
reg.steps = 1, reg.thresh = c(0.6, 0.7, 0.8, 0.9), align.thresh = c(0.6, 0.7, 0.8, 0.9),
prior.1 = 1e-4, prior.c = c(0.02, 0.01, 0.005), prior.12 = NULL,
uniform.priors = FALSE,
ind.traits = TRUE, equal.thresholds = FALSE, similarity.matrix = FALSE) {
m <- dim(effect.est)[2]
snp.combin <- function(x, y, vec) {
I <- iterpc(x, y, labels = vec)
return(getall(I) + 0.0)
}
sim.mat <- diag(0, m)
if (!is.null(prior.12)) {
prior.c <- prior.12 / (prior.1 + prior.12)
}
for (i in reg.thresh) {
for (k in prior.c) {
if (equal.thresholds) {
j <- i
tmp.mat <- diag(1, m)
res <- hyprcoloc(effect.est, effect.se,
binary.outcomes = binary.outcomes, trait.subset = trait.subset, trait.names = trait.names,
snp.id = snp.id, ld.matrix = ld.matrix, trait.cor = trait.cor, sample.overlap = sample.overlap, bb.alg = bb.alg, bb.selection = bb.selection,
reg.steps = reg.steps, reg.thresh = i, align.thresh = j,
prior.1 = prior.1, prior.c = k, uniform.priors = uniform.priors, ind.traits = ind.traits
)
trt.clusts <- res[[1]]$traits
for (its in 1:length(trt.clusts)) {
tmp.clust <- unlist(strsplit(trt.clusts[its], split = ", "))
if (tmp.clust[1] != "None") {
tmp.vec <- which(trait.names %in% tmp.clust)
# coloc.pairs = t(snp.combin(m, 2, tmp.vec));
coloc.pairs <- t(snp.combin(length(tmp.vec), 2, tmp.vec))
tmp.mat[t(coloc.pairs)] <- 1
}
}
sim.mat <- sim.mat + tmp.mat + t(tmp.mat) - diag(1, m)
} else {
for (j in align.thresh) {
tmp.mat <- diag(1, m)
res <- hyprcoloc(effect.est, effect.se,
binary.outcomes = binary.outcomes, trait.subset = trait.subset, trait.names = trait.names,
snp.id = snp.id, ld.matrix = ld.matrix, trait.cor = trait.cor, sample.overlap = sample.overlap, bb.alg = bb.alg, bb.selection = bb.selection,
reg.steps = reg.steps, reg.thresh = i, align.thresh = j,
prior.1 = prior.1, prior.c = k, uniform.priors = uniform.priors, ind.traits = ind.traits
)
trt.clusts <- res[[1]]$traits
for (its in 1:length(trt.clusts)) {
tmp.clust <- unlist(strsplit(trt.clusts[its], split = ", "))
if (tmp.clust[1] != "None") {
tmp.vec <- which(trait.names %in% tmp.clust)
# coloc.pairs = t(snp.combin(m, 2, tmp.vec));
coloc.pairs <- t(snp.combin(length(tmp.vec), 2, tmp.vec))
tmp.mat[t(coloc.pairs)] <- 1
}
}
sim.mat <- sim.mat + tmp.mat + t(tmp.mat) - diag(1, m)
}
}
}
}
sim.mat <- sim.mat / length(reg.thresh) / length(align.thresh) / length(prior.c)
if (equal.thresholds) {
sim.mat <- sim.mat * length(align.thresh)
}
rownames(sim.mat) <- trait.names
colnames(sim.mat) <- trait.names
# annotation_row = data.frame(
# Clusters = factor(dta$cluster.class[match(rownames(smat), obs.names)])
# )
# rownames(annotation_row) <- rownames(smat)
breaksList <- seq(0, 1, by = 0.02)
plot <- pheatmap(
mat = sim.mat,
color = colorRampPalette((brewer.pal(n = 9, name = "Blues")))(length(breaksList)),
breaks = breaksList,
cluster_cols = FALSE,
cluster_rows = FALSE,
border_color = NA,
show_colnames = TRUE,
show_rownames = TRUE,
# annotation_col = annotation_row,
drop_levels = TRUE,
fontsize = 6,
main = "Prior sensitivity heatmap"
)
if (!similarity.matrix) {
return(plot)
} else {
return(list(plot, sim.mat))
}
}
##########################################################
##### Regional colocalisation (rapid) #####
##########################################################
#' rapid.reg
#'
#' @param Zsq matrix of Z-scores
#' @param Wsq ratio matrix of prior standard deviation and observed standard errors squared
#' @param prior.1 prior probability of a SNP being associated with one trait
#' @param prior.2 1 - prior probability of a SNP being associated with an additional trait given that the SNP is associated with at least 1 other trait
#' @param uniform.priors uniform priors
#' @noRd
rapid.reg <- function(Zsq, Wsq, prior.1, prior.2, uniform.priors) {
m <- dim(Zsq)[2]
Q <- dim(Zsq)[1]
if (uniform.priors == T) {
I.unif <- 1
} else {
I.unif <- 0
}
p.1 <- prior.1
p.1.m <- p.1 / Q
prior.all <- I.unif * p.1.m + (1 - I.unif) * prior(prior.1, prior.2, k = m)
prior.sub <- I.unif * p.1.m + (1 - I.unif) * prior(prior.1, prior.2, k = m - 1)
labf <- 0.5 * (log(Wsq) + (Zsq) * (1 - Wsq))
sum.labf <- rowSums(labf)
mx.labf <- which.max(labf)
clc.max <- which.max(sum.labf)
chi <- sum.labf - sum.labf[clc.max]
exp.chi <- exp(chi)
sum.exp.chi <- sum(exp.chi)
sum.labf.subset <- colSums(exp(chi - labf))
rm.trt <- which.max(sum.labf.subset)
reg.prob <- sum.exp.chi / (exp(-sum.labf[clc.max] - log(prior.all)) + sum.exp.chi + (prior.sub / prior.all) * sum(sum.labf.subset))
return(list(reg.prob, clc.max, rm.trt, exp.chi / sum.exp.chi))
}
##########################################################
##### Regional colocalisation #####
##########################################################
#' regional.ABF
#'
#' @param Z matrix of Z-scores
#' @param W ratio matrix of prior standard deviation and observed standard errors
#' @param snps.clc SNPs colocalisation
#' @param rho LD matrix
#' @param trait.cor correlation matrix between traits
#' @param sample.overlap matrix of sample overlap between traits
#' @param epsilon tolerance parameter
#' @param reg.thresh regional probability threshold
#' @param prior.1 prior probability of a SNP being associated with one trait
#' @param prior.2 1 - prior probability of a SNP being associated with an additional trait given that the SNP is associated with at least 1 other trait
#' @param prior.3 prior probability that a trait contains a second causal variant given it contains one already
#' @param prior.4 1 - prior probability that trait two co-localises with trait one given traits one and two already share a causal variant and trait one contains a second causal variant
#' @param flag flag variable
#' @param test.2 test for 2CV
#' @param reg.steps regional step paramter
#' @param cor.adj.priors correlation adjusted priors
#' @param uniform.priors uniform priors
#' @param branch.jump branch jump
#' @param Zsq matrix of Z-scores squared
#' @param Wsq matrix of W squared
#' @param ind.traits are the traits independent or to be treated as independent
#' @noRd
regional.ABF <- function(Z, W, snps.clc, rho, trait.cor, sample.overlap, epsilon, reg.thresh, prior.1, prior.2, prior.3, prior.4, flag, test.2, reg.steps, cor.adj.priors, uniform.priors, branch.jump, Zsq, Wsq, ind.traits) {
m <- dim(Z)[2]
Q <- dim(Z)[1]
trait.cor <- trait.cor * sample.overlap
if (reg.steps > m) {
reg.steps <- m
}
if (uniform.priors == T) {
I.unif <- 1
} else {
I.unif <- 0
}
p.1 <- prior.1
p.1.m <- p.1 / Q
p.2.m <- p.1 * 2 / (Q * (Q - 1))
if (cor.adj.priors == T) {
ave.cor <- trait.cor[lower.tri(trait.cor)]
ave.cor <- mean(abs(ave.cor))
prior.2 <- min(prior.2, 1 - ave.cor^2)
prior.4 <- min(prior.4, 1 - ave.cor^4)
}
if (branch.jump == T & reg.steps > 2) {
jmp <- 1
} else {
jmp <- 0
}
ones <- matrix(1, nrow = dim(snps.clc)[1], ncol = dim(snps.clc)[1])
trait.cor <- as.matrix(kronecker(trait.cor, ones))
log.sum.max.ABF.1 <- sum.max.ABF.1 <- log.sum.max.ABF.2 <- sum.max.ABF.2 <- mpfr(0, 120)
log.sum.ABF.1 <- sum.ABF.1 <- sum.ABF.all.1 <- log.sum.ABF.2 <- sum.ABF.2 <- sum.ABF.all.2 <- mpfr(0, 120)
log.all.traits.ABF.1 <- log.all.traits.ABF.2 <- mpfr(0, 120)
log.max.ABF.1 <- log.max.ABF.2 <- mpfr(0, 120)
mx.ABF.k <- mpfr(0, 120)
NAs <- 0
if (test.2 == 0) {
df <- data.frame(matrix(vector(), 0, 10, dimnames = list(c(), c("log.sum.ABF.full", "log.sum.ABF.all.combs", "log.max.sum.ABF.all.traits", "log.max.SNP.ABF.full", "Post.ratio.2.vs.1and2", "Traits", "SNPs", "NaNs", "reg_bb_alg", "reg_only_trts"))), stringsAsFactors = F)
df[1, ]$reg_bb_alg <- FALSE
reg.prob <- 1
i <- m
count <- 0
while (reg.prob > (1 - jmp) * reg.thresh & i > 0) {
clc.trt <- combn(m, i)
count <- count + dim(clc.trt)[2]
prior1 <- I.unif * p.1.m + (1 - I.unif) * prior(prior.1, prior.2, k = i)
prior2 <- I.unif * p.2.m + (1 - I.unif) * prior(prior.1, prior.2, k = i) * prior(prior.3, prior.4, k = i)
for (j in 1:dim(clc.trt)[2]) {
trt.clc <- clc.trt[, j] + 0.0
if (flag == 0) {
if (ind.traits == T) {
output <- regional1ind(Zsq, Wsq, trt.clc)
} else {
output <- regional1(Z, W, trt.clc, trait.cor, epsilon)
}
if (i == m) {
max.ABF.1 <- prior1 * exp(mpfr(output[[1]][1], 120))
sum.ABF.1 <- max.ABF.1 * output[[1]][2]
clc.max.cvs.1 <- output[[1]][3]
} else {
max.ABF.1 <- prior1 * exp(mpfr(output[[1]][1], 120))
sum.ABF.1 <- max.ABF.1 * output[[2]][1]
clc.max.cvs.1 <- output[[3]][1]
if (mx.ABF.k < sum.ABF.1) {
mx.ABF.k <- sum.ABF.1
df[1, ]$reg_only_trts <- toString(clc.trt[, j])
}
}
if (!is.na(sum.ABF.1)) {
sum.ABF.all.1 <- sum.ABF.all.1 + sum.ABF.1
if (sum.max.ABF.1 < sum.ABF.1) {
sum.max.ABF.1 <- sum.ABF.1
df[1, ]$Traits <- toString(clc.trt[, j])
df[1, ]$SNPs <- toString(clc.max.cvs.1)
}
} else {
NAs <- NAs + 1
}
} else {
output <- regional2(Z, W, snps.clc, trt.clc, rho, trait.cor, epsilon)
max.ABF.1 <- prior1 * exp(mpfr(output[[1]][1], 120))
sum.ABF.1 <- max.ABF.1 * output[[1]][2]
clc.max.cvs.1 <- output[[1]][3]
if (!is.na(sum.ABF.1)) {
sum.ABF.all.1 <- sum.ABF.all.1 + sum.ABF.1
if (sum.max.ABF.1 < sum.ABF.1) {
sum.max.ABF.1 <- sum.ABF.1
df[1, ]$Traits <- toString(clc.trt[, j])
df[1, ]$SNPs <- toString(clc.max.cvs.1)
}
} else {
NAs <- NAs + 1
}
max.ABF.2 <- prior2 * exp(mpfr(output[[2]][1], 120))
sum.ABF.2 <- max.ABF.2 * output[[2]][2]
clc.max.cvs.2 <- snps.clc[, output[[2]][3]]
if (!is.na(sum.ABF.2)) {
sum.ABF.all.2 <- sum.ABF.all.2 + sum.ABF.2
if (sum.max.ABF.2 < sum.ABF.2) {
sum.max.ABF.2 <- sum.ABF.2
df[2, ]$Traits <- toString(clc.trt[, j])
df[2, ]$SNPs <- toString(clc.max.cvs.2)
}
} else {
NAs <- NAs + 1
}
}
}
if (i == m) {
log.max.ABF.1 <- log(max.ABF.1)
sum.ABF.full.1 <- sum.ABF.all.1
log.sum.ABF.1 <- asNumeric(log(sum.ABF.1))
df[1, ]$log.sum.ABF.full <- log.sum.ABF.1
df[1, ]$log.max.SNP.ABF.full <- asNumeric(log.max.ABF.1)
snp.scores.1 <- output[[2]]
if (flag == 1) {
log.max.ABF.2 <- log(max.ABF.2)
sum.ABF.full.2 <- sum.ABF.all.2
log.sum.ABF.2 <- asNumeric(log(sum.ABF.2))
df[2, ]$log.sum.ABF.full <- log.sum.ABF.2
df[2, ]$log.max.SNP.ABF.full <- asNumeric(log.max.ABF.2)
snp.scores.1 <- output[[3]]
snp.scores.2.tmp <- output[[4]]
snp.scores.2 <- ind.snp.score(Q, snp.scores.2.tmp)
}
}
if (flag == 0) {
reg.prob <- sum.ABF.full.1 / (sum.ABF.all.1)
} else {
reg.prob <- (sum.ABF.full.1 + sum.ABF.full.2) / (sum.ABF.all.1 + sum.ABF.all.2)
}
i <- i - 1
if (reg.steps != 0 & i == (m - reg.steps - 1)) {
i <- 0
}
}
if (jmp == 1 | sum.ABF.full.1 / mx.ABF.k >= (1 / min(9, m)) * count) {
df[1, ]$reg_bb_alg <- TRUE
}
log.sum.max.ABF.1 <- asNumeric(log(sum.max.ABF.1))
log.all.traits.ABF.1 <- asNumeric(log(sum.ABF.all.1))
df[1, ]$log.sum.ABF.all.combs <- log.all.traits.ABF.1
df[1, ]$log.max.sum.ABF.all.traits <- log.sum.max.ABF.1
df[1, ]$NaNs <- NAs
out.list <- list(df, snp.scores.1)
if (flag == 1) {
log.sum.max.ABF.2 <- asNumeric(log(sum.max.ABF.2))
log.all.traits.ABF.2 <- asNumeric(log(sum.ABF.all.2))
df[2, ]$log.sum.ABF.all.combs <- log.all.traits.ABF.2
df[2, ]$log.max.sum.ABF.all.traits <- log.sum.max.ABF.2
df[2, ]$NaNs <- NAs
df[2, ]$Post.ratio.2.vs.1and2 <- asNumeric(sum.ABF.all.2 / (sum.ABF.all.1 + sum.ABF.all.2))
out.list <- list(df, snp.scores.1, snp.scores.2)
}
} else {
prior1 <- I.unif * p.1.m + (1 - I.unif) * prior(prior.1, prior.2, k = m)
prior2 <- I.unif * p.2.m + (1 - I.unif) * prior(prior.1, prior.2, k = m) * prior(prior.3, prior.4, k = m)
output <- regional2(Z, W, snps.clc, c(1:m) + 0.0, rho, trait.cor, epsilon)
max.ABF.1 <- prior1 * exp(mpfr(output[[1]][1], 120))
sum.ABF.1 <- max.ABF.1 * output[[1]][2]
max.ABF.2 <- prior2 * exp(mpfr(output[[2]][1], 120))
sum.ABF.2 <- max.ABF.2 * output[[2]][2]
out.list <- list(sum.ABF.2 / (sum.ABF.2 + sum.ABF.1))
}
return(out.list)
}
##########################################################
##### Alignment (rapid) #####
##########################################################
#' rapid.align
#'
#' @param Zsq matrix of Z-scores
#' @param Wsq ratio matrix of prior standard deviation and observed standard errors squared
#' @param prior.1 prior probability of a SNP being associated with one trait
#' @param prior.2 1 - prior probability of a SNP being associated with an additional trait given that the SNP is associated with at least 1 other trait
#' @param uniform.priors uniform priors
#' @noRd
rapid.align <- function(Zsq, Wsq, prior.1, prior.2, uniform.priors) {
m <- dim(Zsq)[2]
Q <- dim(Zsq)[1]
if (uniform.priors == T) {
I.unif <- 1
} else {
I.unif <- 0
}
p.1 <- prior.1
p.1.m <- p.1 / Q
p.m.1 <- p.1 / (m * Q * (Q - 1))
if (m == 2) {
p.m.1 <- 2 * p.m.1
cnst <- 0.25
} else {
cnst <- 1
}
prior.all <- I.unif * p.1.m + (1 - I.unif) * prior(prior.1, prior.2, k = m)
prior.align <- I.unif * p.m.1 + (1 - I.unif) * prior.1 * prior(prior.1, prior.2, k = m - 1)
labf <- 0.5 * (log(Wsq) + (Zsq) * (1 - Wsq))
sum.labf <- rowSums(labf)
mx.labf <- which.max(labf)
clc.max <- which.max(sum.labf)
chi <- sum.labf - sum.labf[clc.max]
sum.exp.chi <- sum(exp(chi))
col.max.labf <- colMax(labf)
exp.labf.std <- exp(t(t(labf) - col.max.labf))
labf.tmp <- t(colSums(exp.labf.std) - t(exp.labf.std))
sum.tmp <- colSums(exp(t(t(chi - labf) + col.max.labf)) * labf.tmp)
rm.trt <- which.max(sum.tmp)
align.prob <- sum.exp.chi / (sum.exp.chi + cnst * (prior.align / prior.all) * sum(sum.tmp))
return(list(align.prob, rm.trt))
}
##########################################################
##### Alignment #####
##########################################################
#' align.ABF.1
#'
#' @param Z matrix of Z-scores
#' @param W ratio matrix of prior standard deviation and observed standard errors
#' @param trait.cor correlation matrix between traits
#' @param sample.overlap matrix of sample overlap between traits
#' @param ld.matrix LD matrix
#' @param epsilon tolerance parameter
#' @param reg.res regional result
#' @param align.thresh alignment probability threshold
#' @param prior.1 prior probability of a SNP being associated with one trait
#' @param prior.2 1 - prior probability of a SNP being associated with an additional trait given that the SNP is associated with at least 1 other trait
#' @param cor.adj.priors correlation adjusted priors
#' @param uniform.priors uniform priors
#' @param Zsq matrix of Z-scores squared
#' @param Wsq matrix of W squared
#' @param ind.traits are the traits independent or to be treated as independent
#' @noRd
align.ABF.1 <- function(Z, W, trait.cor, sample.overlap, ld.matrix, epsilon, reg.res, align.thresh, prior.1, prior.2, cor.adj.priors, uniform.priors, Zsq, Wsq, ind.traits) {
m <- dim(Z)[2]
Q <- dim(Z)[1]
traits <- c(1:m)
trait.cor <- trait.cor * sample.overlap
if (uniform.priors == T) {
I.unif <- 1
} else {
I.unif <- 0
}
p.1 <- prior.1
p.m.1 <- p.1 / (m * Q * (Q - 1))
if (m == 2) {
p.m.1 <- 2 * p.m.1
}
prior.3 <- prior.1
kappa <- 2
if (cor.adj.priors == T) {
ave.cor <- trait.cor[lower.tri(trait.cor)]
ave.cor <- mean(abs(ave.cor))
prior.2 <- min(prior.2, 1 - ave.cor^2)
prior.3 <- prior.1 * (10^(-kappa * ave.cor^2))
p.m.1 <- p.m.1 * (1 - ave.cor)^kappa
}
max.ABF.overall <- sum.max.ABF.co <- mpfr(0, 120)
log.sum.ABF.all.combs <- sum.ABF <- sum.ABF.co <- mpfr(0, 120)
NaNs <- 0
df <- data.frame(matrix(vector(), 0, 3, dimnames = list(c(), c("log.sum.ABF.all.combs", "Trait.no.clc", "NaNs"))), stringsAsFactors = F)
j <- 1
align.prob <- 1
trt.combn <- sample(c(1:m))
prior.algn <- I.unif * p.m.1 + (1 - I.unif) * prior.3 * prior(prior.1, prior.2, k = m - 1)
if (m > 2) {
while (j <= m) {
trt.no.clc <- trt.combn[j] + 0.0
trt.clc <- traits[-trt.no.clc] + 0.0
if (ind.traits == T) {
output <- align1ind(Zsq, Wsq, trt.clc, trt.no.clc)
} else {
output <- align1(Z, W, 1, trt.clc, trt.no.clc, trait.cor, ld.matrix, epsilon)
}
max.ABF <- prior.algn * exp(mpfr(output[[1]][1], 120))
sum.ABF.tmp <- max.ABF * output[[2]][1]
if (!is.nan(sum.ABF.tmp)) {
sum.ABF <- sum.ABF + sum.ABF.tmp
if (max.ABF.overall < sum.ABF.tmp) {
max.ABF.overall <- sum.ABF.tmp
df[1, ]$Trait.no.clc <- toString(trt.no.clc)
}
} else {
NaNs <- NaNs + 1
}
align.prob <- (reg.res) / (reg.res + sum.ABF)
j <- j + 1
}
} else {
trt.no.clc <- 1.0
trt.clc <- traits[-trt.no.clc] + 0.0
if (ind.traits == TRUE) {
output <- align1ind(Zsq, Wsq, trt.clc, trt.no.clc)
} else {
output <- align1(Z, W, 1, trt.clc, trt.no.clc, trait.cor, ld.matrix, epsilon)
}
max.ABF <- prior.algn * exp(mpfr(output[[1]][1], 120))
sum.ABF.tmp <- max.ABF * output[[2]][1]
if (!is.nan(sum.ABF.tmp)) {
sum.ABF <- (sum.ABF + sum.ABF.tmp) / 2
df[1, ]$Trait.no.clc <- toString(trt.no.clc)
} else {
NaNs <- NaNs + 1
}
}
log.sum.ABF.all.combs <- asNumeric(log(sum.ABF))
df[1, ]$log.sum.ABF.all.combs <- log.sum.ABF.all.combs
df[1, ]$NaNs <- NaNs
return(df)
}
##########################################################
##### Alignment 1CV and 2CV #####
##########################################################
#' align.ABF.2
#'
#' @param Z matrix of Z-scores
#' @param W ratio matrix of prior standard deviation and observed standard errors
#' @param snps.clc SNPs colocalisation
#' @param trait.cor correlation matrix between traits
#' @param sample.overlap matrix of sample overlap between traits
#' @param ld.matrix LD matrix
#' @param epsilon tolerance parameter
#' @param reg.res regional result
#' @param align.thresh alignment probability threshold
#' @param prior.1 prior probability of a SNP being associated with one trait
#' @param prior.2 1 - prior probability of a SNP being associated with an additional trait given that the SNP is associated with at least 1 other trait
#' @param prior.3 prior probability that a trait contains a second causal variant given it contains one already
#' @param prior.4 1 - prior probability that trait two co-localises with trait one given traits one and two already share a causal variant and trait one contains a second causal variant
#' @param cor.adj.priors correlation adjusted priors
#' @param uniform.priors uniform priors
#' @noRd
align.ABF.2 <- function(Z, W, snps.clc, trait.cor, sample.overlap, ld.matrix, epsilon, reg.res, align.thresh, prior.1, prior.2, prior.3, prior.4, cor.adj.priors, uniform.priors) {
m <- dim(Z)[2]
Q <- dim(Z)[1]
traits <- c(1:m)
n.cv <- dim(snps.clc)[1]
trait.cor <- trait.cor * sample.overlap
if (uniform.priors == T) {
I.unif <- 1
} else {
I.unif <- 0
}
p.1 <- prior.1
p.m.1 <- p.1 / (m * Q * (Q - 1))
p.1.m.2 <- 2 * p.1 / (m * Q * (Q - 1) * (Q - 2))
p.2.m.1 <- 2 * p.1 / (m * Q * (Q - 1) * (Q - 2))
p.2.m.2 <- 4 * p.1 / (m * Q * (Q - 1) * (Q - 2) * (Q - 3))
p.co.m.1.2 <- p.1 / (m * Q * (Q - 1))
p.co.m.2.1 <- p.1 / (m * Q * (Q - 1))
p.co.m.2.2 <- p.1 / (m * Q * (Q - 1) * (Q - 2))
if (m == 2) {
p.m.1 <- 2 * p.m.1
p.2.m.2 <- 2 * p.2.m.2
p.co.m.1.2 <- p.co.m.1.2 / 2
p.co.m.2.1 <- p.co.m.2.1 / 2
p.co.m.2.2 <- 2 * p.co.m.2.2
}
prior.5 <- prior.1
kappa <- 10
if (cor.adj.priors == T) {
ave.cor <- trait.cor[lower.tri(trait.cor)]
ave.cor <- mean(abs(ave.cor))
prior.2 <- min(prior.2, 1 - ave.cor^2)
prior.3 <- prior.3 * (10^(-kappa * ave.cor^2))
prior.4 <- min(prior.4, 1 - ave.cor^4)
prior.5 <- prior.1 * (10^(-kappa * ave.cor^2))
p.m.1 <- p.m.1 * (1 - ave.cor)^2
p.1.m.2 <- p.1.m.2 * (1 - ave.cor)^4
p.2.m.1 <- p.2.m.1 / (1 - ave.cor)^2
p.2.m.2 <- p.2.m.2 * (1 - ave.cor)^4
p.co.m.1.2 <- p.co.m.1.2 * (1 - ave.cor)^2
p.co.m.2.1 <- p.co.m.2.1 * (1 - ave.cor)^2
p.co.m.2.2 <- p.co.m.2.2 * (1 - ave.cor)^2
}
ones <- matrix(1, nrow = dim(snps.clc)[1], ncol = dim(snps.clc)[1])
trait.cor <- as.matrix(kronecker(trait.cor, ones))
max.ABF.overall <- sum.max.ABF.co <- mpfr(0, 120)
log.sum.ABF.align <- sum.ABF <- sum.ABF.co <- mpfr(0, 120)
NAs <- 0
df <- data.frame(matrix(vector(), 0, 7, dimnames = list(c(), c("log.sum.ABF.co.loc", "log.sum.ABF.align", "log.max.SNP.ABF.full", "Trait.no.clc", "Traits.clc", "SNPs.clc", "NaNs"))), stringsAsFactors = F)
j <- 1
align.prob <- 1
trt.combn <- sample(c(1:m))
prior.no.11 <- I.unif * p.m.1 + (1 - I.unif) * prior.5 * prior(prior.1, prior.2, k = m - 1)
prior.no.12 <- I.unif * p.1.m.2 + (1 - I.unif) * (prior.5 * prior.3) * prior(prior.1, prior.2, k = m - 1)
prior.co.12 <- I.unif * p.co.m.1.2 + (1 - I.unif) * prior.3 * prior(prior.1, prior.2, k = m)
prior.no.21 <- I.unif * p.2.m.1 + (1 - I.unif) * prior.5 * prior(prior.1, prior.2, k = m - 1) * prior(prior.3, prior.4, k = m - 1)
prior.no.22 <- I.unif * p.2.m.2 + (1 - I.unif) * (prior.5 * prior.3) * prior(prior.1, prior.2, k = m - 1) * prior(prior.3, prior.4, k = m - 1)
prior.co.21 <- I.unif * p.co.m.2.1 + (1 - I.unif) * prior(prior.1, prior.2, k = m) * prior(prior.3, prior.4, k = m - 1)
prior.co.22 <- I.unif * p.co.m.2.2 + (1 - I.unif) * prior.3 * prior(prior.1, prior.2, k = m) * prior(prior.3, prior.4, k = m - 1)
while (align.prob > align.thresh & j <= m) {
trt.no.clc <- trt.combn[j] + 0.0
trt.clc <- traits[-trt.no.clc] + 0.0
output_1 <- align12(Z, W, snps.clc, trt.clc, trt.no.clc, ld.matrix, trait.cor, epsilon)
max.ABF <- c(prior.no.11 * exp(mpfr(output_1[[1]][1], 120)), prior.no.12 * exp(mpfr(output_1[[2]][1], 120)))
sum.ABF.no <- sum(max.ABF * c(output_1[[1]][2], output_1[[2]][2]))
if (!is.nan(sum.ABF.no)) {
sum.ABF <- sum.ABF + sum.ABF.no
if (max.ABF.overall < sum.ABF.no) {
max.ABF.overall <- sum.ABF.no
df[1, ]$Trait.no.clc <- toString(trt.no.clc)
}
} else {
NAs <- NAs + 1
}
max.ABF.1 <- prior.co.12 * exp(mpfr(output_1[[3]][1], 120))
sum.ABF.1 <- max.ABF.1 * output_1[[3]][2]
clc.max.cvs.1 <- output_1[[3]][3]
if (!is.na(sum.ABF.1)) {
sum.ABF.co <- sum.ABF.co + sum.ABF.1
if (sum.max.ABF.co < sum.ABF.1) {
sum.max.ABF.co <- sum.ABF.1
log.max.ABF.co <- log(max(max.ABF.1))
df[1, ]$Traits.clc <- toString(trt.clc)
df[1, ]$SNPs.clc <- toString(clc.max.cvs.1)
}
} else {
NAs <- NAs + 1
}
output_2 <- align2(Z, W, snps.clc, trt.clc, trt.no.clc, ld.matrix, trait.cor, epsilon)
max.ABF <- c(prior.no.21 * exp(mpfr(output_2[[1]][1], 120)), prior.no.22 * exp(mpfr(output_2[[2]][1], 120)))
sum.ABF.no <- sum(max.ABF * c(output_2[[1]][2], output_2[[2]][2]))
if (!is.nan(sum.ABF.no)) {
sum.ABF <- sum.ABF + sum.ABF.no
if (max.ABF.overall < sum.ABF.no) {
max.ABF.overall <- sum.ABF.no
df[1, ]$Trait.no.clc <- toString(trt.no.clc)
}
} else {
NAs <- NAs + 1
}
max.ABF.2 <- c(prior.co.21 * exp(mpfr(output_2[[3]][1], 120)), prior.co.22 * exp(mpfr(output_2[[4]][1], 120)))
sum.ABF.2 <- sum(max.ABF.2 * c(output_2[[3]][2], output_2[[4]][2]))
clc.max.cvs.2 <- snps.clc[output_2[[2 + which(max.ABF.2 == max(max.ABF.2))]][3], output_2[[2 + which(max.ABF.2 == max(max.ABF.2))]][4]]
if (!is.na(sum.ABF.2)) {
sum.ABF.co <- sum.ABF.co + sum.ABF.2
if (sum.max.ABF.co < sum.ABF.2) {
sum.max.ABF.co <- sum.ABF.2
log.max.ABF.co <- log(max(max.ABF.2))
df[1, ]$Traits.clc <- toString(trt.clc)
df[1, ]$SNPs.clc <- toString(clc.max.cvs.2)
}
} else {
NAs <- NAs + 1
}
align.prob <- (reg.res + sum.ABF.co) / (reg.res + sum.ABF.co + sum.ABF)
j <- j + 1
}
log.sum.ABF.align <- asNumeric(log(sum.ABF))
df[1, ]$log.sum.ABF.align <- log.sum.ABF.align
df[1, ]$NaNs <- NAs
log.sum.ABF.co.loc <- asNumeric(log(sum.ABF.co))
df[1, ]$log.sum.ABF.co.loc <- log.sum.ABF.co.loc
df[1, ]$log.max.SNP.ABF.full <- asNumeric(log.max.ABF.co)
return(df)
}
##########################################################
##### HyPrColoc (rapid) #####
##########################################################
#' rapid.hyprcoloc
#'
#' @param Zsq matrix of Z-scores
#' @param Wsq ratio matrix of prior standard deviation and observed standard errors squared
#' @param prior.1 prior probability of a SNP being associated with one trait
#' @param prior.2 1 - prior probability of a SNP being associated with an additional trait given that the SNP is associated with at least 1 other trait
#' @param uniform.priors uniform priors
#' @noRd
rapid.hyprcoloc <- function(Zsq, Wsq, prior.1, prior.2, uniform.priors) {
m <- dim(Zsq)[2]
Q <- dim(Zsq)[1]
if (uniform.priors == T) {
I.unif <- 1
} else {
I.unif <- 0
}
p.1 <- prior.1
p.1.m <- p.1 / Q
p.m.1 <- p.1 / (m * Q * (Q - 1))
if (m == 2) {
p.m.1 <- 2 * p.m.1
cnst <- 0.25
} else {
cnst <- 1
}
prior.all <- I.unif * p.1.m + (1 - I.unif) * prior(prior.1, prior.2, k = m)
prior.sub <- I.unif * p.1.m + (1 - I.unif) * prior(prior.1, prior.2, k = m - 1)
prior.align <- I.unif * p.m.1 + (1 - I.unif) * prior.1 * prior(prior.1, prior.2, k = m - 1)
labf <- 0.5 * (log(Wsq) + (Zsq) * (1 - Wsq))
sum.labf <- rowSums(labf)
mx.labf <- which.max(labf)
clc.max <- which.max(sum.labf)
chi <- sum.labf - sum.labf[clc.max]
exp.chi <- exp(chi)
sum.exp.chi <- sum(exp.chi)
sum.labf.subset <- colSums(exp(chi - labf))
rm.trt <- which.max(sum.labf.subset)
reg.prob <- sum.exp.chi / (exp(-sum.labf[clc.max] - log(prior.all)) + sum.exp.chi + (prior.sub / prior.all) * sum(sum.labf.subset))
col.max.labf <- colMax(labf)
exp.labf.std <- exp(t(t(labf) - col.max.labf))
labf.tmp <- t(colSums(exp.labf.std) - t(exp.labf.std))
sum.tmp <- colSums(exp(t(t(chi - labf) + col.max.labf)) * labf.tmp)
align.prob <- sum.exp.chi / (sum.exp.chi + cnst * (prior.align / prior.all) * sum(sum.tmp))
return(list(reg.prob, reg.prob * align.prob, clc.max, exp.chi / sum.exp.chi))
}
##########################################################
##### HyPrColoc #####
##########################################################
#' HyPrColoc
#'
#' `hyprcoloc` is a function used to identify clusters of colocalized traits and candidate causal SNPs in genomic regions
#' @name hyprcoloc
#' @param effect.est matrix of snp regression coefficients (i.e. regression beta values) in the genomic region
#' @param effect.se matrix of standard errors associated with the beta values
#' @param binary.outcomes a binary vector of dimension the number of traits: 1 represents a binary trait 0 otherwise
#' @param trait.subset vector of trait names (or number) from the full trait list: used for trageted colocalization analysis in a region
#' @param trait.names vector of trait names corresponding to the columns in the effect.est matrix
#' @param snp.id vector of SNP IDs
#' @param ld.matrix LD matrix
#' @param trait.cor matrix of pairwise correlations between traits
#' @param sample.overlap matrix of pairwise sample overlap between traits
#' @param bb.alg branch and bound algorithm: TRUE, employ BB algorithm; FALSE, do not
#' @param bb.selection branch and bound algorithm type, e.g. regional or alignment selection
#' @param reg.steps regional step paramter
#' @param reg.thresh threshold probability beyond which traits are believed to share a regional association signal
#' @param align.thresh threshold probability beyond which traits are believed to align at a single causal variant
#' @param prior.1 prior probability of a SNP being associated with one trait
#' @param prior.c conditional colocalization prior: probability of a SNP being associated with an additional trait given that the SNP is associated with at least 1 other trait
#' @param prior.12 COLOC prior p12: prior probability of a SNP being associated with any two traits
#' @param sensitivity perform senstivity analysis
#' @param sense.1 first sensitivity analysis
#' @param sense.2 second sensitivity analysis
#' @param uniform.priors uniform priors
#' @param ind.traits are the traits independent or to be treated as independent
#' @param snpscores output estimated posterior probability explained each SNP
#' @return A data.frame of HyPrColoc results: each row is a cluster of colocalized traits or is coded NA (if no colocalization is identified)
#' @return If snpscores = TRUE: additionally returns a list of posterior probability explained by each SNPs and for each cluster of colocalized traits identified
#' @import compiler Rmpfr iterpc
#' @importFrom Rcpp evalCpp
#' @useDynLib hyprcoloc
#' @examples
#' # Regression coefficients and standard errors from ten GWAS studies
#' # (Traits 1-5, 6-8 & 9-10 are the clusters of colocalized traits)
#' betas <- hyprcoloc::test.betas
#' head(betas)
#' ses <- hyprcoloc::test.ses
#' head(ses)
#'
#' # Trait names and SNP IDs
#' traits <- paste0("T", 1:10)
#' rsid <- rownames(betas)
#'
#' # Colocalisation analyses
#' results <- hyprcoloc(betas, ses, trait.names = traits, snp.id = rsid)
#' @author Christopher Foley <chris.neal.foley@gmail.com> & James Staley <jrstaley95@gmail.com>
#' @export
#' @md
hyprcoloc <- function(effect.est, effect.se, binary.outcomes = rep(0, dim(effect.est)[2]),
trait.subset = c(1:dim(effect.est)[2]), trait.names = c(1:dim(effect.est)[2]),
snp.id = c(1:dim(effect.est)[1]), ld.matrix = diag(1, dim(effect.est)[1], dim(effect.est)[1]),
trait.cor = diag(1, dim(effect.est)[2], dim(effect.est)[2]),
sample.overlap = matrix(rep(1, dim(effect.est)[2]^2), nrow = dim(effect.est)[2]),