I am using Efron's local fdr procedure. But, I want to change the null from
N(0,1) to N(0, 0.002). I can access the function but I have no idea what to
change. In other words, I want nulltype to be N(0,0.002) instead of N(0,1)
in his function. Anyone has any ideas. This is his code for the local fdr:
function (zz, bre = 120, df = 7, pct = 0, pct0 = 1/4, nulltype = 1,
type = 0, plot = 1, mult, mlests, main = " ", sw = 0)
{
call = match.call()
if (length(bre) > 1) {
lo <- min(bre)
up <- max(bre)
bre <- length(bre)
}
else {
if (length(pct) > 1) {
lo <- pct[1]
up <- pct[2]
}
else {
if (pct == 0) {
lo <- min(zz)
up <- max(zz)
}
if (pct < 0) {
med = median(zz)
ra = med + (1 - pct) * (range(zz) - med)
lo = ra[1]
up = ra[2]
}
if (pct > 0) {
v <- quantile(zz, c(pct, 1 - pct))
lo <- v[1]
up <- v[2]
}
}
}
zzz <- pmax(pmin(zz, up), lo)
breaks <- seq(lo, up, length = bre)
zh <- hist(zzz, breaks = breaks, plot = F)
x <- (breaks[-1] + breaks[-length(breaks)])/2
yall <- y <- zh$counts
K <- length(y)
N <- length(zz)
if (pct > 0) {
y[1] <- min(y[1], 1)
y[K] <- min(y[K], 1)
}
if (type == 0) {
X <- cbind(1, ns(x, df = df))
f <- glm(y ~ ns(x, df = df), poisson)$fit
}
else {
X <- cbind(1, poly(x, df = df))
f <- glm(y ~ poly(x, df = df), poisson)$fit
}
l <- log(f)
Fl <- cumsum(f)
Fr <- cumsum(rev(f))
D <- (y - f)/(f + 1)^0.5
D <- sum(D[2:(K - 1)]^2)/(K - 2 - df)
if (D > 1.5)
warning(paste("f(z) misfit = ", round(D, 1), ". Rerun
with
increased df",
sep = ""))
if (nulltype == 3) {
fp0 = matrix(NA, 6, 4)
colnames(fp0) = c("delta", "sigleft",
"p0", "sigright")
}
else {
fp0 = matrix(NA, 6, 3)
colnames(fp0) = c("delta", "sigma", "p0")
}
rownames(fp0) = c("thest", "theSD", "mlest",
"mleSD", "cmest",
"cmeSD")
fp0["thest", 1:2] = c(0, 1)
fp0["theSD", 1:2] = 0
imax <- seq(l)[l == max(l)][1]
xmax <- x[imax]
if (length(pct0) == 1) {
pctup <- 1 - pct0
pctlo <- pct0
}
else {
pctlo <- pct0[1]
pctup <- pct0[2]
}
lo0 <- quantile(zz, pctlo)
hi0 <- quantile(zz, pctup)
nx <- length(x)
i0 <- (1:nx)[x > lo0 & x < hi0]
x0 <- x[i0]
y0 <- l[i0]
if (nulltype == 3) {
X00 <- cbind((x0 - xmax)^2, pmax(x0 - xmax, 0)^2)
}
else {
X00 <- cbind(x0 - xmax, (x0 - xmax)^2)
}
lr <- lm(y0 ~ X00)
co <- lr$coef
if (nulltype == 3) {
cmerror = I(is.na(co[3]) | is.na(co[2]))
if (!cmerror)
cmerror = I(co[2] >= 0 | co[2] + co[3] >= 0)
}
else {
cmerror = is.na(co[3])
if (!cmerror)
cmerror = I(co[3] >= 0)
}
if (cmerror) {
if (nulltype == 3)
stop("CM estimation failed. Rerun with nulltype = 1 or
2.")
else if (nulltype == 2)
stop("CM estimation failed. Rerun with nulltype = 1.")
else {
X0 <- cbind(1, x - xmax, (x - xmax)^2)
warning("CM estimation failed, middle of histogram
non-normal")
}
}
else {
if (nulltype == 3) {
X0 <- cbind(1, (x - xmax)^2, pmax(x - xmax, 0)^2)
sigs <- 1/sqrt(-2 * (c(co[2], co[2] + co[3])))
fp0["cmest", c(1, 2, 4)] <- c(xmax, sigs)
}
else {
X0 <- cbind(1, x - xmax, (x - xmax)^2)
xmaxx <- -co[2]/(2 * co[3]) + xmax
sighat <- 1/sqrt(-2 * co[3])
fp0["cmest", 1:2] <- c(xmaxx, sighat)
}
l0 <- as.vector(X0 %*% co)
f0 <- exp(l0)
p0 <- sum(f0)/sum(f)
f0 <- f0/p0
fp0["cmest", 3] <- p0
}
b = 4.3 * exp(-0.26 * log(N, 10))
if (missing(mlests)) {
med = median(zz)
sc = diff(quantile(zz)[c(2, 4)])/(2 * qnorm(0.75))
mlests = locmle(zz, xlim = c(med, b * sc))
if (N > 5e+05) {
warning("length(zz) > 500,000: For ML estimation, a wider
interval than optimal was used. To use the optimal interval, rerun with
mlests = c(",
mlests[1], ", ", b * mlests[2], ").\n", sep
= "")
mlests = locmle(zz, xlim = c(med, sc))
}
}
if (!is.na(mlests[1])) {
if (N > 5e+05)
b = 1
if (nulltype == 1) {
Cov.in = list(x = x, X = X, f = f, sw = sw)
ml.out = locmle(zz, xlim = c(mlests[1], b * mlests[2]),
d = mlests[1], s = mlests[2], Cov.in = Cov.in)
mlests = ml.out$mle
}
else mlests = locmle(zz, xlim = c(mlests[1], b * mlests[2]),
d = mlests[1], s = mlests[2])
fp0["mlest", 1:3] = mlests[1:3]
fp0["mleSD", 1:3] = mlests[4:6]
}
if (sum(is.na(fp0[c(3, 5), 1:2])) == 0 & nulltype > 1)
if (abs(fp0["cmest", 1] - mlests[1]) > 0.05 |
abs(log(fp0["cmest",
2]/mlests[2])) > 0.05)
warning("Discrepancy between central matching and maximum
likelihood estimates.\nConsider rerunning with nulltype = 1")
if (is.na(mlests[1])) {
if (nulltype == 1) {
if (is.na(fp0["cmest", 1]))
stop("CM and ML Estimation failed, middle of histogram
non-normal")
else stop("ML estimation failed. Rerun with nulltype=2")
}
else warning("ML Estimation failed")
}
if (nulltype < 2) {
delhat = xmax = xmaxx = mlests[1]
sighat = mlests[2]
p0 = mlests[3]
f0 = dnorm(x, delhat, sighat)
f0 = (sum(f) * f0)/sum(f0)
}
fdr = pmin((p0 * f0)/f, 1)
f00 <- exp(-x^2/2)
f00 <- (f00 * sum(f))/sum(f00)
p0theo <- sum(f[i0])/sum(f00[i0])
fp0["thest", 3] = p0theo
fdr0 <- pmin((p0theo * f00)/f, 1)
f0p <- p0 * f0
if (nulltype == 0)
f0p <- p0theo * f00
F0l <- cumsum(f0p)
F0r <- cumsum(rev(f0p))
Fdrl <- F0l/Fl
Fdrr <- rev(F0r/Fr)
Int <- (1 - fdr) * f * (fdr < 0.9)
if (sum(x <= xmax & fdr == 1) > 0)
xxlo <- min(x[x <= xmax & fdr == 1])
else xxlo = xmax
if (sum(x >= xmax & fdr == 1) > 0)
xxhi <- max(x[x >= xmax & fdr == 1])
else xxhi = xmax
if (sum(x >= xxlo & x <= xxhi) > 0)
fdr[x >= xxlo & x <= xxhi] <- 1
if (sum(x <= xmax & fdr0 == 1) > 0)
xxlo <- min(x[x <= xmax & fdr0 == 1])
else xxlo = xmax
if (sum(x >= xmax & fdr0 == 1) > 0)
xxhi <- max(x[x >= xmax & fdr0 == 1])
else xxhi = xmax
if (sum(x >= xxlo & x <= xxhi) > 0)
fdr0[x >= xxlo & x <= xxhi] <- 1
if (nulltype == 1) {
fdr[x >= mlests[1] - mlests[2] & x <= mlests[1] + mlests[2]] =
1
fdr0[x >= mlests[1] - mlests[2] & x <= mlests[1] + mlests[2]]
= 1
}
p1 <- sum((1 - fdr) * f)/N
p1theo <- sum((1 - fdr0) * f)/N
fall <- f + (yall - y)
Efdr <- sum((1 - fdr) * fdr * fall)/sum((1 - fdr) * fall)
Efdrtheo <- sum((1 - fdr0) * fdr0 * fall)/sum((1 - fdr0) *
fall)
iup <- (1:K)[x >= xmax]
ido <- (1:K)[x <= xmax]
Eleft <- sum((1 - fdr[ido]) * fdr[ido] * fall[ido])/sum((1 -
fdr[ido]) * fall[ido])
Eleft0 <- sum((1 - fdr0[ido]) * fdr0[ido] * fall[ido])/sum((1 -
fdr0[ido]) * fall[ido])
Eright <- sum((1 - fdr[iup]) * fdr[iup] * fall[iup])/sum((1 -
fdr[iup]) * fall[iup])
Eright0 <- sum((1 - fdr0[iup]) * fdr0[iup] * fall[iup])/sum((1 -
fdr0[iup]) * fall[iup])
Efdr <- c(Efdr, Eleft, Eright, Efdrtheo, Eleft0, Eright0)
Efdr[which(is.na(Efdr))] = 1
names(Efdr) <- c("Efdr", "Eleft", "Eright",
"Efdrtheo", "Eleft0",
"Eright0")
if (nulltype == 0)
f1 <- (1 - fdr0) * fall
else f1 <- (1 - fdr) * fall
if (!missing(mult)) {
mul = c(1, mult)
EE = rep(0, length(mul))
for (m in 1:length(EE)) {
xe = sqrt(mul[m]) * x
f1e = approx(xe, f1, x, rule = 2, ties = mean)$y
f1e = (f1e * sum(f1))/sum(f1e)
f0e = f0
p0e = p0
if (nulltype == 0) {
f0e = f00
p0e = p0theo
}
fdre = (p0e * f0e)/(p0e * f0e + f1e)
EE[m] = sum(f1e * fdre)/sum(f1e)
}
EE = EE/EE[1]
names(EE) = mul
}
Cov2.out = loccov2(X, X0, i0, f, fp0["cmest", ], N)
Cov0.out = loccov2(X, matrix(1, length(x), 1), i0, f, fp0["thest",
], N)
if (sw == 3) {
if (nulltype == 0)
Ilfdr = Cov0.out$Ilfdr
else if (nulltype == 1)
Ilfdr = ml.out$Ilfdr
else if (nulltype == 2)
Ilfdr = Cov2.out$Ilfdr
else stop("With sw=3, nulltype must equal 0, 1, or 2.")
return(Ilfdr)
}
if (nulltype == 0)
Cov = Cov0.out$Cov
else if (nulltype == 1)
Cov = ml.out$Cov.lfdr
else Cov = Cov2.out$Cov
lfdrse <- diag(Cov)^0.5
fp0["cmeSD", 1:3] = Cov2.out$stdev[c(2, 3, 1)]
if (nulltype == 3)
fp0["cmeSD", 4] = fp0["cmeSD", 2]
fp0["theSD", 3] = Cov0.out$stdev[1]
if (sw == 2) {
if (nulltype == 0) {
pds = fp0["thest", c(3, 1, 2)]
stdev = fp0["theSD", c(3, 1, 2)]
pds. = t(Cov0.out$pds.)
}
else if (nulltype == 1) {
pds = fp0["mlest", c(3, 1, 2)]
stdev = fp0["mleSD", c(3, 1, 2)]
pds. = t(ml.out$pds.)
}
else if (nulltype == 2) {
pds = fp0["cmest", c(3, 1, 2)]
stdev = fp0["cmeSD", c(3, 1, 2)]
pds. = t(Cov2.out$pds.)
}
else stop("With sw=2, nulltype must equal 0, 1, or 2.")
colnames(pds.) = names(pds) = c("p0", "delhat",
"sighat")
names(stdev) = c("sdp0", "sddelhat",
"sdsighat")
return(list(pds = pds, x = x, f = f, pds. = pds., stdev = stdev))
}
p1 <- seq(0.01, 0.99, 0.01)
cdf1 <- rep(0, 99)
fd <- fdr
if (nulltype == 0)
fd <- fdr0
for (i in 1:99) cdf1[i] <- sum(f1[fd <= p1[i]])
cdf1 <- cbind(p1, cdf1/cdf1[99])
mat <- cbind(x, fdr, Fdrl, Fdrr, f, f0, f00, fdr0, yall,
lfdrse, f1)
namat <- c("x", "fdr", "Fdrleft",
"Fdrright", "f", "f0",
"f0theo", "fdrtheo", "counts",
"lfdrse", "p1f1")
if (nulltype == 0)
namat[c(3, 4, 10)] <- c("Fdrltheo", "Fdrrtheo",
"lfdrsetheo")
dimnames(mat) <- list(NULL, namat)
z.2 = rep(NA, 2)
m = order(fd)[nx]
if (fd[nx] < 0.2) {
z.2[2] = approx(fd[m:nx], x[m:nx], 0.2, ties = mean)$y
}
if (fd[1] < 0.2) {
z.2[1] = approx(fd[1:m], x[1:m], 0.2, ties = mean)$y
}
if (plot > 0) {
if (plot == 2 | plot == 3)
oldpar <- par(mfrow = c(1, 2), pty = "m")
else if (plot == 4)
oldpar = par(mfrow = c(1, 3), pty = "m")
hist(zzz, breaks = breaks, xlab = " ", main = main)
yt <- pmax(yall * (1 - fd), 0)
for (k in 1:K) lines(c(x[k], x[k]), c(0, yt[k]), lwd = 2,
col = 6)
if (nulltype == 3)
title(xlab = paste("delta=", round(xmax, 3),
"sigleft=",
round(sigs[1], 3), " sigright=", round(sigs[2],
3), "p0=", round(fp0["cmest", 3], 3)))
if (nulltype == 1 | nulltype == 2)
title(xlab = paste("MLE: delta:", round(mlests[1],
3), "sigma:", round(mlests[2], 3), "p0:",
round(mlests[3],
3)), sub = paste("CME: delta:",
round(fp0["cmest",
1], 3), "sigma:", round(fp0["cmest", 2], 3),
"p0:", round(fp0["cmest", 3], 3)))
lines(x, f, lwd = 3, col = 3)
if (nulltype == 0)
lines(x, p0theo * f00, lwd = 2, lty = 2, col = 4)
else lines(x, p0 * f0, lwd = 2, lty = 2, col = 4)
if (!is.na(z.2[2]))
points(z.2[2], -0.5, pch = 24, col = "red", bg =
"yellow")
if (!is.na(z.2[1]))
points(z.2[1], -0.5, pch = 24, col = "red", bg =
"yellow")
if (nulltype == 1 | nulltype == 2)
Ef <- Efdr[1]
else if (nulltype == 0)
Ef <- Efdr[4]
if (plot == 2 | plot == 4) {
if (nulltype == 0)
fdd <- fdr0
else fdd = fdr
matplot(x, cbind(fdd, Fdrl, Fdrr), type = "l", lwd = 3,
xlab = " ", ylim = c(0, 1.1), main = "fdr
(solid); Fdr's
(dashed)")
title(xlab = paste("Efdr= ", round(Ef, 3)))
abline(0, 0, lty = 3, col = 2)
lines(c(0, 0), c(0, 1), lty = 3, col = 2)
}
if (plot == 3 | plot == 4) {
if (sum(is.na(cdf1[, 2])) == nrow(cdf1))
warning("cdf1 not available")
else {
plot(cdf1[, 1], cdf1[, 2], type = "l", lwd = 3,
xlab = "fdr level", ylim = c(0, 1), ylab = "f1
proportion
< fdr level",
main = "f1 cdf of estimated fdr")
title(sub = paste("Efdr= ", round(Ef, 3)))
lines(c(0.2, 0.2), c(0, cdf1[20, 2]), col = 4,
lty = 2)
lines(c(0, 0.2), rep(cdf1[20, 2], 2), col = 4,
lty = 2)
text(0.05, cdf1[20, 2], round(cdf1[20, 2], 2))
abline(0, 0, col = 2)
lines(c(0, 0), c(0, 1), col = 2)
}
}
if (plot > 1)
par(oldpar)
}
if (nulltype == 0) {
ffdr <- approx(x, fdr0, zz, rule = 2, ties = "ordered")$y
}
else ffdr <- approx(x, fdr, zz, rule = 2, ties = "ordered")$y
vl = list(fdr = ffdr, fp0 = fp0, Efdr = Efdr, cdf1 = cdf1,
mat = mat, z.2 = z.2)
if (!missing(mult))
vl$mult = EE
vl$call = call
vl
}
<environment: namespace:locfdr>
--
Thanks,
Jim.
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