OME
Experiments were performed on children on their ability to differentiate a signal in broadband noise. The noise was played from a pair of speakers and a signal was added to just one channel; the subject had to turn his/her head to the channel with the added signal. The signal was either coherent (the amplitude of the noise was increased for a period) or incoherent (independent noise was added for the same period to form the same increase in power). The threshold used in the original analysis was the stimulus loudness needs to get 75% correct responses. Some of the children had suffered from otitis media with effusion (OME).
 Keywords
 datasets
Usage
OME
Format
The OME
data frame has 1129 rows and 7 columns:
ID
 Subject ID (1 to 99, with some IDs missing). A few subjects were measured at different ages.
OME

"low"
or"high"
or"N/A"
(at ages other than 30 and 60 months). Age
 Age of the subject (months).
Loud
 Loudness of stimulus, in decibels.
Noise

Whether the signal in the stimulus was
"coherent"
or"incoherent"
. Correct

Number of correct responses from
Trials
trials. Trials
 Number of trials performed.
Background
The experiment was to study otitis media with effusion (OME), a very common childhood condition where the middle ear space, which is normally airfilled, becomes congested by a fluid. There is a concomitant fluctuating, conductive hearing loss which can result in various language, cognitive and social deficits. The term ‘binaural hearing’ is used to describe the listening conditions in which the brain is processing information from both ears at the same time. The brain computes differences in the intensity and/or timing of signals arriving at each ear which contributes to sound localisation and also to our ability to hear in background noise. Some years ago, it was found that children of 78 years with a history of significant OME had significantly worse binaural hearing than children without such a history, despite having equivalent sensitivity. The question remained as to whether it was the timing, the duration, or the degree of severity of the otitis media episodes during critical periods, which affected later binaural hearing. In an attempt to begin to answer this question, 95 children were monitored for the presence of effusion every month since birth. On the basis of OME experience in their first two years, the test population was split into one group of high OME prevalence and one of low prevalence.
Examples
library(MASS)
# Fit logistic curve from p = 0.5 to p = 1.0
fp1 < deriv(~ 0.5 + 0.5/(1 + exp((xL75)/scal)),
c("L75", "scal"),
function(x,L75,scal)NULL)
nls(Correct/Trials ~ fp1(Loud, L75, scal), data = OME,
start = c(L75=45, scal=3))
nls(Correct/Trials ~ fp1(Loud, L75, scal),
data = OME[OME$Noise == "coherent",],
start=c(L75=45, scal=3))
nls(Correct/Trials ~ fp1(Loud, L75, scal),
data = OME[OME$Noise == "incoherent",],
start = c(L75=45, scal=3))
# individual fits for each experiment
aa < factor(OME$Age)
ab < 10*OME$ID + unclass(aa)
ac < unclass(factor(ab))
OME$UID < as.vector(ac)
OME$UIDn < OME$UID + 0.1*(OME$Noise == "incoherent")
rm(aa, ab, ac)
OMEi < OME
library(nlme)
fp2 < deriv(~ 0.5 + 0.5/(1 + exp((xL75)/2)),
"L75", function(x,L75) NULL)
dec < getOption("OutDec")
options(show.error.messages = FALSE, OutDec=".")
OMEi.nls < nlsList(Correct/Trials ~ fp2(Loud, L75)  UIDn,
data = OMEi, start = list(L75=45), control = list(maxiter=100))
options(show.error.messages = TRUE, OutDec=dec)
tmp < sapply(OMEi.nls, function(X)
{if(is.null(X)) NA else as.vector(coef(X))})
OMEif < data.frame(UID = round(as.numeric((names(tmp)))),
Noise = rep(c("coherent", "incoherent"), 110),
L75 = as.vector(tmp), stringsAsFactors = TRUE)
OMEif$Age < OME$Age[match(OMEif$UID, OME$UID)]
OMEif$OME < OME$OME[match(OMEif$UID, OME$UID)]
OMEif < OMEif[OMEif$L75 > 30,]
summary(lm(L75 ~ Noise/Age, data = OMEif, na.action = na.omit))
summary(lm(L75 ~ Noise/(Age + OME), data = OMEif,
subset = (Age >= 30 & Age <= 60),
na.action = na.omit), cor = FALSE)
# Or fit by weighted least squares
fpl75 < deriv(~ sqrt(n)*(r/n  0.5  0.5/(1 + exp((xL75)/scal))),
c("L75", "scal"),
function(r,n,x,L75,scal) NULL)
nls(0 ~ fpl75(Correct, Trials, Loud, L75, scal),
data = OME[OME$Noise == "coherent",],
start = c(L75=45, scal=3))
nls(0 ~ fpl75(Correct, Trials, Loud, L75, scal),
data = OME[OME$Noise == "incoherent",],
start = c(L75=45, scal=3))
# Test to see if the curves shift with age
fpl75age < deriv(~sqrt(n)*(r/n  0.5  0.5/(1 +
exp((xL75slope*age)/scal))),
c("L75", "slope", "scal"),
function(r,n,x,age,L75,slope,scal) NULL)
OME.nls1 <
nls(0 ~ fpl75age(Correct, Trials, Loud, Age, L75, slope, scal),
data = OME[OME$Noise == "coherent",],
start = c(L75=45, slope=0, scal=2))
sqrt(diag(vcov(OME.nls1)))
OME.nls2 <
nls(0 ~ fpl75age(Correct, Trials, Loud, Age, L75, slope, scal),
data = OME[OME$Noise == "incoherent",],
start = c(L75=45, slope=0, scal=2))
sqrt(diag(vcov(OME.nls2)))
# Now allow random effects by using NLME
OMEf < OME[rep(1:nrow(OME), OME$Trials),]
OMEf$Resp < with(OME, rep(rep(c(1,0), length(Trials)),
t(cbind(Correct, TrialsCorrect))))
OMEf < OMEf[, match(c("Correct", "Trials"), names(OMEf))]
## Not run: 
# ## these fail in R on most platforms
# fp2 < deriv(~ 0.5 + 0.5/(1 + exp((xL75)/exp(lsc))),
# c("L75", "lsc"),
# function(x, L75, lsc) NULL)
# try(summary(nlme(Resp ~ fp2(Loud, L75, lsc),
# fixed = list(L75 ~ Age, lsc ~ 1),
# random = L75 + lsc ~ 1  UID,
# data = OMEf[OMEf$Noise == "coherent",], method = "ML",
# start = list(fixed=c(L75=c(48.7, 0.03), lsc=0.24)), verbose = TRUE)))
#
# try(summary(nlme(Resp ~ fp2(Loud, L75, lsc),
# fixed = list(L75 ~ Age, lsc ~ 1),
# random = L75 + lsc ~ 1  UID,
# data = OMEf[OMEf$Noise == "incoherent",], method = "ML",
# start = list(fixed=c(L75=c(41.5, 0.1), lsc=0)), verbose = TRUE)))
## 