Continuation Ratio Ordinal Logistic Setup
Creates several new variables which help set up a dataset with an
ordinal response variable y for use in fitting a forward continuation
ratio (CR) model. The CR model can be fitted with binary logistic
regression if each input observation is replicated the proper
number of times according to the y value, a new binary y
is computed that has at most one y=1 per subject,
and if a cohort variable is used to define the current
qualifying condition for a cohort of subjects, e.g., y≥q 2.
cr.setup creates the needed auxilliary variables. See
predab.resample and validate.lrm for information about
validating CR models (e.g., using the bootstrap to sample with
replacement from the original subjects instead of the records used in
the fit, validating the model separately for user-specified values of
cohort).
cr.setup(y)
y |
a character, numeric, |
a list with components y, cohort, subs, reps. y is a new binary
variable that is to be used in the binary logistic fit. cohort is
a factor vector specifying which cohort condition currently applies.
subs is a vector of subscripts that can be used to replicate other
variables the same way y was replicated. reps specifies how many
times each original observation was replicated. y, cohort, subs are
all the same length and are longer than the original y vector.
reps is the same length as the original y vector.
The subs vector is suitable for passing to validate.lrm or calibrate,
which pass this vector under the name cluster on to predab.resample so that bootstrapping can be
done by sampling with replacement from the original subjects rather than
from the individual records created by cr.setup.
Frank Harrell
Department of Biostatistics
Vanderbilt University
fh@fharrell.com
Berridge DM, Whitehead J: Analysis of failure time data with ordinal categories of response. Stat in Med 10:1703–1710, 1991.
y <- c(NA, 10, 21, 32, 32)
cr.setup(y)
set.seed(171)
y <- sample(0:2, 100, rep=TRUE)
sex <- sample(c("f","m"),100,rep=TRUE)
sex <- factor(sex)
table(sex, y)
options(digits=5)
tapply(y==0, sex, mean)
tapply(y==1, sex, mean)
tapply(y==2, sex, mean)
cohort <- y>=1
tapply(y[cohort]==1, sex[cohort], mean)
u <- cr.setup(y)
Y <- u$y
cohort <- u$cohort
sex <- sex[u$subs]
lrm(Y ~ cohort + sex)
f <- lrm(Y ~ cohort*sex) # saturated model - has to fit all data cells
f
#Prob(y=0|female):
# plogis(-.50078)
#Prob(y=0|male):
# plogis(-.50078+.11301)
#Prob(y=1|y>=1, female):
plogis(-.50078+.31845)
#Prob(y=1|y>=1, male):
plogis(-.50078+.31845+.11301-.07379)
combinations <- expand.grid(cohort=levels(cohort), sex=levels(sex))
combinations
p <- predict(f, combinations, type="fitted")
p
p0 <- p[c(1,3)]
p1 <- p[c(2,4)]
p1.unconditional <- (1 - p0) *p1
p1.unconditional
p2.unconditional <- 1 - p0 - p1.unconditional
p2.unconditional
## Not run:
dd <- datadist(inputdata) # do this on non-replicated data
options(datadist='dd')
pain.severity <- inputdata$pain.severity
u <- cr.setup(pain.severity)
# inputdata frame has age, sex with pain.severity
attach(inputdata[u$subs,]) # replicate age, sex
# If age, sex already available, could do age <- age[u$subs] etc., or
# age <- rep(age, u$reps), etc.
y <- u$y
cohort <- u$cohort
dd <- datadist(dd, cohort) # add to dd
f <- lrm(y ~ cohort + age*sex) # ordinary cont. ratio model
g <- lrm(y ~ cohort*sex + age, x=TRUE,y=TRUE) # allow unequal slopes for
# sex across cutoffs
cal <- calibrate(g, cluster=u$subs, subset=cohort=='all')
# subs makes bootstrap sample the correct units, subset causes
# Predicted Prob(pain.severity=0) to be checked for calibration
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.