cr.setup {Design} | R Documentation

## Continuation Ratio Ordinal Logistic Setup

### Description

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`).

### Usage

    cr.setup(y)

### Arguments

`y` | a character, numeric, `category`, or `factor` vector containing values of the response variable. For `category` or `factor` variables, the `levels` of the variable are assumed to be listed in an ordinal way.

### Value

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`.

### Author(s)

Frank Harrell
Department of Biostatistics
Vanderbilt University
f.harrell@vanderbilt.edu

### References

Berridge DM, Whitehead J: Analysis of failure time data with ordinal categories of response. Stat in Med 10:1703–1710, 1991.

### See Also

`lrm`, `glm`, `predab.resample`

### Examples

    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

    # In S-Plus:
    #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)

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