cut point for a continuous variable in a model fit with coxph or survfit.

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Description

Determine the optimal cut point for a continuous variable in a coxph or survfit model.

Usage

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cutp(x, ...)

## S3 method for class 'coxph'
cutp(x, ..., defCont = 3)

## S3 method for class 'survfit'
cutp(x, ..., defCont = 3)

Arguments

x

A survfit or coxph object

defCont

definition of a continuous variable.
If the variable has > defCont unique values, it is treated as continuous and a cut point is determined.

...

Additional arguments (not implemented).

Details

For a cut point mu, of a predictor K, the variable is split into two groups, those >= mu and those < mu.
The score (or log-rank) statistic, sc, is calculated for each unique element k in K and uses

  • e1[i] the number of events

  • n1[i] the number at risk

in those above the cut point, respectively.
The basic statistic is

sc[k] = sum (e1[i] - n1[i] * e[i] / n[i])


The sum is taken across times with observed events, to D, the largest of these.
It is normalized (standardized), in the case of censoring, by finding s^2 which is:

s^2 = (1 / (D - 1)) * sum[i:D](1 - sum[j:i](1 / (D - j + 1))^2 )

The test statistic is then

Q = max(abs(sc[k])) / s * sqrt((D - 1))

Under the null hypothesis that the chosen cut point does not predict survival, the distribution of Q has a limiting distibution which is the supremum of the absolute value of a Brownian bridge:

p= P(Q >= q) = 2 sum[i:Inf](-1)^(i + 1) * e^(-2 * i^2 *q^2)

Value

A list of data.tables.
There is one list element per continuous variable.
Each has a column with possible values of the cut point (i.e. unique values of the variable), and the additional columns:

U

The score (log-rank) test for a model with the variable 'cut' into into those >= the cutpoint and those below.

Q

The test statistic.

p

The p-value.

The tables are ordered by p-value, lowest first.

References

Contal C, O'Quigley J, 1999. An application of changepoint methods in studying the effect of age on survival in breast cancer. Computational Statistics & Data Analysis 30(3):253–70. ScienceDirect (paywall)

Mandrekar JN, Mandrekar, SJ, Cha SS, 2003. Cutpoint Determination Methods in Survival Analysis using SAS. Proceedings of the 28th SAS Users Group International Conference (SUGI). Paper 261-28. SAS (free)

Examples

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## Mandrekar et al. above
data("bmt", package="KMsurv")
b1 <- bmt[bmt$group==1, ] # ALL patients
c1 <- coxph(Surv(t2, d3) ~ z1, data=b1) # z1=age
c1 <- cutp(c1)$z1
data.table::setorder(c1, "z1")
## [] below is used to print data.table to console
c1[]

## Not run: 
## compare to output from survival::coxph
matrix(
    unlist(
        lapply(26:30,
               function(i) c(i, summary(coxph(Surv(t2, d3) ~ z1 >= i, data=b1))$sctest))),
    ncol=5,
    dimnames=list(c("age", "score_test", "df", "p")))
cutp(coxph(Surv(t2, d3) ~ z1, data=bmt[bmt$group==2, ]))$z1[]
cutp(coxph(Surv(t2, d3) ~ z1, data=bmt[bmt$group==3, ]))[[1]][]
## K&M. Example 8.3, pg 273-274.
data("kidtran", package="KMsurv")
k1 <- kidtran
## patients who are male and black
k2 <- k1[k1$gender==1 & k1$race==2, ]
c2 <- coxph(Surv(time, delta) ~ age, data=k2)
print(cutp(c2))
## check significance of computed value
summary(coxph(Surv(time, delta) ~ age >= 58, data=k2))
k3 <- k1[k1$gender==2 & k1$race==2, ]
c3 <- coxph(Surv(time, delta) ~ age, data=k3)
print(cutp(c3))
## doesn't apply to binary variables e.g. gender
print(cutp(coxph(Surv(time, delta) ~ age + gender, data=k1)))

## End(Not run)