# cutp: *cut p*oint for a continuous variable in a model fit with... In survMisc: Miscellaneous Functions for Survival Data

## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```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.table`s.
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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35``` ```## 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) ```

survMisc documentation built on May 29, 2017, 3:50 p.m.