| Title: | Finding Optimal Three-Group Splits Based on a Survival Outcome |
|---|---|
| Description: | Provides fast procedures for exploring all pairs of cutpoints of a single covariate with respect to survival and determining optimal cutpoints using a hierarchical method and various ordered logrank tests. |
| Authors: | Pingping Qu and John Crowley |
| Maintainer: | Pingping Qu <[email protected]> |
| License: | GPL-3 |
| Version: | 1.0.0 |
| Built: | 2024-11-16 03:49:17 UTC |
| Source: | https://github.com/cran/rolr |
Using a hierarchical method, rhier is used to find two optimal
cutpoints to divide the entire dataset into three groups based on a
continuous covariate and a survival outcome. Making use of the running
logrank test (rlr), the method first identifies an optimal
cutpoint that gives the largest logrank statistic to split into two groups,
and then repeats the process in each of the resulting groups to find
additional two cutpoints. It then takes the cutpoint that gives the larger
test statistic between the two as the second optimal cutpoint.
rhier(times, status, x, ns = 15, alt = "decrease", method = "approximate")rhier(times, status, x, ns = 15, alt = "decrease", method = "approximate")
times |
Survival outcome. |
status |
Censoring indicator which takes 1 when an event occurs at end of study and 0 otherwise. |
x |
A continuous covariate. |
ns |
Minimum number of subjects in each group after dichotomizing the covariate. |
alt |
A character that takes either |
method |
A character that takes either |
Returns a list with one element being the two optimal cutpoints obtained.
See main package help page.
library(rolr) #simulate data with true underlying cutpoints and hazard goes up as covariate goes up d=simdata(nn = 150, hr = c(1, 2, 3), hazard.func = "step", props=c(1/3, 1/3, 1/3), censoring.rate = 0) #finding optimal cutpoints using alt = 'decrease' option res=rhier(times=d$times, status=d$status, x=d$x, ns=15, alt='decrease') #do it again using alt = 'increase', the results are the same as earlier #because it doesn't matter what you choose for the alt option res2=rhier(times=d$times, status=d$status, x=d$x, ns=15, alt='increase')library(rolr) #simulate data with true underlying cutpoints and hazard goes up as covariate goes up d=simdata(nn = 150, hr = c(1, 2, 3), hazard.func = "step", props=c(1/3, 1/3, 1/3), censoring.rate = 0) #finding optimal cutpoints using alt = 'decrease' option res=rhier(times=d$times, status=d$status, x=d$x, ns=15, alt='decrease') #do it again using alt = 'increase', the results are the same as earlier #because it doesn't matter what you choose for the alt option res2=rhier(times=d$times, status=d$status, x=d$x, ns=15, alt='increase')
rlr is used to calculate a logrank test for every two groups
obtained from dichotomizing a continuous covariate x at a particular point.
It will examine all values in x except the first and last ns points.
rlr(times, status, x, ns = 15, trend = "decrease", method = "approximate")rlr(times, status, x, ns = 15, trend = "decrease", method = "approximate")
times |
Survival outcome. |
status |
Censoring indicator which takes 1 when an event occurs at the end of a study and 0 otherwise. |
x |
A continuous covariate. |
ns |
Minimum number of subjects in each group, whether it is the group
with |
trend |
A character that takes either |
method |
A character that takes either |
When the association is positive, that is, larger covariate values
leading to worse survival, and you enter trend = "decrease", the test
statistics will be positive, but if you enter trend = "increase" the
test statistics will be negative. Opposite is true when the association
is negative. You want to make sure to enter the option so that the
resulting test statistics are positive.
A matrix of four columns as the following -
xcutoff - All cutpoints that have been used to dichotomize the sample
(that is, all values of the covariate x except the first and last ns points)
L - Numerators of the logrank z tests for all cutpoints considered.
V - Denominators of the logrank z tests for all cutpoints considered.
logrank.stat - The logrank z tests for all cutpoints considered.
See main package help page.
library(rolr) ##### -------- Example 1 #simulate survival where hazard increases as covariate increases d=simdata(nn = 150, hr.linear = 2, hazard.func = "linear", censoring.rate = 0) #using trend = 'decrease', the test statistics are positive, which is good res=rlr(times=d$times, status=d$status, x=d$x, ns=15, trend='decrease') head(res) #do it again with trend = 'increase', now the test statistics are negative. #So you want to switch to trend='decrease'. res2=rlr(times=d$times, status=d$status, x=d$x, ns=15, trend='increase') head(res2) #Note that the test statistics are the same except the signs res[,'logrank.stat']+res2[,'logrank.stat'] #do it with exact method, how close is it to the approximate method? res3=rlr(times=d$times, status=d$status, x=d$x, ns=15, trend='decrease', method="exact") cor(res[,'logrank.stat'], res3[,'logrank.stat']) ##### -------- Example 2 #Simulate survival where hazard decreases as covariate increases d=simdata(nn = 150, hr.linear = 1/3, hazard.func = "linear", censoring.rate = 0) #using trend = 'decrease', and the test statistics are negative, which #is not good res=rlr(times=d$times, status=d$status, x=d$x, ns=15, trend='decrease') head(res) #do it again with trend = 'increase', now the test statistics are positive, #which is good res2=rlr(times=d$times, status=d$status, x=d$x, ns=15, trend='increase') head(res2) #Note that the test statistics are the same except the signs res[,'logrank.stat']+res2[,'logrank.stat'] #do it with exact method, how close is it to the approximate method? res3=rlr(times=d$times, status=d$status, x=d$x, ns=15, trend='increase', method="exact") cor(res[,'logrank.stat'], res3[,'logrank.stat'])library(rolr) ##### -------- Example 1 #simulate survival where hazard increases as covariate increases d=simdata(nn = 150, hr.linear = 2, hazard.func = "linear", censoring.rate = 0) #using trend = 'decrease', the test statistics are positive, which is good res=rlr(times=d$times, status=d$status, x=d$x, ns=15, trend='decrease') head(res) #do it again with trend = 'increase', now the test statistics are negative. #So you want to switch to trend='decrease'. res2=rlr(times=d$times, status=d$status, x=d$x, ns=15, trend='increase') head(res2) #Note that the test statistics are the same except the signs res[,'logrank.stat']+res2[,'logrank.stat'] #do it with exact method, how close is it to the approximate method? res3=rlr(times=d$times, status=d$status, x=d$x, ns=15, trend='decrease', method="exact") cor(res[,'logrank.stat'], res3[,'logrank.stat']) ##### -------- Example 2 #Simulate survival where hazard decreases as covariate increases d=simdata(nn = 150, hr.linear = 1/3, hazard.func = "linear", censoring.rate = 0) #using trend = 'decrease', and the test statistics are negative, which #is not good res=rlr(times=d$times, status=d$status, x=d$x, ns=15, trend='decrease') head(res) #do it again with trend = 'increase', now the test statistics are positive, #which is good res2=rlr(times=d$times, status=d$status, x=d$x, ns=15, trend='increase') head(res2) #Note that the test statistics are the same except the signs res[,'logrank.stat']+res2[,'logrank.stat'] #do it with exact method, how close is it to the approximate method? res3=rlr(times=d$times, status=d$status, x=d$x, ns=15, trend='increase', method="exact") cor(res[,'logrank.stat'], res3[,'logrank.stat'])
Using the modified ordered logrank test (MOL), the rmolr
function finds two optimal cutpoints to divide the entire dataset into three
groups based on a continuous covariate and a survival outcome. It is a fast
procedure that makes use of the running logrank test (rlr)
to improve on computing speed.
rmolr(times, status, x, ns = 15, alt = "decrease", method = "approximate")rmolr(times, status, x, ns = 15, alt = "decrease", method = "approximate")
times |
Survival outcome. |
status |
Censoring indicator which takes 1 when an event occurs at end of study and 0 otherwise. |
x |
A continuous covariate. |
ns |
Minimum number of subjects in each group after dichotomizing the covariate. |
alt |
A character that takes either |
method |
A character that takes either |
When the true association is positive, that is, larger covariate
values lead to worse survival, and you enter alt = "decrease", the test
statistics will be positive, but if you enter trend = "increase" the
test statistics will be negative. Opposite is true when the true association
is negative. You want to make sure to enter the option so that the
resulting test statistics are positive.
Returns a list with two elements, with the first being the test statistics for all cutpoints considered and the second being the best splits from the MOL tests.
See main package help page.
library(rolr) ##### -------- Example 1 #simulate data with true cutpoints and hazard goes up as covariate goes up d=simdata(nn = 150, hr = c(1, 2, 3), hazard.func = "step", props=c(1/3, 1/3, 1/3), censoring.rate = 0) #using alt = 'decrease', the test statistics are positive, so the results #are correct. res=rmolr(times=d$times, status=d$status, x=d$x, ns=15, alt='decrease') names(res) #do it again using alt = 'increase', now the test statistics are negative #so the results are not right. So you have to switch back to alt='decrease' #to get positive statistics and the correct optimal cutpoints here. res2=rmolr(times=d$times, status=d$status, x=d$x, ns=15, alt='increase') names(res2) ##### -------- Example 2 #Simulate data with true cutpoints and hazard goes down as covariate goes up d=simdata(nn = 150, hr = c(3, 2, 1), hazard.func = "step", props=c(1/3, 1/3, 1/3), censoring.rate = 0) #using alt = 'decrease', the test statistics are negative and so the results #are not right. res=rmolr(times=d$times, status=d$status, x=d$x, ns=15, alt='decrease') res[['best.splits.molr']] #do it again using alt = 'increase', now the test statistics are positive #and thus the results are correct. res2=rmolr(times=d$times, status=d$status, x=d$x, ns=15, alt='increase') res2[['best.splits.molr']]library(rolr) ##### -------- Example 1 #simulate data with true cutpoints and hazard goes up as covariate goes up d=simdata(nn = 150, hr = c(1, 2, 3), hazard.func = "step", props=c(1/3, 1/3, 1/3), censoring.rate = 0) #using alt = 'decrease', the test statistics are positive, so the results #are correct. res=rmolr(times=d$times, status=d$status, x=d$x, ns=15, alt='decrease') names(res) #do it again using alt = 'increase', now the test statistics are negative #so the results are not right. So you have to switch back to alt='decrease' #to get positive statistics and the correct optimal cutpoints here. res2=rmolr(times=d$times, status=d$status, x=d$x, ns=15, alt='increase') names(res2) ##### -------- Example 2 #Simulate data with true cutpoints and hazard goes down as covariate goes up d=simdata(nn = 150, hr = c(3, 2, 1), hazard.func = "step", props=c(1/3, 1/3, 1/3), censoring.rate = 0) #using alt = 'decrease', the test statistics are negative and so the results #are not right. res=rmolr(times=d$times, status=d$status, x=d$x, ns=15, alt='decrease') res[['best.splits.molr']] #do it again using alt = 'increase', now the test statistics are positive #and thus the results are correct. res2=rmolr(times=d$times, status=d$status, x=d$x, ns=15, alt='increase') res2[['best.splits.molr']]
The rolr package provides three main functions, rsolr12,
rmolr, and rhier, for fast computation of
three-group optimal cutpoints using two simple OLR tests, a
modified OLR test, and a hierarchical method, respectively.
Pingping Qu and John Crowley
Crowley J., Mitchell A., Qu P., Morgan G. and Barlogie B. Optimal three group splits based on a survival outcome. In: Frontiers of Biostatistical Methods and Applications in Clinical Oncology, 2017.
Liu P. Y. and Tsai W. Y. A modified logrank test for censored survival data under order restrictions. Statistics and probablility Letters 41:57-63, 1999.
Liu P. Y., Tsai W. Y. and Wolf, M. Design and analysis for survival data under order restrictions with a modified logrank test. Statistics in medicine 17:1469-1479, 1998.
Crowley J., LeBlanc M., Gentleman R. and Salmon, S. Exploratory methods in survival analysis. In: IMS Laecture Notes 27:55-77, 1995.
LeBlanc M. and Crowley J. Survival trees by goodness of split. Journal of the American Statistical Association 88:457-467, 1993.
Liu P. Y., Greeen S., Wolf M. and Crowley J. Testing against ordered alternatives for censored survival data. Journal of the American Statistical Association 88:163-160, 1993.
Crowley J. Some extensions of the logrank test. In: Medical Informatics. D. A. B. Lindberg and P. L. Reicherts, Eds. Lecture Notes 4:213-223, 1979.
Using two simple ordered logrank tests (SOL-1 and SOL-2), the
rsolr12 function finds two optimal cutpoints to divide the entire
dataset into three groups based on a continuous covariate and a survival
outcome. It is a fast procedure that makes use of the running logrank test
(rlr) to improve on computing speed.
rsolr12(times, status, x, ns = 15, alt = "decrease", method = "approximate")rsolr12(times, status, x, ns = 15, alt = "decrease", method = "approximate")
times |
Survival outcome. |
status |
Censoring indicator which takes 1 when an event occurs at end of study and 0 otherwise. |
x |
A continuous covariate. |
ns |
Minimum number of subjects in each group after dichotomizing the covariate. |
alt |
A character that takes either |
method |
A character that takes either |
When the association is positive, that is, larger covariate
values leading to worse survival, and you enter alt = "decrease", the test
statistics will be positive, but if you enter trend = "increase" the
test statistics will be negative. Opposite is true when the association
is negative. You want to make sure to enter the option so that the
resulting test statistics are positive.
Returns a list with three elements, the first one being the test
statistics for all cutpoints considered (except the first and last ns
points), and the second and third elements being the best splits obtained
from using the SOL-1 and SOL-2 tests.
See main package help page.
library(rolr) ##### -------- Example 1 #simulate data with 2 underlying true cutpoints and hazard goes up as x goes up d=simdata(nn = 150, hr = c(1, 2, 3), hazard.func = "step", props=c(1/3, 1/3, 1/3), censoring.rate = 0) #using alt = 'decrease', the test statistics are positive, so it is good res=rsolr12(times=d$times, status=d$status, x=d$x, ns=15, alt='decrease') names(res) res[['best.splits.solr1']] res[['best.splits.solr2']] #do it again using alt = 'increase', now the test statistics are negative and #so the results are not right. So you have to switch back to alt='decrease' to #get positive statistics and the correct optimal cutpoints here. res2=rsolr12(times=d$times, status=d$status, x=d$x, ns=15, alt='increase') res2[['best.splits.solr1']] res2[['best.splits.solr2']] ##### -------- Example 2 #simulate data with true cutpoints and hazard goes down as covariate goes up d=simdata(nn = 150, hr = c(3, 2, 1), hazard.func = "step", props=c(1/3, 1/3, 1/3), censoring.rate = 0) #using alt = 'decrease', the test statistics are negative (so the results #are not right). res=rsolr12(times=d$times, status=d$status, x=d$x, ns=15, alt='decrease') res[['best.splits.solr1']] res[['best.splits.solr2']] #do it again using alt = 'increase', now it is right res2=rsolr12(times=d$times, status=d$status, x=d$x, ns=15, alt='increase') res2[['best.splits.solr1']] res2[['best.splits.solr2']]library(rolr) ##### -------- Example 1 #simulate data with 2 underlying true cutpoints and hazard goes up as x goes up d=simdata(nn = 150, hr = c(1, 2, 3), hazard.func = "step", props=c(1/3, 1/3, 1/3), censoring.rate = 0) #using alt = 'decrease', the test statistics are positive, so it is good res=rsolr12(times=d$times, status=d$status, x=d$x, ns=15, alt='decrease') names(res) res[['best.splits.solr1']] res[['best.splits.solr2']] #do it again using alt = 'increase', now the test statistics are negative and #so the results are not right. So you have to switch back to alt='decrease' to #get positive statistics and the correct optimal cutpoints here. res2=rsolr12(times=d$times, status=d$status, x=d$x, ns=15, alt='increase') res2[['best.splits.solr1']] res2[['best.splits.solr2']] ##### -------- Example 2 #simulate data with true cutpoints and hazard goes down as covariate goes up d=simdata(nn = 150, hr = c(3, 2, 1), hazard.func = "step", props=c(1/3, 1/3, 1/3), censoring.rate = 0) #using alt = 'decrease', the test statistics are negative (so the results #are not right). res=rsolr12(times=d$times, status=d$status, x=d$x, ns=15, alt='decrease') res[['best.splits.solr1']] res[['best.splits.solr2']] #do it again using alt = 'increase', now it is right res2=rsolr12(times=d$times, status=d$status, x=d$x, ns=15, alt='increase') res2[['best.splits.solr1']] res2[['best.splits.solr2']]
simdata is used to simulate survival data from an
exponential distribution.
When the hazard function is a step function, we assume 3 underlying groups
obtained by applying two cutpoints x1 and x2 to the covariate so that group
1 is x < x1, group 2 is x >= x1 and x < x2, and group 3
is x >= x2.
The hazard is a function of the covariate x simulated
from a uniform distribution from [0, 2]; it can be either
a linear function, a step function (with three groups), or a constant (in
which case no association exists between the covariate and survival).
simdata(nn = 300, const = 365, hr = c(1, 2, 3), hr.linear = 3, props = c(1/3, 1/3, 1/3), hazard.func = "step", censoring.rate = 0, seed = 1)simdata(nn = 300, const = 365, hr = c(1, 2, 3), hr.linear = 3, props = c(1/3, 1/3, 1/3), hazard.func = "step", censoring.rate = 0, seed = 1)
nn |
Sample size. |
const |
A constant that all of the hazard functions will be divided by. The bigger it is, the longer the survival times will be. Default is 365. |
hr |
A three-element vector representing the hazards for each of the
groups 1 to 3 when the |
hr.linear |
A scalar representing the hazard ratio when the covariate
increases by one unit. This is used with |
props |
A three-element vector representing the proportions of groups
1 to 3 when |
hazard.func |
A character that can take either |
censoring.rate |
The amount of censoring desired. Default = 0. |
seed |
The random seed used to generate the data. Default = 1. |
A data frame with survival times (times), censoring indicator
(status), covariate (x), three groups obtained by cutting the covariate
if hazard.func = "step" (x3), and censoring rate (censoring.rate).
library(rolr) #simulate survival with a step hazard function d1=simdata(nn = 150, hr = c(1, 2, 3), props = c(1/3, 1/3, 1/3), hazard.func = "step", censoring.rate = 0) head(d1) #simulate survival with a linear hazard function d2=simdata(nn = 150, hr.linear = 2, hazard.func = "linear", censoring.rate = 0) head(d2) #simulate survival with no association with the covariate d3=simdata(nn = 150, hazard.func = "none", censoring.rate = 0) head(d3)library(rolr) #simulate survival with a step hazard function d1=simdata(nn = 150, hr = c(1, 2, 3), props = c(1/3, 1/3, 1/3), hazard.func = "step", censoring.rate = 0) head(d1) #simulate survival with a linear hazard function d2=simdata(nn = 150, hr.linear = 2, hazard.func = "linear", censoring.rate = 0) head(d2) #simulate survival with no association with the covariate d3=simdata(nn = 150, hazard.func = "none", censoring.rate = 0) head(d3)