riskRegression (version 2018.04.21)

influenceCoxTest: Influence test [Experimental!!]

Description

Compare two estimates using their influence function

Usage

influenceCoxTest(object, ...)
# S3 method for list
influenceCoxTest(object, newdata, times, type, cause, ...)
# S3 method for default
influenceCoxTest(object, object2, tanh.transform = FALSE,
  conf.level = 0.95, nsim.band = 10000, ...)

Arguments

object

either a list of models or an object of class predictCox or predictCSC.

...

additional arguments to be passed to lower level functions.

newdata

A data.frame or data.table containing the values of the predictor variables defining subject specific predictions.

times

Time points at which to evaluate the predictions.

type

the type of predicted value.

cause

Identifies the cause of interest among the competing events.

object2

same as predict1 but for another model.

tanh.transform

Should the comparison be made on the arc-tangent scale or on the original scale ?

conf.level

Level of confidence.

nsim.band

the number of simulations used to compute the quantiles for the confidence bands.

Examples

# NOT RUN {
library(lava)
library(survival)
n <- 100

#### Under H1
set.seed(1)
newdata <- data.frame(X1=1)

## simulate non proportional hazard using lava
m <- lvm()
regression(m) <- y ~ 1
regression(m) <- s ~ exp(-2*X1)
distribution(m,~X1) <- binomial.lvm()
distribution(m,~cens) <- coxWeibull.lvm(scale=1)
distribution(m,~y) <- coxWeibull.lvm(scale=1,shape=~s)
eventTime(m) <- eventtime ~ min(y=1,cens=0)
d <- as.data.table(sim(m,n))
setkey(d, eventtime)

## fit cox models
m.cox <- coxph(Surv(eventtime, status) ~ X1, 
               data = d, y = TRUE, x = TRUE)

mStrata.cox <- coxph(Surv(eventtime, status) ~ strata(X1), 
                     data = d, y = TRUE, x = TRUE)

## compare models
# one time point
influenceCoxTest(list(m.cox, mStrata.cox), tanh.transform = FALSE,
                 type = "survival", newdata = newdata, times = 0.5)
influenceCoxTest(list(m.cox, mStrata.cox), tanh.transform = TRUE,
                 type = "survival", newdata = newdata, times = 0.5)
                                 
# several timepoints
influenceCoxTest(list(m.cox, mStrata.cox), tanh.transform = TRUE,
                 type = "survival", newdata = newdata, times = seq(0.1,1,by=0.1))
influenceCoxTest(list(m.cox, mStrata.cox), tanh.transform = FALSE,
                 type = "survival", newdata = newdata, times = seq(0.1,1,by=0.1))

#### Under H0 (Cox) ####
set.seed(1)
## simulate proportional hazard using lava
m <- lvm()
regression(m) <- y ~ 1
distribution(m,~X1) <- binomial.lvm()
distribution(m,~cens) <- coxWeibull.lvm()
distribution(m,~y) <- coxWeibull.lvm()
eventTime(m) <- eventtime ~ min(y=1,cens=0)
d <- as.data.table(sim(m,n))
setkey(d, eventtime)

## fit cox models
Utime <- sort(unique(d$eventtime))
m.cox <- coxph(Surv(eventtime, status) ~ X1, 
               data = d, y = TRUE, x = TRUE)

mStrata.cox <- coxph(Surv(eventtime, status) ~ strata(X1), 
                     data = d, y = TRUE, x = TRUE)

p.cox <- predictCox(m.cox, newdata = newdata, time = Utime, type = "survival")
p.coxStrata <- predictCox(mStrata.cox, newdata = newdata, time = Utime, type = "survival")
autoplot(p.cox)
autoplot(p.coxStrata)
 
## compare models
influenceCoxTest(list(m.cox, mStrata.cox), tanh.transform = TRUE,
                 type = "survival", newdata = newdata, times = Utime[1:(n-10)])
influenceCoxTest(list(m.cox, mStrata.cox), tanh.transform = FALSE,
                 type = "survival", newdata = newdata, times = Utime[1:(n-10)])

#### Under H0 (CSC) ####
set.seed(1)
ff <- ~ f(X1,2) + f(X2,-0.033)
ff <- update(ff, ~ .+ f(X3,0) + f(X4,0) + f(X5,0))
ff <- update(ff, ~ .+ f(X6,0) + f(X7,0) + f(X8,0) + f(X9,0))
d <- sampleData(n, outcome = "competing.risk", formula = ff)
d[,X1:=as.numeric(as.character(X1))]
d[,X2:=as.numeric(as.character(X2))]
d[,X3:=as.numeric(as.character(X3))]
d[,X4:=as.numeric(as.character(X4))]
d[,X5:=as.numeric(as.character(X5))]
setkey(d, time)

Utime <- sort(unique(d$time))

## fit cox models
m.CSC <- CSC(Hist(time, event) ~ X1 + X2, data = d)
mStrata.CSC <- CSC(Hist(time, event) ~ strata(X1) + X2 + X3, data = d)

## compare models
influenceCoxTest(list(m.CSC, mStrata.CSC), tanh.transform = TRUE,
                 cause = 1, newdata = data.frame(X1=1,X2=1,X3=1), times = Utime[1:20])
influenceCoxTest(list(m.CSC, mStrata.CSC), tanh.transform = FALSE,
                 cause = 1, newdata = data.frame(X1=1,X2=1,X3=1), times = Utime[1:20]) 

# }