riskRegression (version 2018.04.21)

predict.CauseSpecificCox: Predicting absolute risk from cause-specific Cox models

Description

Apply formula to combine two or more Cox models into absolute risk (cumulative incidence function)

Usage

# S3 method for CauseSpecificCox
predict(object, newdata, times, cause,
  landmark = NA, keep.times = 1L, keep.newdata = 1L, keep.strata = 1L,
  se = FALSE, band = FALSE, iid = FALSE, average.iid = FALSE,
  nsim.band = 10000, log.transform = TRUE, product.limit = TRUE,
  conf.level = 0.95, store.iid = "full", ...)

Arguments

object

The fitted cause specific Cox model

newdata

A data frame containing the values of the variables in the right hand side of 'coxph' for each subject.

times

Vector of times at which to return the estimated absolute risk.

cause

Identifies the cause of interest among the competing events.

landmark

the starting time for the computation of the cumulative risk

keep.times

Logical. If TRUE add the evaluation times to the output.

keep.newdata

Logical. If TRUE add the value of the covariates used to make the prediction in the output list.

keep.strata

Logical. If TRUE add the value of the strata used to make the prediction in the output list.

se

Logical. If TRUE add the standard errors to the output.

band

Logical. If TRUE add the confidence band to the output.

iid

Logical. If TRUE add the influence function to the output.

average.iid

Logical. If TRUE add the average of the influence function over newdata to the output.

nsim.band

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

log.transform

Should the confidence intervals/bands be computed on the log(-log) scale and be backtransformed. Otherwise they are computed on the original scale and truncated (if necessary).

product.limit

Logical. If true the survival is computed using the product limit estimator. Otherwise the exponential approximation is used (i.e. exp(-cumulative hazard)).

conf.level

Level of confidence.

store.iid

Implementation used to estimate the influence function and the standard error. Can be "full" or "minimal".

...

not used

Value

A list containing:

• absRisk: (data table) the predictions for each subject (in rows) and each time (in columns).

• absRisk.se: (data table) the standard errors of the predictions.

• (absRisk.iid): (array) the value of the influence of each subject used to fit the object (dim 3) for each subject in newdata (dim 1) and each time (dim 2).

• (absRisk.average.iid): (matrix) the average value of the influence over the subjects in newdata, for each subject used to fit the object (dim 1) and each time (dim 2).

• times: (vector) the evaluation times.

Details

This function computes the absolute risk as given by formula 2 of (Ozenne et al., 2017). Confidence intervals and confidence bands can be computed using a first order von Mises expansion. See the section "Construction of the confidence intervals" in (Ozenne et al., 2017).

When setting log.transform to TRUE, the standard error that is returned is before back-transformation to the original scale.

A detailed explanation about the meaning of the argument store.iid can be found in (Ozenne et al., 2017) Appendix B "Saving the influence functions".

Note: for Cox regression models with time varying covariates it does not make sense to use this function, because the predicted risk has to be a measurable function of the data available at the time origin.

References

Brice Ozenne, Anne Lyngholm Sorensen, Thomas Scheike, Christian Torp-Pedersen and Thomas Alexander Gerds. riskRegression: Predicting the Risk of an Event using Cox Regression Models. The R Journal (2017) 9:2, pages 440-460.

Examples

# NOT RUN {
library(survival)

## generate data
set.seed(5)
d <- sampleData(80,outcome="comp") ## training dataset
nd <- sampleData(4,outcome="comp") ## validation dataset
d$time <- round(d$time,1) ## create tied events
ttt <- sort(sample(x = unique(d$time), size = 10))

## estimate a CSC model based on the coxph function
CSC.fit <- CSC(Hist(time,event)~ X3+X8, data=d, method = "breslow")

## compute the absolute risk of cause 1, in the validation dataset
## at time 1:10
CSC.risk <-  predict(CSC.fit, newdata=nd, times=1:10, cause=1)
CSC.risk

## add the standard error/confidence intervals
## (computed on the log log scale and backtransformed)
CSC.riskSE <-  predict(CSC.fit,newdata=nd,times=1:10,cause=1,se=TRUE,
                        log.transform = TRUE)
as.data.table(CSC.riskSE)[1:5]
exp(-exp(
 log(-log(CSC.riskSE$absRisk)) - 1.96 * CSC.riskSE$absRisk.se
))

## extract the iid for the absolute risk
CSC.iid <- predict(CSC.fit, newdata = d, se = TRUE,
                   cause = 1, times = ttt[1], iid = TRUE,
                   log.transform = FALSE)
rowMeans(CSC.iid$absRisk.iid[,1,]) ## the iid decomposition has 0 expectation
sqrt(rowSums(CSC.iid$absRisk.iid[,1,]^2))[1:5]
as.data.table(CSC.iid)[1:5]

## same but the iid decomposition is averaged over the patients
CSC.aviid <- predict(CSC.fit, newdata = d,
                   cause = 1, times = ttt[1],
                   average.iid = TRUE,
                   log.transform = FALSE)
CSC.aviid$absRisk.average.iid[1:5,]
colMeans(CSC.iid$absRisk.iid[,1,1:5])

## compute absolute risks with CI for cause 2
## (without displaying the value of the covariates)
predict(CSC.fit,newdata=nd,times=1:10,cause=2,se=TRUE,
        log.transform = TRUE, keep.newdata = FALSE)

## other example
library(survival)
CSC.fit.s <- CSC(list(Hist(time,event)~ strata(X1)+X2+X9,
 Hist(time,event)~ X2+strata(X4)+X8+X7),data=d, method = "breslow")
predict(CSC.fit.s,cause=1,times=ttt,se=1L) ## note: absRisk>1 due to small number of observations

## using the cph function instead of coxph
CSC.cph <- CSC(Hist(time,event)~ X1+X2,data=d, method = "breslow", fitter = "cph")#' 
predict(CSC.cph, newdata = d, cause = 2, times = ttt)

## landmark analysis
T0 <- 1
predCSC_afterT0 <- predict(CSC.fit, newdata = d, cause = 2, times = ttt[ttt>T0], landmark = T0)
predCSC_afterT0

# }