confint.ate: Confidence Intervals and Confidence Bands for the Predicted...
In bozenne/riskRegressionLight: Light version of the package riskRegression

Description Usage Arguments Details Author(s) Examples

Confidence intervals and confidence Bands for the predicted absolute risk (cumulative incidence function).

## S3 method for class 'ate'
confint(object, parm = NULL, level = 0.95,
  nsim.band = 10000, meanRisk.transform = "none",
  diffRisk.transform = "none", ratioRisk.transform = "none",
  seed = NA, bootci.method = "perc", ...)

`object`	A `ate` object, i.e. output of the `ate` function.
`parm`	not used. For compatibility with the generic method.
`level`	[numeric, 0-1] Level of confidence.
`nsim.band`	[integer, >0]the number of simulations used to compute the quantiles for the confidence bands.
`meanRisk.transform`	[character] the transformation used to improve coverage of the confidence intervals for the mean risk in small samples. Can be `"none"`, `"log"`, `"loglog"`, `"cloglog"`.
`diffRisk.transform`	[character] the transformation used to improve coverage of the confidence intervals for the risk difference in small samples. Can be `"none"`, `"atanh"`.
`ratioRisk.transform`	[character] the transformation used to improve coverage of the confidence intervals for the risk ratio in small samples. Can be `"none"`, `"log"`.
`seed`	[integer, >0] seed number set when performing simulation for the confidence bands. If not given or NA no seed is set.
`bootci.method`	[character] Method for constructing bootstrap confidence intervals. Either "perc" (the default), "norm", "basic", "stud", or "bca".
`...`	not used.

Confidence bands and confidence intervals computed via the influence function are automatically restricted to the interval [0;1].

Confidence intervals obtained via bootstrap are computed using the boot.ci function of the boot package. p-value are obtained using test inversion method (finding the smallest confidence level such that the interval contain the null hypothesis).

Brice Ozenne

library(survival)
library(data.table)

## ## generate data ####
set.seed(10)
d <- sampleData(70,outcome="survival")
d[, X1 := paste0("T",rbinom(.N, size = 2, prob = c(0.51)))]
## table(d$X1)

#### stratified Cox model ####
fit <- coxph(Surv(time,event)~X1 + strata(X2) + X6,
             data=d, ties="breslow", x = TRUE, y = TRUE)

#### average treatment effect ####
fit.ate <- ate(fit, treatment = "X1", times = 1:3, data = d,
               se = TRUE, iid = TRUE, band = TRUE)
print(fit.ate, type = "meanRisk")

## manual calculation of se
dd <- copy(d)
dd$X1 <- rep(factor("T0", levels = paste0("T",0:2)), NROW(dd))
out <- predictCox(fit, newdata = dd, se = TRUE, times = 1:3, average.iid = TRUE)
term1 <- -out$survival.average.iid
term2 <- sweep(1-out$survival, MARGIN = 2, FUN = "-", STATS = colMeans(1-out$survival))
sqrt(colSums((term1 + term2/NROW(d))^2)) 

## note
out2 <- predictCox(fit, newdata = dd, se = TRUE, times = 1:3, iid = TRUE)
mean(out2$survival.iid[,1,1])
out$survival.average.iid[1,1]

## check confidence intervals (no transformation)
fit.ate$meanRisk[, .(lower = meanRisk + qnorm(0.025) * meanRisk.se,
                     upper = meanRisk + qnorm(0.975) * meanRisk.se)]

## add confidence intervals computed on the log-log scale
## and backtransformed
outCI <- confint(fit.ate,
                 meanRisk.transform = "loglog", diffRisk.transform = "atanh",
                 ratioRisk.transform = "log")
print(outCI, type = "meanRisk")

newse <- fit.ate$meanRisk[, meanRisk.se/(meanRisk*log(meanRisk))]
fit.ate$meanRisk[, .(lower = exp(-exp(log(-log(meanRisk)) - 1.96 * newse)),
                     upper = exp(-exp(log(-log(meanRisk)) + 1.96 * newse)))]