riskRegression (version 2022.03.22)

anova.ate: Risk Comparison Over Time

Description

Comparison of risk differences or risk ratios over all timepoints.

Usage

# S3 method for ate
anova(
  object,
  allContrast = NULL,
  type = "diff",
  estimator = object$estimator[1],
  test = "CvM",
  transform = NULL,
  alternative = "two.sided",
  n.sim = 10000,
  print = TRUE,
  ...
)

Arguments

object

A ate object, i.e. output of the ate function.

allContrast

[matrix] contrast for which the risks should be compared. Matrix with two rows, the first being the sequence of reference treatments and the second the sequence of alternative treatments.

type

[character vector] the functionnal used to compare the risks: "diffRisk" or "ratioRisk".

estimator

[character] The type of estimator relative to which the comparison should be performed.

test

[character] The type of statistic used to compare the risks over times: "KM" (extremum risk), "CvM" (sum of squares of the risk), or "sum" (sum of the risks).

transform

[character] Should a transformation be used, e.g. the test is performed after log-transformation of the estimate, standard error, and influence function.

alternative

[character] a character string specifying the alternative hypothesis, must be one of "two.sided", "greater" or "less".

n.sim

[integer, >0] the number of simulations used to compute the p-values.

print

[logical] should the results be displayed?

...

Not used.

Details

Experimental!!!

Examples

library(survival)
library(data.table)

if (FALSE) {
## simulate data
set.seed(12)
n <- 200
dtS <- sampleData(n,outcome="survival")
dtS$X12 <- LETTERS[as.numeric(as.factor(paste0(dtS$X1,dtS$X2)))]
dtS <- dtS[dtS$X12!="D"]

## model fit
fit <- cph(formula = Surv(time,event)~ X1+X6,data=dtS,y=TRUE,x=TRUE)
seqTime <- 1:10
ateFit <- ate(fit, data = dtS, treatment = "X1", contrasts = NULL,
              times = seqTime, B = 0, iid = TRUE, se = TRUE, verbose = TRUE, band = TRUE)

## display
autoplot(ateFit)

## inference (two sided)
statistic <- ateFit$diffRisk$estimate/ateFit$diffRisk$se
confint(ateFit, p.value = TRUE, method.band = "bonferroni")$diffRisk
confint(ateFit, p.value = TRUE, method.band = "maxT-simulation")$diffRisk

anova(ateFit, test = "KS")
anova(ateFit, test = "CvM")
anova(ateFit, test = "sum")

## manual calculation (one sided)
n.sim <- 1e4
statistic <- ateFit$diffRisk[, estimate/se]
iid.norm <- scale(ateFit$iid$GFORMULA[["1"]]-ateFit$iid$GFORMULA[["0"]],
                  scale = ateFit$diffRisk$se)

ls.out <- lapply(1:n.sim, function(iSim){
iG <- rnorm(NROW(iid.norm))
iCurve <- t(iid.norm) %*% iG
data.table(max = max(iCurve), L2 = sum(iCurve^2), sum = sum(iCurve),
maxC = max(iCurve) - max(statistic),
L2C = sum(iCurve^2) - sum(statistic^2),
sumC = sum(iCurve) - sum(statistic),
sim = iSim)
})

dt.out <- do.call(rbind,ls.out)
dt.out[,.(max = mean(.SD$maxC>=0),
          L2 = mean(.SD$L2C>=0),
          sum = mean(.SD$sumC>=0))]

## permutation
n.sim <- 250
stats.perm <- vector(mode = "list", length = n.sim)
pb <- txtProgressBar(max = n.sim, style=3)
treatVar <- ateFit$variables["treatment"]

for(iSim in 1:n.sim){ ## iSim <- 1
iData <- copy(dtS)
iIndex <- sample.int(NROW(iData), replace = FALSE)
iData[, c(treatVar) := .SD[[treatVar]][iIndex]]

iFit <- update(fit, data = iData)
iAteSim <- ate(iFit, data = iData, treatment = treatVar,
               times = seqTime, verbose = FALSE)
iStatistic <- iAteSim$diffRisk[,estimate/se]
stats.perm[[iSim]] <- cbind(iAteSim$diffRisk[,.(max = max(iStatistic),
                                                L2 = sum(iStatistic^2),
                                                sum = sum(iStatistic))],
                            sim = iSim)
stats.perm[[iSim]]$maxC <- stats.perm[[iSim]]$max - max(statistic)
stats.perm[[iSim]]$L2C <- stats.perm[[iSim]]$L2 - sum(statistic^2)
stats.perm[[iSim]]$sumC <- stats.perm[[iSim]]$sum - sum(statistic)
setTxtProgressBar(pb, iSim)
}

dtstats.perm <- do.call(rbind,stats.perm)
dtstats.perm[,.(max = mean(.SD$maxC>=0),
                L2 = mean(.SD$L2C>=0),
                sum = mean(.SD$sumC>=0))]
}