safeLogrankTest {safestats}

Safe Logrank Test

Description

A safe test to test whether there is a difference between two survival curves. This function builds on the Mantel-Cox version of the logrank test.

Usage

safeLogrankTest(
  formula,
  designObj = NULL,
  ciValue = NULL,
  data = NULL,
  survTime = NULL,
  group = NULL,
  pilot = FALSE,
  exact = TRUE,
  computeZ = TRUE,
  ...
)

safeLogrankTestStat(
  z,
  nEvents,
  designObj,
  ciValue = NULL,
  dataNull = 1,
  sigma = 1
)

Arguments

formula

a formula expression as for other survival models, of the form Surv(time, status) ~ groupingVariable, see Surv for more details.

designObj

a safe logrank design obtained from designSafeLogrank.

ciValue

numeric, represents the ciValue-level of the confidence sequence. Default ciValue=NULL, and ciValue = 1 - alpha, where alpha is taken from the design object.

data

an optional data frame in which to interpret the variables occurring in survTime and group.

survTime

an optional survival time object of class 'Surv' created with Surv, or a name of a column in the data set of class 'Surv'. Does not need specifying if a formula is provided, therefore set to NULL by default.

group

an optional factor, a grouping variable. Currently, only two levels allowed. Does not need specifying if a formula is provided, therefore set to NULL by default.

pilot

a logical indicating whether a pilot study is run. If TRUE, it is assumed that the number of samples is exactly as planned. The default null h0=1 is used, alpha=0.05, and alternative="twoSided" is used. To change these default values, please use designSafeLogrank.

exact

a logical indicating whether the exact safe logrank test needs to be performed based on the hypergeometric likelihood. Default is TRUE, if FALSE then the safe z-test (for Gaussian data) applied to the logrank z-statistic is used instead.

computeZ

logical. If TRUE computes the logrank z-statistic. Default is TRUE.

...

further arguments to be passed to or from methods.

z

numeric representing the observed logrank z statistic.

nEvents

numeric > 0, observed number of events.

dataNull

numeric > 0, the null hypothesis corresponding to the z statistics. By default dataNull = 1 representing equality of the hazard ratio.

sigma

numeric > 0, scaling in the data.

Value

Returns an object of class 'safeTest'. An object of class 'safeTest' is a list containing at least the following components:

statistic

the value of the summary, i.e., z-statistic or the e-value.

nEvents

The number of observed events.

eValue

the e-value of the safe test.

confSeq

An anytime-valid confidence sequence.

estimate

To be implemented: An estimate of the hazard ratio.

testType

"logrank".

dataName

a character string giving the name(s) of the data.

designObj

an object of class "safeDesign" obtained from designSafeLogrank.

sumStats

a list containing.the time of events, the progression of the risk sets and events.

call

the expression with which this function is called.

Functions

• safeLogrankTestStat(): Safe Logrank Test based on Summary Statistic Z All provided data (i.e., z-scores) are assumed to be centred on a hazard ratio = 1, thus, log(hr) = 0 , and the proper (e.g., hypergeometric) scaling is applied to the data, so sigma = 1. The null hypothesis in the design object pertains to the population and is allowed to differ from log(theta) = 0.

Examples

# Example taken from survival::survdiff

designObj <- designSafeLogrank(hrMin=1/2)

ovData <- survival::ovarian
ovData$survTime <- survival::Surv(ovData$futime, ovData$fustat)

safeLogrankTest(formula=survTime~ rx, data=ovData, designObj=designObj)

safeLogrankTest(survTime=survTime, group=rx, data=ovData, designObj=designObj)

# Examples taken from coin::logrank_test
## Example data (Callaert, 2003, Tab. 1)
#'
callaert <- data.frame(
  time = c(1, 1, 5, 6, 6, 6, 6, 2, 2, 2, 3, 4, 4, 5, 5),
  group = factor(rep(0:1, c(7, 8)))
)

designObj <- designSafeLogrank(hrMin=1/2)

safeLogrankTest(survival::Surv(callaert$time)~callaert$group,
                designObj = designObj)

safeLogrankTest(survTime=survival::Surv(callaert$time),
                group=callaert$group, designObj = designObj)

result <- safeLogrankTest(survTime=survival::Surv(callaert$time),
                group=callaert$group, designObj = designObj)

result

##  Sequentially
# Greater
eValueGreater <- exp(cumsum(result$sumStats$logEValueGreater))
# Less
eValueLess <- exp(cumsum(result$sumStats$logEValueLess))

# twoSided
eValueTwoSided <- 1/2*eValueGreater+1/2*eValueLess

eValueTwoSided
result$eValue

###### Example switching between safe exact and safe Gaussian logrank test

designObj <- designSafeLogrank(0.8, alternative="less")

dat <- safestats::generateSurvData(300, 300, 2, 0.0065, 0.0065*0.8, seed=1)
survTime <- survival::Surv(dat$time, dat$status)

resultE <- safeLogrankTest(survTime ~ dat$group,
                           designObj = designObj)

resultG <- safeLogrankTest(survTime ~ dat$group,
                           designObj = designObj, exact=FALSE)

resultE
resultG

###### Example switching between safe exact and safe Gaussian logrank test other side

designObj <- designSafeLogrank(1/0.8, alternative="greater")

resultE <- safeLogrankTest(survTime ~ dat$group,
                           designObj = designObj)

resultG <- safeLogrankTest(survTime ~ dat$group,
                           designObj = designObj, exact=FALSE)

if (log(resultE$eValue) >= 0 && log(resultG$eValue) >= 0 )
  stop("one-sided wrong")