oceTest {oceCens}

Tests for ordered composite endpoints with censoring.

Description

An ordered composite endpoint (oce) is a way of ranking responses by ordering several types of responses by order of importance. Rank by the most important response, then break ties with the next most important, and so on. The tests here are based on two sample tests. Let Y0 and Y1 be the oce score in the control arm and treatment arm, respectively. Then here we estimate both the win ratio (WR), P[Y1>Y0]/P[Y0>Y1], or the Mann-Whitney parameter, P[Y1>Y0] + (1/2) Pr[Y1=Y0]. Different methods are used to estimate those parameters, and inferences are done by bootstrap percentile methods.

Usage

oceTest(
  data,
  oceTime,
  oceStatus,
  group,
  id = NULL,
  oceNames = NULL,
  method = c("all", "npmle", "coxph", "simple"),
  ciMethod = c("WLW", "bootstrap"),
  conf.int = FALSE,
  conf.level = 0.95,
  nBoot = 2000,
  plot = FALSE,
  ...
)

Arguments

data

data.frame name, must have variables with names listed in oceTime, oceStatus, group

oceTime

character vector with ordered (primary is first) names of different time-to-event variables.

oceStatus

character vector with ordered names of status (0=censored, 1=event) variables.

group

name of group variable.

id

name of ID variable, NULL creates integer IDs.

oceNames

long names of ordered endpoints, NULL uses oceTime.

method

Estimation method, one of 'all', 'npmle', 'coxph' or 'simple'. Default is 'all' which calculates all of the three methods. See details.

ciMethod

confidence interval method, default is 'bootstrap'

conf.int

Logical, should confidence intervals be calculated.

conf.level

confidence level.

nBoot

number of bootstrap replicates (ignored if conf.int=FALSE).

plot

logical, plot oce score by group as survival functions (NPMLE version, except if method='coxph'). For more control over those plots see either plot.oceNPMLE or plot.oceCoxph.

...

holder space for future arguments.

Details

This idea is to stack the time to first event for the k different types of events. So if TAU is the maximum time that any individual is in the study, then the primary type of event has scores that fall into (0,TAU], the secondary type has scores that fall into (TAU,2*TAU], and so on. Then we rank by the primary type (e.g., death), but if there are many ties in the primary type (e.g., many that did not die during the study), then we break ties by the secondary type of event, and so on.

The difficulty is when there is censoring in time, because that imposes interval censoring on the score scale. This can be handled with interval censoring methods (although in a non-standard way). The 'npmle' method calculates a nonparametric maximum likelihood estimate of the 'survival' distribution of the ordering score for each arm, then gets the estimates by numeric integration. The 'coxph' method uses an interval censored proportional hazards model treating the oce scores as time using coxph from the survival R package. The 'simple' method uses part of the 'coxph' method together with a more simple estimator. Each method produces a win ratio (P[Y1>Y0]/P[Y0>Y1]) and a Mann-Whitney (P[Y1>Y0] + (1/2) Pr[Y1=Y0]) estimate. Details are given in Follmann, et al (2020).

When ciMethod="bootstrap" inferences are done by nonparametric bootstrap percentile method (see percci) in order to account for the correlation among the different types of responses. When ciMethod="WLW" and method="coxph", then the win ratio is calculated by the Cox model with the standard errors of the log(HR) or log(WR) calculated by the robust sandwich method suggested by Wei, Lin, and Weissfeld (1989). P-values are all two-sided and test the null hypothesis of no difference between the arms (for the win ratio, the null value is 1, while for the MW the null value is 0).

For access to the coxph output see oceCoxph, or for the NPMLE output see oceNPMLE.

Value

If conf.int=FALSE then a vector of estimates determined by method results. If conf.int=TRUE then a matrix is returned with a row for each estimate, and 4 columns for the Estimate, lower confidence limit, upper confidence limit, and two-sided p-value.

References

Follmann, D., Fay, M. P., Hamasaki, T., and Evans, S. (2020). Analysis of ordered composite endpoints. Statistics in Medicine, 39(5), 602-616.

Wei, L. J., Lin, D. Y., & Weissfeld, L. (1989). Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. Journal of the American statistical association, 84(408), 1065-1073.

Examples

data(simScenario5)
oceTest(data=simScenario5, oceTime=c("T1","T2","T3"),
 oceStatus=c("I1","I2","I3"), group=c("Z"), id = "PATID",
 oceNames = c("Death","Stroke/MI","Bleed"), method=c("all"))