ROC-Based Methods for Comparing Survival Distributions with Right, Left, and Doubly Censored Data

Implements nonparametric and semiparametric methods for comparing two survival distributions under non-proportional hazards (non-PH) with right, left, or doubly censored data. The methods are based on the Receiver Operating Characteristic (ROC) curve length and its kernel-based estimate (Bantis et al. (2021) ) and the overlap coefficient (OVL) and its kernel-based estimate (Schmid and Schmidt (2006) ), as well as a new joint inference approach involving both the kernel-based ROC length and the kernel-based OVL. These methods do not require prior knowledge of the underlying non-PH pattern. The methods also accommodate the "last is censored" phenomenon for right-censored data by using flexible parametric approaches only for the portion of the tail of the distribution that corresponds to time values beyond the last observed event (see also Bantis et al. (2017) ). The analogous "first is censored" phenomenon is also accommodated for left-censored data.

ROCsurvcomp

Overview

ROCsurvcomp is an R package for comparing survival curves under non-proportional hazards (non-PH) using ROC-based methods. Traditional log-rank test may lose power when the proportional hazards assumption is violated. Other methods, such as the Fleming-Harrington (FH) family of weighted log-rank tests require prior knowledge of the underlying non-PH patterns, and incorrectly specified patterns may lead to a substantial loss of statistical power. This package provides alternative approaches for comparing survival curves based on ROC curve, without requiring prior knowledge of the underlying non-PH pattern, and can accommodate right, left, and doubly censored data.

Key Features

• Implements nonparametric and semiparametric kernel-based approaches for comparing two survival distributions
• Designed for handling non-proportional hazards settings
• Methods include:
  • ROC length-based test
  • Overlap coefficient (OVL)-based test
  • Joint ROC length-OVL-based test
• Supports right, left and doubly-censored survival data
• Permutation-based inference with two-sided hypothesis testing

Installation

You can install the package from GitHub:

# install.packages("remotes")    # if not installed
remotes::install_github("mmrahman13/ROCsurvcomp")

Usage

Basic Example

library(ROCsurvcomp)
library(PWEXP)

# Generating right-censored data with crossing survivals
set.seed(126)
n_trt <- 50
break_trt <- c(2, 4)
rate_trt <- c(log(2)/3, log(2)/7, log(2)/20)
rate.censor_trt <- c(log(2)/55, log(2)/62, log(2)/68)
event_trt <- PWEXP::rpwexp(n_trt, rate = rate_trt, breakpoint = break_trt)
censor_trt <- PWEXP::rpwexp(n_trt, rate = rate.censor_trt, breakpoint = break_trt)

n_ctrl <- 50
rate_ctrl <- log(2)/10
rate.censor_ctrl <- log(2)/58
event_ctrl <- rexp(n_ctrl, rate = rate_ctrl)
censor_ctrl <- rexp(n_ctrl, rate = rate.censor_ctrl)

# Observed time and censoring status (0 = event, 1 = right-censored)
time_trt <- pmin(event_trt, censor_trt)
status_trt <- ifelse(event_trt <= censor_trt, 0, 1)
time_ctrl <- pmin(event_ctrl, censor_ctrl)
status_ctrl <- ifelse(event_ctrl <= censor_ctrl, 0, 1)
time <- c(time_trt, time_ctrl)
status <- c(status_trt, status_ctrl)
group <- c(rep(1, n_trt), rep(2, n_ctrl))

# Run `surv.comp()` function
# Note: n_perm = 1000 is used here only for illustration purposes. Highly recommended n_perm to be set at 50,000 or more.
surv.comp(
  time = time,
  status = status,
  group = group,
  censor_type = "right",
  method = "joint_method",
  n_perm = 1000,
  progress = TRUE,
  plot = TRUE
)

Methodology

This package implements ROC-based approaches for comparing two survival curves:

• ROC Length: Measures separation between two distributions without relying on any stochastic ordering
• Overlap Coefficient (OVL): Quantifies the similarity between two distributions using the common area between two probability density functions
• Joint Test: Combines ROC length and OVL-based methods by constructing convex hull of the permuted samples based on their Euclidean distance from the origin.

These methods are especially useful when:

• The proportional hazards assumption is violated
• Treatment effects are not constant over time and no prior information about the pattern of effects is available
• Survival curves cross.

Authors

Mohammod Mahmudur Rahman
PhD Student, Department of Biostatistics & Data Science
University of Kansas Medical Center

Leonidas Bantis
Associate Professor, Department of Biostatistics & Data Science
University of Kansas Medical Center