Inference for Treatment Effects on Terminal and Non-Terminal Events under Competing Risks

Description

This package implements procedures for treatment effect inference on a terminal event and a non-terminal event. It estimates the effect size using either event-specific win ratios, RICH or RITCH, and the corresponding confidence intervals are provided. For easy comparison, results for the win ratio (Finkelstein and Schoenfeld 1999, Pocock et al. 2012; Bebu and Lachin 2016) are also included. Moreover, testing procedures are provided for the global null hypothesis of no treatment effect on either event. Additionally, it offers confidence intervals for linear combinations of the effect size estimates using fixed or data-driven weights. Finite-sample correction and transformations are used to improve type I error control in moderate samples. For further details, see Yang and Troendle (2021), Yang et al. (2022), and Yang (2025).

Details

Value

No return value, called for side effects.

Author(s)

Daewoo Pak and Song Yang \ Maintainer: Daewoo Pak dpak@yonsei.ac.kr

References

Yang, S. (2025). Testing and Estimation of Treatment Effects in Clinical Trials for Terminal and Non-Terminal Events Subject to Competing Risks. Statistics in Medicine. doi:10.1002/sim.70205

Yang, S., Troendle, J., Pak, D., & Leifer, E. (2022). Event‐specific win ratios for inference with terminal and non‐terminal events. Statistics in Medicine, 41(7), 1225–1241. doi:10.1002/sim.9266

Yang, S., & Troendle, J. (2021). Event-specific win ratios and testing with terminal and non-terminal events. Clinical Trials, 18(2), 180–187. doi:10.1177/1740774520972408

Bebu, I., & Lachin, J. M. (2016). Large sample inference for a win ratio analysis of a composite outcome based on prioritized components. Biostatistics, 17(1), 178–187. doi:10.1093/biostatistics/kxv032

Pocock, S. J., Ariti, C. A., Collier, T. J., & Wang, D. (2012). The win ratio: a new approach to the analysis of composite endpoints in clinical trials based on clinical priorities. European Heart Journal, 33(2), 176–182. doi:10.1093/eurheartj/ehr352

Finkelstein, D. M., & Schoenfeld, D. A. (1999). Combining mortality and longitudinal measures in clinical trials. Statistics in Medicine, 18(11), 1341–1354. doi:10.1002/(SICI)1097-0258(19990615)18:11<1341::AID-SIM129>3.0.CO;2-7

See Also

tnt.analysis

Examples

# Example: Treatment effect analysis using colon cancer trial data
data("colon_wr")

yh   <- colon_wr$yh     # non-terminal event time
hcen <- colon_wr$hcen   # censoring indicator for non-terminal event
yd   <- colon_wr$yd     # terminal event time
dcen <- colon_wr$dcen   # censoring indicator for terminal event
z    <- colon_wr$z      # treatment group (0 = control, 1 = treatment)

# Run the analysis
# The output includes test statistics and confidence intervals
# for RICH and RITCH measures (among others)
res <- tnt.analysis(
  yh, hcen, yd, dcen, z,
  lin   = c(0.5, 0.5),
  alpha = 0.05
)

# Display results
print(res)

Internal functions for the TxEffectsSurvival package

Description

This page documents internal functions of the TxEffectsSurvival package. These functions are not intended to be called directly by users, but rather support the implementation of user-facing functions such as tnt.analysis.

Value

No return value; these functions are called for their side effects or to support higher-level routines.

Colon cancer trial example data (Obs vs Lev+5FU) for semi-competing risks analyses

Description

A derived dataset from survival::colon, restricted to subjects in the Obs and Lev+5FU arms (excluding Lev). It is organized for semi-competing risks analyses with a non-terminal event (recurrence) and a terminal event (death). Each row corresponds to one subject.

Usage

data("colon_wr")

Format

A data frame with one row per subject and the following variables:

yh

Time to non-terminal event (recurrence).

hcen

Status for the non-terminal event: 1 = recurrence observed, 0 = censored.

yd

Time to terminal event (death).

dcen

Status for the terminal event: 1 = death observed, 0 = censored.

z

Treatment indicator: 0 = Obs, 1 = Lev+5FU.

Details

The source data are survival::colon. We first restrict to rx != "Lev" and then, per subject, extract event time/status for recurrence (etype = 1) and death (etype = 2). The original treatment factor is recoded to a binary indicator z \in \{0,1\}.

Source

survival package, dataset colon.

Examples

# Load example dataset
data("colon_wr")

# Contents of colon_wr:
#   yh    : Time to non-terminal event (recurrence)
#   hcen  : Event indicator for recurrence (1 = recurrence, 0 = censored)
#   yd    : Time to terminal event (death)
#   dcen  : Event indicator for death (1 = death, 0 = censored)
#   z     : Treatment group (0 = Obs, 1 = Lev+5FU)

Inference for Treatment Effects on Terminal and Non-Terminal Events under Competing Risks

Description

tnt.analysis provides several procedures for evaluating treatment effects on terminal and non-terminal events in the presence of competing risks. Based on the methodologies proposed in Yang et al. (2022) and Yang (2025), the function implements a variety of robust and flexible semiparametric and nonparametric estimation and hypothesis testing procedures that accommodate complex event-time structures with semi-competing risks.

Specifically, the function primarily provides the following inferential procedures for estimation and hypothesis testing:

• Event-Specific Win Ratios (ESWR): Event-specific win ratios obtained separately for terminal and non-terminal events, enabling powerful and interpretable global tests (linear combination, maximum, and \chi^2), as proposed by Yang and Troendle (2021).

• Log-Rank Generalized Rank Estimator (LRGRE): A generalized rank-based estimator extending the log-rank test to semi-competing risks settings, providing robust group comparisons for non-terminal and terminal events.

• Integrated Cumulative Hazard (ICH): A nonparametric estimator calculated as the ratio of integrated cause-specific hazard in the treatment group over that in the control group. Values less than 1 indicate a beneficial effect. Robust to violations of proportional hazards.

• Integrated Transformed Cumulative Hazard (ITCH): A stabilized version of ICH using a monotone transformation \Phi(t)=1 - \exp(-t) to improve performance under heavy censoring or non-PH conditions.

• Linear Combination Tests: Global tests that combine event-specific estimates using either user-specified or data-adaptive weights. The default weight is l = (0.5, 0.5). Applicable to ESWR, LRGRE, ICH, and ITCH.

• Maximum Test: A global test based on the maximum of event-specific test statistics, which rejects the global null if and only if at least one event-specific estimate is significant. It ensures coherency and tends to offer greater power when treatment effects differ across event types.

• Test of Proportional Hazards: A diagnostic test for assessing whether the proportional hazards assumption holds for the terminal event and the non-terminal event.

• Test of Equal Hazard Ratios: A diagnostic test for evaluating whether the hazard ratios for the terminal and non-terminal events are equal, assuming proportional hazards hold for both.

Usage

## Default S3 method:
tnt.analysis(nonterm_time, nonterm_event, term_time, term_event, z,
lin = c(0.5, 0.5), alpha = 0.05, repnum = 1e6, tau_r = 0.9, ...)

Arguments

Details

These methods follow the statistical inference framework proposed by Yang (2025), without relying on parametric assumptions or restrictive model specifications. They are well-suited for semi-competing risks settings, where non-terminal events (e.g., hospitalizations) may be censored by terminal events (e.g., death), and both types are clinically important.

Global tests—including the linear combination, maximum, and \chi^2 tests—offer flexible approaches to detecting treatment effects on either or both event types. Inference remains valid regardless of whether the proportional hazards assumption holds, with ICH and ITCH estimators providing additional robustness under non-proportional hazards.

In the implementation, the total trial duration is defined as \tau = \max(\{yh, yd\}) + 0.001. This upper bound is applied in the estimation of both ESWR and LRGRE. For ICH and ITCH, the analysis window is further truncated to \tau_0 = \tau \times \texttt{tau\_r}, where tau_r is a user-defined proportion (default = 0.9). Log transformations are used for the data-driven test, while log-log transformations are used for confidence intervals for non-terminal and terminal events. To improve finite-sample performance, a small-sample correction factor (cn) is applied to standard errors and test statistics. Specifically, cn = 1 + 15 / \max(n, 100) is used for the chi-square test and the maximum test, while cn = 1 + 10 / \max(n, 100) is used for the data-driven test and the corresponding confidence intervals.

To apply the package for univariate survival data analysis, see Example 2 in the Examples section below.

Value

An object of class "tnt.analysis", which is a named list containing the following elements:

References

Yang, S. (2025). Testing and Estimation of Treatment Effects in Clinical Trials for Terminal and Non-Terminal Events Subject to Competing Risks. Statistics in Medicine. doi:10.1002/sim.70205

Yang, S., Troendle, J., Pak, D., & Leifer, E. (2022). Event‐specific win ratios for inference with terminal and non‐terminal events. Statistics in Medicine, 41(7), 1225–1241. doi:10.1002/sim.9266

Examples

# Example 1: joint analysis of non-terminal and terminal events
data("colon_wr")

yh   <- colon_wr$yh     # non-terminal event time
hcen <- colon_wr$hcen   # censoring indicator for non-terminal event
yd   <- colon_wr$yd     # terminal event time
dcen <- colon_wr$dcen   # censoring indicator for terminal event
z    <- colon_wr$z      # treatment group (0 = control, 1 = treatment)

# Run the analysis
# The output includes test statistics and confidence intervals
# for RICH and RITCH measures (among others)
res <- tnt.analysis(
  yh, hcen, yd, dcen, z,
  lin   = c(0.5, 0.5),
  alpha = 0.05
)

# Display results
print(res)

# Example 2: univariate analysis (workaround)
# tnt.analysis is primarily designed for joint analysis of non-terminal and terminal events,
# but univariate analysis can be conducted by assigning identical inputs to both.

res <- tnt.analysis(yh, hcen, yh, hcen, z)
res$global.tests$lincomb
res$ci.results$lincomb