Interval-censored data frequently arise in survival analysis when the exact time of an event is unknown but is known to occur within a specific time interval. Traditional methods like the Kaplan-Meier estimator are inadequate for such data, necessitating specialized approaches. This paper presents an R library designed to handle interval-censored data, emphasizing the use of Turnbull’s estimator for nonparametric survival estimation. The package offers flexible functionalities, including the calculation of survival estimates, the generation of both static and interactive plots, and the construction of bootstrap-based confidence bands. Additionally, the library provides users with detailed outputs such as Turnbull intervals and their corresponding weights, which are instrumental in understanding the survival distribution and serve as an analogue to Kaplan-Meier weights in right-censored contexts. These weights enable the extension of survival analysis methods to more complex models, including multi-state frameworks. The practical utility of the library is demonstrated using real-world datasets, highlighting its potential to support advanced survival analysis and foster the development of new estimators beyond traditional survival probabilities.

We propose a new goodness-of-fit procedure designed to verify the reciprocal property that characterizes the fatigue-life or Birnbaum-Saunders (BS) distribution. Under this property, scaling a random variable that takes positive values by its median results in the same distribution as its reciprocal, a feature frequently encountered in reliability and survival studies. Our procedure employs total time on test (TTT) curves to compare the behavior of the observed data and its reciprocal counterpart, capturing both local and global discrepancies through supremum- and area-based statistics. We establish the theoretical validity of these statistics under mild assumptions, showing that they deliver accurate inference for moderate to large samples. Simulation evidence indicates that our TTT-based procedures are sensitive to subtle departures from log-symmetry, particularly when the distribution underlying the data has heavier or lighter tails than the assumed one. Illustrative real data examples further reveal how overlooking deviations from the reciprocal property can distort reliability estimates and predictions of failure times, showing the practical importance of the new goodness-of-fit procedure. Overall, our findings strengthen the BS framework and provide robust tools for model validation and selection when log-symmetric modeling assumptions are in place.

Reliable quantification of treatment benefit in late-phase clinical trials increasingly requires modeling patient histories that include progression, adverse events, and treat ment switches. Conventional multi-state analyses often invoke the Markov property and assume independent right censoring— conditions rarely satisfied in oncology, immunology, or cell-therapy programs, where intermediate events and informative dropout are common. This article presents a systematic review and bibliometric synthesis of 48 peer reviewed studies published through 11 June 2025 that (i) relax the Markov assumption and (ii) address complex observation schemes such as left truncation, interval censoring, or informative censoring, identified through Web of Science and Scopus searches following preferred reporting items for systematic reviews and meta-analyses 2020 guidelines. A recurring set of methodological strategies emerges across the literature, including semi-Markov transition-intensity models, illness–death and semi-competing risks frameworks, landmarking for dynamic prediction, and inverse-probability-of-censoring weighting. Estimation approaches range from nonparametric product integrals to semiparametric weighted likelihoods and Bayesian Markov chain Monte Carlo, with recent contributions exploring saddle-point approximations and subsampling for large-scale electronic health records. To complement this synthesis, we include a compact simulation contrasting baseline and landmark Aalen–Johansen estimators under semi-Markov dynamics with history-dependent censoring, and a bibliometric network analysis mapping collaboration patterns, thematic clusters, and structural gaps. The findings highlight the need for scalable, auditable software, robust diagnostics aligned with the International Council for Harmonization E9(R1) estimand framework (which links clinical trial objectives to precise statistical targets), and better integration of high-dimensional biomarkers; limitations include the English-language restriction and reliance on bibliometric metadata. Addressing these priorities may enhance both the methodological robustness and regulatory applicability of non-Markov survival models.

This paper focuses on the estimation of the conditional survival function in the presence of interval-censored data. While estimation is relatively straightforward for qualitative covariates using Turnbull’s estimator, the case of continuous covariates, particularly under interval censoring, poses additional methodological challenges. We describe existing kernel-based approaches, such as those using Nadaraya-Watson weights, applicable under right censoring. The main contribution of this work is the proposal of two novel methodologies tailored for estimating the conditional survival function when data are interval-censored. These methods use kernel weights and a modified EM algorithm to provide practical ways to solve this challenging problem.