Non-Markov multi-state survival analysis with complex censoring: A structured synthesis of models, estimators, and applications

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.