{"id":"606af8b8-a3ea-45cd-8314-f7d514483bfd","arxiv_id":"2502.03479","paper_version":6,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A mostly tutorial and application paper claims semi-Markov models with the DSH estimator produce smoother transition probability curves than Aalen-Johansen in the EBMT stem cell transplant data, without quantitative validation.","lead":"This paper applies semi-Markov and Markov renewal models to stem cell transplant patient data, comparing two ways of estimating transition probabilities between clinical states. It reports that the semi-Markov approach with the Dabrowska-Sun-Horowitz estimator gives smoother curves, but the comparison is qualitative and no code is provided.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'smoother curves' claim is unsupported: it rests on visual inspection of four plots, with no quantitative smoothness metric, no uncertainty quantification, and no released code; a convolution artefact cannot be excluded.","rationale":"The reader's overall CONDITIONAL verdict is reasonable, but I do not share the specific weakest assumption about convolution truncation. For the progressive EBMT state graph, the renewal series R = sum Q^(p) is finite, so the Section 8.2 note about 'no change after three or four convolutions' likely reflects an exact zero tail rather than an unquantified approximation error. My concern is that the central empirical claim, DSH 'consistently yields smoother probability curves,' is supported only by visual inspection of four plots. The paper itself concedes in Section 5.2 that the smoothing effect lacks a formal theoretical justification, and Section 6.3 provides no quantitative smoothness metric, no uncertainty quantification, and no code. The four-way model/estimator comparison also creates a conceptual problem: 'Markov model with DSH' is not a well-defined estimator for a calendar-time Markov process unless time-homogeneity is assumed and stated. A quantitative smoothness metric with bootstrap confidence intervals, plus a simulation under a known Markov truth, would settle whether the apparent smoothness advantage is real, statistically meaningful, and attributable to the semi-Markov/DSH procedure rather than to estimator or plotting artifacts. Until that check is performed, the abstract's claim is not established, so the conditional verdict should remain unchanged.","tokens_in":26170,"tokens_out":14505,"duration_ms":146882,"concrete_test":"Release the code used to produce Figures 6-9. On a common calendar-time grid (e.g., days 0 to 6000 in steps of 30), compute a quantitative smoothness metric, such as total variation or the L1 norm of first differences, for the AJ and DSH estimated transition probability curves on the EBMT data, and construct bootstrap confidence intervals clustered by patient for the DSH-minus-AJ difference within the semi-Markov model. Then simulate data from a known Markov process and fit both estimators: if DSH is smoother than AJ under a known Markov truth, the claimed smoothing is an estimator artifact rather than a semi-Markov property; if the DSH-minus-AJ difference is not significantly positive in the semi-Markov EBMT comparison, the central claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"For the EBMT graph (TX to PLT/AE/Relapse/Death; PLT/AE to Rec&AE/Relapse/Death; Rec&AE to Relapse/Death; absorbing states), the process is progressive and the maximum path length is at most 3, so R = sum_p Q^(p) has finitely many nonzero terms. The Section 8.2 statement 'after three or four convolutions there is no change' corresponds to an exact zero tail, not a truncation error; the reader's specific concern does not land. The load-bearing problem is upstream. The paper's advertised finding that 'the DSH estimator consistently yields smoother probability curves' is established only by looking at Figures 6-9. Section 5.2 explicitly says this smoothness 'lacks a formal theoretical justification,' and Section 6.3 reports no quantitative smoothness metric, no confidence bands, no bootstrap intervals, and no code. Moreover, 'Markov model with the DSH estimator' is not a standard estimator of a calendar-time Markov process unless the Markov model is assumed time-homogeneous, which the paper never states. Without a reproducible, quantitative definition of smoothness and a significance statement, the claimed consistency of DSH smoothness could be a visual or plotting artifact (different time grids, jump locations, or line rendering), and the central claim would be unsupported. For the abstract's claim to hold, DSH must be measurably and reproducibly smoother, not merely appear so in two figures.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops and applies a Markov renewal proportional hazards model with the Dabrowska-Sun-Horowitz (DSH) estimator for transition probabilities, and compares it with Aalen-Johansen (AJ) estimation under Markov and semi-Markov assumptions. The methodological core is a review and reorganization of existing asymptotic theory, followed by a simulation study and an application to the EBMT hematopoietic stem cell transplantation dataset. The central empirical claim is that the DSH estimator consistently yields smoother transition probability curves than AJ, and that semi-Markov models delay absorption into absorbing states relative to Markov models. The paper also presents an appendix reorganizing the weak convergence proof for the regression coefficients and baseline cumulative hazards.","tokens_in":26433,"tokens_out":7490,"duration_ms":70012,"significance":"If the empirical claim were quantitatively supported, the paper would provide useful practical guidance for clinical multi-state modeling and would make a case for preferring semi-Markov models with the DSH estimator. The paper has clear strengths: it gives a comprehensive and readable review of Markov renewal theory, a transparent plug-in estimation framework, an explicit simulation algorithm, and a real-data application in a clinically important setting. It also candidly acknowledges limitations, including the lack of formal justification for the smoothing effect and the unquantified truncation error. However, the paper ships no code or machine-checked proofs, and its main advertised finding rests on visual inspection. The asymptotic results are largely borrowed from prior work by Dabrowska, Sun and Horowitz, Spitoni et al., and others, so the novel contribution is primarily expository and empirical rather than theoretical.","major_comments":[{"comment":"The central claim that \"the DSH estimator consistently yields smoother probability curves\" is not supported by any quantitative evidence. Section 6.3 reports only qualitative observations about Figures 6–9, and Section 5.2 explicitly concedes that the smoothing effect \"lacks a formal theoretical justification.\" To make the claim reproducible, the authors should define a smoothness metric (e.g., total variation, number of monotonicity changes, integrated squared second difference), report its value for each estimator, and provide pointwise confidence bands or bootstrap intervals for the transition probabilities. Without this, the apparent smoothness could be an artifact of plotting choices, different time grids, or visual perception.","section":"Abstract; §6.3, Figs. 6–9"},{"comment":"The four modeling approaches listed in Section 6.3 include \"a Markov model with the DSH estimator\" and \"a Semi-Markov model with the AJ estimator,\" but these combinations are not well defined. The DSH estimator in Eq. (15) targets transition probabilities of a Markov renewal/semi-Markov process, while the AJ estimator targets a Markov process. Applying DSH under a Markov assumption, or AJ under a semi-Markov assumption, is a model misspecification unless the intended data-generating model and the target estimand are explicitly stated. As written, the comparison confounds the choice of estimator with the choice of model, so the observed differences in smoothness and absorption timing cannot be attributed to the estimator alone.","section":"§6.3, Eqs. (10)–(15)"},{"comment":"The paper admits that the infinite renewal convolution bR = sum_p bQ^(p) is truncated after three or four convolutions and that \"theoretically, the error is still to be estimated.\" For the EBMT application, the state graph is progressive and the maximum path length is at most 3, so the tail is exactly zero there; the reader's truncation concern does not land for that dataset. However, the paper presents the truncation rule as a general computational strategy for Markov renewal processes without restricting to progressive graphs. Since recurrent states make the convolution sum genuinely infinite, the authors should either prove a finite-support condition, provide an explicit error bound, or clearly limit the method to progressive processes.","section":"§8.2, Eq. (15)"},{"comment":"The proof of Theorem 4.2 relies on Lemma 8.5, but the fourth-moment bound is not established. The function f(n,a)=4n^3-(6+12a)n^2+(4-12a+12a^2)n is claimed to be nonnegative after minimizing at a=(n+1)/2, yielding 4n^3-12n^2+n; this quantity is negative for small n (e.g., n=1 gives -7). The argument covers only n≥12 and leaves small jump counts untreated. In addition, the proof of Theorem 4.3 is only a statement that Hadamard differentiability \"can be verified,\" with no detailed verification. Since the abstract claims to show weak convergence of the estimator, the manuscript should either complete the missing cases and verification, or explicitly identify Theorem 4.3 as a cited result from Dabrowska (1995) and Spitoni et al. (2012).","section":"§8.5, Lemma 8.5 and Theorem 4.3"}],"minor_comments":[{"comment":"The expression bP(s,t)=bP(0,t)/bP(0,s) is mathematically imprecise because transition probability matrices do not commute; the correct Markov expression is P(0,t)P(0,s)^{-1} or, better, the product integral over (s,t]. Please revise the notation to avoid ambiguity.","section":"§8.3.1"},{"comment":"Only the semi-Markov DSH model's coefficient estimates are reported. For a fair comparison of the four approaches, the authors should report coefficient estimates and standard errors for all fitted models, or at least state explicitly why only one model's coefficients are shown.","section":"Table 3, §6.3"},{"comment":"The title \"Markov Renewal Proportional Hazards is All You Need\" and the abstract's language \"we demonstrate\" overstate the evidence, given the paper's own admissions in §5.2 and §8.2 that the smoothing effect has no formal justification and the truncation error is unquantified. More cautious wording would better match the manuscript's contributions.","section":"Title and abstract"},{"comment":"Since the EBMT state graph is progressive and has maximum path length 3, the statement \"after three or four convolutions there is no change in the estimate\" is exact for that dataset, not a truncation approximation. The authors should say this explicitly to prevent readers from misreading the statement as a general convergence claim.","section":"§8.2"},{"comment":"Several bibliographic entries contain formatting issues (e.g., \"V oelkel\" in [70], incomplete package references in Table 5), and the Sankey diagram in Figure 5 has small, hard-to-read labels. Please proofread the reference list and provide a higher-resolution vector figure.","section":"References and Figure 5"}],"recommendation":"major_revision","confidential_remarks":"The paper is best viewed as a tutorial-style methods comparison with a real-data application. Its novelty relative to Dabrowska, Sun and Horowitz (1994), Dabrowska (1995), and Spitoni et al. (2012) is limited, and the main empirical claim needs quantitative support before it can be accepted. The proof of Lemma 8.5 has a genuine gap and must be fixed or the theorem attributed to prior work. The manuscript is within the scope of stat.AP if revised to supply reproducible smoothness metrics, confidence bands, and code."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take: this is a tutorial-style application of the Dabrowska-Sun-Horowitz estimator to the EBMT data. The genuinely new parts are a simulation, an application, and a reorganized proof of asymptotic normality; the estimator, the asymptotics, and the prediction formula come from prior work (Dabrowska, Sun and Horowitz; Spitoni et al.). The paper is honest about that, which I respect.\n\nWhat it does well: the proof reorganization in Appendix 8.5 is genuinely more readable than the original sources; Lemma 3.2 gives a clean reformulation of the prediction-probability formula; Table 1 is a useful comparison of semi-Markov versus Markov machinery. The paper also states plainly, in Section 5.2, that the smoothness claim 'lacks a formal theoretical justification.' That is the right kind of honesty.\n\nThe soft spots are where the abstract overreaches. The central claim—DSH consistently yields smoother curves—is supported only by visual inspection of Figures 6-9. There is no quantitative smoothness metric, no confidence bands, no bootstrap intervals, and no code. For a paper whose stated aim is to address the lack of computational tools, releasing no code is a real gap. The stress-test note about infinite convolution truncation actually does not land: the EBMT model is progressive with maximum path length 3, so the renewal sum is finite and 'no change after three or four convolutions' is an exact zero tail, not a truncation error. The load-bearing issue is upstream: the smoothness comparison is qualitative. There is also an unresolved ambiguity: 'Markov model with the DSH estimator' is not a standard estimator of a calendar-time Markov process unless the Markov model is assumed time-homogeneous, and the paper never states that. So the four-way comparison is not as clean as presented.\n\nWho is this for? A reader who wants a self-contained walkthrough of Markov renewal estimation and a compact restatement of the DSH asymptotics will get value. A reader looking for a new method or a validated empirical finding will not. It is honest, coherent, and not wrong on its own terms, but the advertised conclusion is unsupported.\n\nRecommendation: I would send it to a serious referee rather than desk-reject—it is a coherent tutorial with a useful proof reorganization, and an editor can reasonably ask for the smoothness claim to be quantified and the code released. But I would not accept the empirical claim as stated, and I would cite it only as a tutorial, not as a source of new results.","headline":"A readable tutorial re-derivation of the DSH estimator whose advertised smoothness claim rests only on eyeballing four plots; send it to review only if the claim is quantified or the paper is repositioned as a tutorial.","tokens_in":26995,"tokens_out":2843,"would_cite":false,"duration_ms":25153,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["60K15"],"pacs":[],"model":"deepseek-v4-flash","headline":"Sojourn-aware multi-state models give smoother, later transition curves for transplant patients than memoryless Markov models.","keywords":["semi-Markov models","Markov renewal processes","transition probabilities","Dabrowska-Sun-Horowitz estimator","Aalen-Johansen estimator","multi-state models","survival analysis","stem-cell transplant data"],"falsifier":"Compute the DSH transition probabilities for the same transplant cohort with the renewal series $R = \\sum_p Q^{(p)}$ extended to ten or twenty convolutions and with bootstrap standard errors; if the probability curves move by more than the width of their confidence bands, the reported smoothness and delayed absorption are truncation artifacts.","tokens_in":25908,"feed_emoji":"📈","tokens_out":16467,"duration_ms":130883,"temperature":0.7,"pith_summary":"This paper argues that in multi-state clinical modeling, recording and using the time spent in each state (the sojourn time) makes patient trajectories more realistic than a memoryless Markov model, and that the Dabrowska-Sun-Horowitz (DSH) estimator of transition probabilities, which is derived from the Markov renewal equation, produces smoother probability curves than the classical Aalen-Johansen (AJ) product-integral estimator. The demonstration is on a stem-cell transplant registry with six clinical states, where the DSH estimator smooths transitions into prolonged states such as relapse, and the semi-Markov model delays the accumulation of probability in absorbing states such as relapse or death. The paper also reorganizes the asymptotic theory for the semi-parametric Markov renewal Cox regression model, proving weak convergence of the regression coefficients and the baseline hazards with empirical process tools and the Burkholder-Davis-Gundy inequality. If the claims hold, clinical modelers get a more temporally sensitive framework and a concrete formula—$P(t) = R * G(t)$—for computing transition probabilities.","feed_headline":"Sojourn times smooth transplant-state survival curves","feed_subtitle":"The DSH estimator smooths relapse and death probabilities versus Aalen-Johansen in transplant data.","key_machinery":"The central object is the Markov renewal function and the renewal equation it solves. With the semi-Markov kernel $Q_{ij}(x)$ (probability that the next transition from $i$ goes to $j$ within sojourn $x$), the diagonal state-survival matrix $G$, and the matrix convolution $Q * P$, the transition probability matrix satisfies $P(t) = G(t) + Q * P(t)$; the unique solution is $P(t) = R * G(t)$, where $R = \\sum_{p=0}^{\\infty} Q^{(p)}$ is the Markov renewal function. Plugging in estimators for $Q$ and $G$ yields the DSH estimator, and $R$ is truncated at a few convolution terms in practice. A second load-bearing component is the Cox-type intensity model $\\alpha_{ij}(x) = \\alpha_{0ij}(x) e^{\\beta^T Z_{ij}}$ with its profile likelihood; the asymptotic results for $\\beta$ and the baseline hazard are carried by empirical process theory and the Burkholder-Davis-Gundy inequality.","core_discovery":"The paper's central claim is that transition probabilities in multi-state clinical processes should be modeled as a Markov renewal process, because the distribution of sojourn times carries information that memoryless Markov models discard. On the transplant data, the DSH estimator—obtained by plugging nonparametric estimates of the semi-Markov kernel (the probability that the next transition from state $i$ goes to $j$ within sojourn time $x$) into the renewal solution—is consistently smoother than the AJ estimator, with the difference most visible in states with long dwell times, and the semi-Markov models shift probability out of absorbing states such as relapse and death toward later times. The paper also states and proves weak convergence of the Cox-regression parameter and baseline hazard in this Markov renewal model, and gives a bootstrap scheme for confidence bands.","pith_inferences":["Editorial inference: The smoothness of DSH may be partly a convolution artifact rather than evidence for semi-Markov structure; one could test by simulating a true memoryless Markov process and checking whether DSH still appears smoother.","Editorial inference: A formal bound on the truncation error of the renewal series $R = \\sum_p Q^{(p)}$ is missing; a total-variation or spectral-radius argument could turn the practical stopping rule into a provable approximation.","Editorial inference: The progressive-state assumption excludes back transitions such as relapse followed by recovery; extending the method to recurrent states would require another truncation strategy and is not covered by the current comparison."],"forward_implications":["If sojourn time matters as claimed, Markov-based analyses of transplant data will tend to overstate how quickly patients reach relapse or death; semi-Markov models move those probabilities later.","The DSH estimator gives smoother curves for states with prolonged sojourns, such as recovery with adverse events and relapse, which is useful for sparse low-frequency transitions.","The stated weak-convergence results justify confidence intervals and bootstrap confidence bands for the Markov renewal Cox model, following the paper's bootstrap scheme.","Lemma 3.2 provides a practical formula for prediction probabilities $P(s,t)$ from an arbitrary calendar time $s$, supporting dynamic prediction of patient trajectories."],"supporting_citations":[{"why":"Supplies the Markov renewal Cox regression model, the profile likelihood, and the DSH transition-probability estimator that the paper compares.","marker":"[31]"},{"why":"Provides the renewal equation P = G + Q*P and its solution P = R*G, the identity underlying the DSH estimator.","marker":"[20]"},{"why":"Gives the plug-in estimators for the semi-Markov kernel and the censored risk-process framework used for estimation.","marker":"[34]"},{"why":"Supplies the asymptotic distribution and covariance formulas for transition-probability estimators in Markov renewal multi-state models.","marker":"[61]"},{"why":"The dissertation source of the profile likelihood, estimating equations, and consistency for the Markov renewal proportional hazards model.","marker":"[62]"},{"why":"Introduces the bootstrap procedure for transition probabilities and confidence bands in the semiparametric Markov renewal model, which the paper adapts.","marker":"[24]"}],"fun_headline_variants":["Semi-Markov models capture sojourn times for smoother transplant risks","Sojourn-aware DSH curves beat memoryless AJ in transplant states","Markov renewal adds temporal nuance to transplant outcome curves","Sojourn-dependent transitions smooth stem-cell survival probabilities","Non-Markovian sojourns refine post-transplant relapse and death risk"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The comparison depends on assuming that truncating the repeated-convolution series $R = \\sum_{p} Q^{(p)}$ after three or four terms leaves an error too small to change the curves; the paper says this error is still to be quantified.","fun_headline_variants_meta":{"raw":{"variants":["Semi-Markov models capture sojourn times for smoother transplant risks","Sojourn-aware DSH curves beat memoryless AJ in transplant states","Markov renewal adds temporal nuance to transplant outcome curves","Sojourn-dependent transitions smooth stem-cell survival probabilities","Non-Markovian sojourns refine post-transplant relapse and death risk"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000467,"raw_usage":{"total_tokens":2275,"prompt_tokens":840,"completion_tokens":1435,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":456,"completion_tokens_details":{"reasoning_tokens":1344}},"tokens_in":456,"tokens_out":1435,"duration_ms":10349,"temperature":1.0,"reasoning_tokens":1344,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T13:55:52.213493+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the DSH transition probabilities for the same transplant cohort with the renewal series $R = \\sum_p Q^{(p)}$ extended to ten or twenty convolutions and with bootstrap standard errors; if the probability curves move by more than the width of their confidence bands, the reported smoothness and delayed absorption are truncation artifacts.","supporting_citations":[{"cited_title":"M., S UN, G.- W","cited_arxiv_id":null,"evidence_quote":"Supplies the Markov renewal Cox regression model, the profile likelihood, and the DSH transition-probability estimator that the paper compares."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the renewal equation P = G + Q*P and its solution P = R*G, the identity underlying the DSH estimator."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the plug-in estimators for the semi-Markov kernel and the censored risk-process framework used for estimation."},{"cited_title":"and P UTTER , H","cited_arxiv_id":null,"evidence_quote":"Supplies the asymptotic distribution and covariance formulas for transition-probability estimators in Markov renewal multi-state models."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The dissertation source of the profile likelihood, estimating equations, and consistency for the Markov renewal proportional hazards model."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the bootstrap procedure for transition probabilities and confidence bands in the semiparametric Markov renewal model, which the paper adapts."}],"review_version":1}