{"id":"cde2df47-0c18-4bbd-9a1b-6f4e3177d9ee","arxiv_id":"2412.13608","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"DP-MoSt fits continuous sigmoidal disease trajectories and uses a two-level mixture to identify which biomarkers split into sub-trajectories and which patients belong to each subgroup.","lead":"This paper introduces DP-MoSt, a statistical model that groups Parkinson's patients by how their symptom scores change over the course of disease. It aims to improve on standard subtype-and-stage methods by producing continuous trajectories instead of discrete event stages.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The TD_score claim may be exactly backwards: in Eq. (2), ξ_b weights the no-split term, so ξ_b>0.5 indicates absence of a sub-trajectory, not its presence.","rationale":"The reader's weakest_assumption focused on GPPM time shifts; my strongest concern is the ξ interpretation, which the reader mentioned in the rationale but did not put first. The inconsistency is more load-bearing because it directly inverts the headline result for any choice of time shifts. If Eq. (2) is the fitted model, the reported 'ξ_b > 0.5' for TD_score means TD_score is not the split-driving biomarker, and the other four scores have ξ_b < 0.5, i.e., they exhibit sub-trajectories. This would reverse Figure 2 and Table 1. The synthetic evaluation is also ambiguous: a ROC curve for ξ only makes sense if high ξ indicates the presence of a sub-trajectory, which contradicts Eq. (2). The manuscript needs either a corrected equation or a corrected interpretation. Because the code is public, the discrepancy can be resolved quickly; the reader's CONDITIONAL verdict remains appropriate, but the condition should include this check.","tokens_in":8274,"tokens_out":5507,"duration_ms":46798,"concrete_test":"Check the released code (github.com/alessandro-viani/DP-MoSt) to see whether the implemented likelihood uses ξ_b as the weight of the single-trajectory term (as in Eq. 2) or as the weight of the sub-trajectory mixture (as implied by the text). Then run the synthetic benchmark with one known split biomarker (B=1, two equal groups, high SNR) and record the MAP estimate of ξ_b: if ξ_b>0.5 for the known split, the printed equation is wrong but the interpretation is consistent; if ξ_b<0.5, the Section 3.2 interpretation is reversed. This single check settles which side of the inconsistency is in the code.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central empirical claim that TD_score governs the split is internally inconsistent with the model equation. In Eq. (2), the likelihood for each biomarker is ξ_b · p(x|θ_b^0, σ_b) + (1−ξ_b)·[π_j p(x|θ_b^1)+(1−π_j)p(x|θ_b^2)]. Thus ξ_b is the mixture weight for the no-split (single-trajectory) component, and 1−ξ_b is the weight for the sub-population mixture. Yet Section 2.1 defines ξ_b as 'the probability that the evolution ... can be split into multiple sub-trajectories,' and Section 3.2 interprets ξ_b > 0.5 as evidence that TD_score 'primarily governs the split.' If Eq. (2) is what was fitted, a biomarker with ξ_b > 0.5 is the one least likely to exhibit sub-trajectories; the TD_score result would then indicate the absence of a split, and the other scores (with ξ_b < 0.5) would be the splitting biomarkers. This would invert Figure 2 and Table 1. The synthetic ROC evaluation of ξ (Section 3.1) is also affected: if the equation is correct, a high ξ cannot be a positive indicator for detecting sub-trajectories. The paper therefore contains a sign/notation error that determines the direction of the main result.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces DP-MoSt, a probabilistic two-level mixture model for disease progression that assumes each biomarker follows one of two sigmoidal sub-trajectories with probability governed by a biomarker-level parameter ξ_b, while subject-level memberships π_j link the biomarkers. Time shifts to an absolute disease time axis are taken from GPPM. The method is evaluated on synthetic data generated from the same sigmoidal model and on PPMI data, where the authors claim that the TD_score is the main biomarker driving the split into two sub-populations. The manuscript provides the model objective, a description of an EM procedure, synthetic experiments with ROC/OSPA metrics, and a comparison with SuStaIn on PPMI data.","tokens_in":8622,"tokens_out":3135,"duration_ms":31326,"significance":"If the model and its reported findings were correct, DP-MoSt would be a useful addition to disease progression modelling: it offers continuous trajectories, per-biomarker uncertainty about the split, and per-subject membership probabilities, and the authors have released code for the method. The synthetic benchmark covers several biomarker counts and noise levels, and the PPMI application targets a clinically meaningful TD/PIGD distinction. However, the central interpretation of ξ_b appears internally inconsistent with the likelihood equation used for fitting, which directly affects the headline PPMI result and the synthetic ROC evaluation. The paper therefore needs a substantial correction and re-analysis before its conclusions can be accepted.","major_comments":[{"comment":"There is a load-bearing inconsistency between the definition of ξ_b and its use in Eq. (2). In Eq. (2), the first term, ξ_b · p(x_j^b | θ_b^0, σ_b), is the single-trajectory (no-split) contribution, and the second term, (1 − ξ_b) · [π_j p(x_j^b | θ_b^1, σ_b) + (1 − π_j) p(x_j^b | θ_b^2, σ_b)], is the split contribution. Thus larger ξ_b means a smaller weight on the sub-trajectory mixture. Yet §2.1 defines ξ_b as 'the probability that the evolution ... can be split into multiple sub-trajectories,' and §3.2 states that TD_score 'primarily governs the split into two sub-groups (ξ_b > 0.5).' Under Eq. (2) as written, ξ_b > 0.5 indicates that the biomarker is predominantly NOT split; the biomarkers with ξ_b < 0.5 would be the split candidates. This reverses the interpretation of Figure 2 and Table 1, and it also affects the synthetic ROC evaluation in §3.1. The authors must either correct Eq. (2) so that ξ_b multiplies the mixture term, or revise the text and results to match the equation actually fitted.","section":"§2.1, Eq. (2) vs. §3.2"},{"comment":"The EM optimization is not fully specified. The paper gives the MAP objective in Eq. (3) and describes the model as a two-level mixture, but it does not provide the E-step or M-step update equations, nor the derivation of the posterior parameterization. Without these updates, the reported synthetic and PPMI results cannot be reproduced or independently checked, and it is unclear whether the fitted parameters correspond to Eq. (2) or to a different likelihood. Please include the complete EM updates or, failing that, a precise reference to supplementary material containing them.","section":"§2.2, Eq. (3)"},{"comment":"The synthetic data are generated from the same sigmoidal, additive-Gaussian model assumed by DP-MoSt, with known ξ_b and π_j. Consequently, the experiments mainly establish self-consistency under the model's own generative assumptions; they do not test robustness to misspecification such as non-sigmoidal trajectories, non-Gaussian noise, or incorrect time-shift estimates. Since the paper's real-data claim depends on GPPM time shifts that are not jointly optimized with the mixture model, please add a misspecification experiment (for example, generate trajectories with a different functional form or perturb the time shifts) and report the resulting effect on ξ_b and subgroup assignment.","section":"§3.1, synthetic validation"},{"comment":"The PPMI application optimizes individual time shifts with GPPM, while §3.1 explicitly validates only the clustering component and the paper states that the time-shift method's effectiveness is 'already proven.' However, the final inferred trajectories and sub-population memberships of DP-MoSt depend directly on these time shifts, and the paper provides no sensitivity analysis of the clustering to GPPM time-shift uncertainty. Please quantify this sensitivity (e.g., by perturbing the estimated shifts or by comparing against a joint optimization) before claiming that the TD_score split is biologically real.","section":"§3.2, PPMI time-shift estimation"}],"minor_comments":[{"comment":"The observation vector notation is inconsistent: the definition says x_j^b = (x_j^b(\\tilde{t}_1), ..., x_j^1(\\tilde{t}_{k_j})) but the last component should be x_j^b(\\tilde{t}_{k_j}), not x_j^1(\\tilde{t}_{k_j}).","section":"§2.1, Eq. (1)"},{"comment":"The name 'SuStaIn' is spelled inconsistently as 'SuStain' in several places (e.g., §1 and §3.2). Please use one spelling throughout.","section":"Throughout"},{"comment":"The table header 'N°% data' is confusing; it should be something like 'Percentage of data' or 'Share of subjects'.","section":"Table 1"},{"comment":"The text says 'k_{1:J} = 1, i.e. one time point for each subject,' but the earlier model definition allows multiple time points. Clarify whether the synthetic benchmark indeed uses a single time point per subject and, if so, discuss the relevance to longitudinal data.","section":"§3.1, data generation"},{"comment":"The number of MCMC steps is written as '100 000 MCMC steps'; use a consistent numeric format (e.g., 100,000) and specify the number of burn-in iterations if applicable.","section":"§3.2, SuStaIn setup"},{"comment":"In Eq. (2), the conditioning on time points is omitted after the first display; please state once that all densities are conditional on the estimated time points t_j to avoid ambiguity.","section":"§2.1, Eq. (2)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript reports an interesting method and openly provides code, which is commendable. However, the sign/notation inconsistency around ξ_b is not a cosmetic issue: it determines whether the PPMI result is interpreted as TD_score driving the split or as TD_score being the least split biomarker. The authors should also provide the full EM updates and a sensitivity analysis for the GPPM time-shift step. I recommend major revision rather than rejection because the issue is correctable, but the current text cannot be accepted as reporting its stated findings."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe one thing you need to know about arXiv:2412.13608: the central real-data claim is probably exactly backwards as written. Eq. (2) gives the per-biomarker likelihood as ξ_b · p(x|θ^0) + (1−ξ_b)·[π_j p(x|θ^1) + (1−π_j)p(x|θ^2)]. So ξ_b is the weight on the no-split trajectory, not the probability of a split. The paper defines ξ_b as the probability that the evolution can be split, then interprets ξ_b > 0.5 for TD_score as evidence that it primarily governs the split. If the equation is what was fitted, a high ξ_b means the biomarker does not split; the other scores (with ξ_b < 0.5) are the ones that split. That inverts Figure 2 and Table 1. The prior p(ξ) with location 1 also pulls toward no split, consistent with the equation but not with the prose. This is not a minor typo; it is the main empirical result.\n\nWhat is genuinely new: the two-level mixture with per-biomarker split probability ξ_b and shared subject membership π_j is not in SuStaIn or MM-DCM, and the model notation is clean enough to work with. The synthetic benchmark is reasonably thorough (B = 2, 5, 10, three SNR levels, ROC curves), and the code is public, which earns credit.\n\nThe other soft spots, in proportion: the EM updates are absent, so the optimization is underspecified; the synthetic data are generated from the same sigmoidal model, so they test self-consistency rather than external validity; and the PPMI application uses GPPM time shifts without a sensitivity analysis. But the sign/notation error is load-bearing.\n\nThis deserves a serious referee because the model idea is salvageable and the error is likely correctable with a revised notation or a corrected equation. As written, however, the headline result is unsupported. I would send it to peer review with a note that the ξ interpretation must be resolved, and I would expect a revised version to be far more convincing.\n\n— [Your name]","headline":"The paper's main result is likely inverted: Eq. (2) makes ξ_b the no-split weight, so the TD_score finding says the opposite of what the authors claim.","tokens_in":9147,"tokens_out":3216,"would_cite":false,"duration_ms":28054,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"DP-MoSt finds that a single Parkinson's score, TD_score, governs the split into two disease sub-trajectories.","keywords":["disease progression modelling","patient stratification","Parkinson's disease","subtype discovery","expectation maximisation","biomarker trajectories","mixture model","PPMI dataset"],"falsifier":"Re-run the DP-MoSt analysis on PPMI with an alternative time-axis estimation, such as jointly optimising the time shifts inside the EM procedure or using DCM-style warping, and check whether the TD_score split with $\\xi_b > 0.5$ persists; if it disappears, the reported sub-populations are an artifact of the time-shift method.","tokens_in":8126,"feed_emoji":"🧠","tokens_out":6450,"duration_ms":51759,"temperature":0.7,"pith_summary":"This paper introduces DP-MoSt, a probabilistic method that recovers sub-trajectories and sub-populations in degenerative disease progression from longitudinal observations. The method learns continuous sigmoidal biomarker trajectories on a long-term disease time axis while estimating, for each biomarker, the probability that it splits into distinct sub-trajectories. On the PPMI Parkinson's dataset, DP-MoSt identifies a single governing split: the tremor-dominant score (TD_score) separates a tremor-dominant sub-population from a postural-instability/gait-dominant (PIGD) sub-population. The authors argue that this continuous, uncertainty-aware formulation addresses limitations of discrete event-based methods such as SuStaIn.","feed_headline":"New model splits Parkinson's patients by tremor vs gait scores","feed_subtitle":"Unsupervised DP-MoSt separates tremor-dominant from PIGD sub-trajectories on PPMI data, with per-biomarker confidence.","key_machinery":"The central object is a two-level trajectory mixture model over an absolute disease time axis. At the first level, each biomarker $b$ either follows a single sigmoidal trajectory or splits into two sub-trajectories with probability $\\xi_b$; at the second level, each subject belongs to one of two sub-populations with probability $\\pi_j$, and the likelihood combines these across all biomarkers. Time shifts that place short-term observations on the long-term disease axis are taken from the Gaussian Process Progression Model (GPPM), and the full set of parameters is estimated by maximum a posteriori expectation-maximisation, with the Laplace prior on $\\xi_b$ keeping the model from inventing splits.","core_discovery":"The central claim is that DP-MoSt effectively identifies both sub-trajectories and sub-populations in heterogeneous disease cohorts. The model combines a per-biomarker probability $\\xi_b$ of trajectory splitting with per-subject membership probabilities $\\pi_j$ in a two-level mixture, and fits these with expectation-maximisation under a Laplace prior that penalises unnecessary splits. Applied to PPMI, the method finds that only TD_score exceeds the $\\xi_b > 0.5$ threshold, creating two sub-populations whose clinical labels are predominantly tremor-dominant (76%) and PIGD (62%), while other biomarkers such as PIGD_score, MCATOT, NP2PTOT, and NP3PTOT show overlapping distributions across sub-populations. The authors frame this as a clinically meaningful partitioning that SuStaIn does not achieve, since SuStaIn places 72% of subjects into one unbalanced group.","pith_inferences":["If the TD_score split is a genuine disease subtype marker, the two sub-populations should differ in downstream clinical outcomes such as rate of motor decline or response to dopaminergic therapy; this is an external prediction the paper does not test.","The method's reliance on GPPM time shifts is testable: applying the same mixture model to the raw observation times without the GPPM alignment would reveal how much of the split is driven by the time-axis construction.","The two-level $\\xi_b$ / $\\pi_j$ formulation generalises naturally to more than two sub-populations, which the authors flag as future work; an ordered multi-subtype version could make contact with ordinal staging approaches.","Ignoring temporal correlation within subjects (done for fair comparison with SuStaIn) may under-use the longitudinal structure; a version that models within-subject correlation could sharpen subgroup assignments."],"forward_implications":["DP-MoSt can be applied to other degenerative diseases with longitudinal biomarker data to uncover subtype-specific trajectories without requiring discrete event stages.","The per-biomarker confidence $\\xi_b$ provides a direct, interpretable measure of which biomarkers are informative for subtyping, which could guide biomarker selection in clinical studies.","The recovered TD/PIGD split on PPMI suggests the method reproduces clinically recognised Parkinson's subtypes without using the labels during training.","Because trajectories are continuous, the model captures multimodal biomarker distributions that reflect the full disease history, a feature discrete event models cannot represent.","The method's balanced sub-populations (56%/44%) contrast with SuStaIn's unbalanced 72%/28% split, suggesting improved robustness in stratifying heterogeneous cohorts."],"supporting_citations":[{"why":"Supplies the Gaussian process progression model used to estimate the absolute disease time axis via time shifts.","marker":"[8]"},{"why":"Defines SuStaIn, the state-of-the-art baseline for subtype and stage inference that DP-MoSt is compared against.","marker":"[19]"},{"why":"Introduces t-SuStaIn with timescales, the recent extension whose discrete-event limitations motivate the continuous approach.","marker":"[18]"},{"why":"Describes MM-DCM, the mixture extension of disease course mapping whose all-biomarker split assumption DP-MoSt relaxes.","marker":"[11]"},{"why":"Provides the continuous disease trajectory model (DCM) underpinning the sigmoidal trajectory formulation.","marker":"[12]"},{"why":"Defines the PPMI cohort and clinical subtype labels used for the real-data validation.","marker":"[2]"}],"fun_headline_variants":["DP-MoSt separates Parkinson's tremor and gait trajectories","New probabilistic model finds Parkinson's sub-trajectories","Parkinson's patients split by biomarker-specific trajectories","DP-MoSt reveals tremor-dominant vs PIGD subgroups in PPMI","Unsupervised model detects distinct Parkinson's progression paths"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The real-data result depends on the assumption that the GPPM-estimated time shifts put every patient on a correct absolute disease timeline; only the clustering step is validated on synthetic data, so biased shifts would invalidate the subgroup assignments.","fun_headline_variants_meta":{"raw":{"variants":["DP-MoSt separates Parkinson's tremor and gait trajectories","New probabilistic model finds Parkinson's sub-trajectories","Parkinson's patients split by biomarker-specific trajectories","DP-MoSt reveals tremor-dominant vs PIGD subgroups in PPMI","Unsupervised model detects distinct Parkinson's progression paths"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000218,"raw_usage":{"total_tokens":1436,"prompt_tokens":936,"completion_tokens":500,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":552,"completion_tokens_details":{"reasoning_tokens":417}},"tokens_in":552,"tokens_out":500,"duration_ms":4536,"temperature":1.0,"reasoning_tokens":417,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T12:57:31.232948+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the DP-MoSt analysis on PPMI with an alternative time-axis estimation, such as jointly optimising the time shifts inside the EM procedure or using DCM-style warping, and check whether the TD_score split with $\\xi_b > 0.5$ persists; if it disappears, the reported sub-populations are an artifact of the time-shift method.","supporting_citations":[{"cited_title":"NeuroIm- age 190, 56–68 (2019)","cited_arxiv_id":null,"evidence_quote":"Supplies the Gaussian process progression model used to estimate the absolute disease time axis via time shifts."},{"cited_title":"Nature communications9(1), 4273 (2018)","cited_arxiv_id":null,"evidence_quote":"Defines SuStaIn, the state-of-the-art baseline for subtype and stage inference that DP-MoSt is compared against."},{"cited_title":"In: International Conference on In- formation Processing in Medical Imaging","cited_arxiv_id":null,"evidence_quote":"Introduces t-SuStaIn with timescales, the recent extension whose discrete-event limitations motivate the continuous approach."},{"cited_title":"In: International Conference on Information Processing in Medical Imaging","cited_arxiv_id":null,"evidence_quote":"Describes MM-DCM, the mixture extension of disease course mapping whose all-biomarker split assumption DP-MoSt relaxes."},{"cited_title":"Journal of Machine Learning Research18(133), 1–33 (2017)","cited_arxiv_id":null,"evidence_quote":"Provides the continuous disease trajectory model (DCM) underpinning the sigmoidal trajectory formulation."},{"cited_title":"Neurological Sciences39, 1971–1976 (2018), https://link.springer.com/article/10.1007/s10072-018-3522-z","cited_arxiv_id":null,"evidence_quote":"Defines the PPMI cohort and clinical subtype labels used for the real-data validation."}],"review_version":1}