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REVIEW 3 major objections 5 minor 46 references

Robust parametric modeling of Alzheimer's disease progression

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper claims that a single latent disease progression score, linearly mapped from age and shared across biomarkers, suffices to model Alzheimer's progression when biomarker curves are fit jointly with a robust M-estimator and a…

desk verdict Solid engineering contribution undermined by a false novelty claim (modified Stannard is just reparameterized Richards) and a test protocol that turns the state-of-the-art comparison into a self-fit exercise. read the letter →

arxiv 1908.05338 v3 pith:TKS62RFQ submitted 2019-08-14 stat.AP cs.CVeess.IV

Mostafa Mehdipour Ghazi , Mads Nielsen , Akshay Pai , Marc Modat , M. Jorge Cardoso , Sébastien Ourselin , Lauge S{o}rensen This is my paper · ORCID
classification stat.APcs.CVeess.IV MSC 62P1062F3562G0762H30
keywords Alzheimer'sdiseaseprogressionmodelingM-estimationgeneralizedlogisticfunctionmodifiedStannardkerneldensityestimationBayesianclassifierbiomarkertrajectories
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that Alzheimer's disease progression can be captured by a single latent disease progression score per patient, with every biomarker following a monotone S-shaped curve of that score, and that this simple parametric picture is accurate enough to predict biomarker values and clinical status from age. The authors introduce a modified Stannard logistic function and fit it jointly across biomarkers using robust M-estimation, which suppresses the influence of outliers. On ADNI test data the model reaches an average normalized mean absolute error of 0.991 across 16 biomarkers and a multiclass AUC of 0.934 in clinical status classification, compared with 1.552 NMAE for the analogous Jedynak model. Trained on ADNI, it also transfers to the NACC cohort with NMAE 1.182 and AUC 0.929, suggesting the learned disease timeline is not specific to one cohort. The inflection points of the fitted curves give a temporal ordering of biomarkers, with CSF, PET, and an early memory test preceding MRI and later cognitive scales.

What carries the argument

The load-bearing machinery is the modified Stannard logistic function, $$g(s;\$\theta$)=\left[1+\tfrac{1}{\gamma}$e^{{-\frac{b}}${\gamma}(s-c)}\right]^{-\gamma},$$ a flexible S-shaped curve whose asymmetry parameter $\gamma$ lets the model describe slow-then-fast or fast-then-slow biomarker change while keeping the inflection point at $c$; and the robust fitting scheme, which alternates between estimating biomarker parameters $\theta_k$ and subject parameters $(\alpha_i,\beta_i)$ under the logistic-loss M-estimator $\rho(r)=\ln\cosh(r)$, down-weighting large residuals so outliers do not distort the curves. Bootstrap resampling quantifies the estimates, inflection points provide a temporal ordering of biomarkers, and kernel density estimates of the DPS distributions feed a Bayesian classifier.

What would settle it

Fit the model twice using disjoint biomarker sets, say CSF and PET versus MRI and cognitive tests, and compare the DPS assigned to each patient-visit; if the two estimates disagree by more than measurement noise, or if adding a quadratic term in age such as $s=\alpha t+\beta t^2$ yields a materially lower validation loss, then the single-axis linear DPS assumption fails and the inflection-point ordering is not trustworthy.

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Extended reading notes

Core claim

The paper's claim is that a parametric, robust extension of the earlier Jedynak model captures AD progression accurately. Concretely, each subject's age $t_{i,j}$ is mapped to a progression score $s_{i,j}=\alpha_i t_{i,j}+\beta_i$, each biomarker $k$ is modeled as a modified Stannard function $f(s;\theta_k)$ with an asymmetry parameter $\gamma$, and all parameters are fit jointly by minimizing $\sum_{i,j,k} w_i \rho\!\left((y_{i,j,k}-f(s_{i,j};\theta_k))/\sigma_k\right)$ with the logistic loss $\rho(r)=\ln\cosh(r)$. On the ADNI test set the model attains an average normalized MAE of 0.991 across 16 biomarkers and a multiclass AUC of 0.934 for CN/MCI/AD classification (0.931 before ensemble bagging), compared with NMAE 1.552 for the analogous Jedynak model. The same model, trained on ADNI, transfers to the NACC cohort with NMAE 1.182 and AUC 0.929, and the inflection points order CSF, PET, and an early memory test before MRI and later cognitive tests.

Load-bearing premise

The model assumes a patient's whole disease state is one number—the disease progression score—that grows linearly with age and that every biomarker is a monotone S-shaped function of that same number; if real Alzheimer's trajectories are multidimensional, or if progression speed varies with disease stage rather than age, the fitted curves and the ordering derived from their inflection points are not valid.

Editorial extensions

If this is right

  • With age as the only input, the fitted model predicts all 16 modeled ADNI biomarker values—volumetric MRI, PET, CSF, and cognitive scores—on a common progression axis.
  • The inflection-point ordering implies a fixed sequence of biomarker abnormality: amyloid beta, amyloid PET, and the RAVLT memory test turn early, MRI atrophy follows, and cognitive scales turn last; the paper uses this ordering for staging.
  • The Bayesian classifier built on DPS densities separates cognitively normal, MCI, and AD with multiclass AUC around 0.93, so the same progression score used for curve fitting also carries diagnostic information.
  • Since an ADNI-trained model predicts NACC values with only moderately higher error, the fitted disease timeline generalizes across cohorts and across different sets of available biomarkers.
  • The model needs only two distinct visits per subject and tolerates missing biomarker measurements, so it can be applied to sparse clinical datasets.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable consequence of the single-axis assumption: if progression is truly one-dimensional, the DPS estimated from one biomarker subset should agree with the DPS estimated from another; disagreements would reveal that Alzheimer's has more than one temporal dimension.
  • The fact that an asymmetric curve (modified Stannard) beats symmetric Verhulst and Richards variants suggests biomarker dynamics are not symmetric around the inflection point; a follow-up could model the asymmetry parameter $\gamma$ per biomarker as a marker of early versus late acceleration.
  • Robust M-estimation could be repurposed as an outlier detector: large residuals under logistic loss would flag individual visits as suspect, for instance measurement errors or atypically fast progressors—an application the paper does not develop.
  • The cross-cohort result implies a strategy for smaller cohorts: train the parametric template on a large, richly measured cohort and then calibrate only per-subject progression rates on a smaller cohort, rather than refitting all curves.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper proposes a robust parametric disease progression model for Alzheimer's disease, extending the approach of Jedynak et al. (2012, 2015). The model maps each subject's age to a disease progression score (DPS) via a subject-specific linear transformation and jointly fits constrained generalized logistic curves to longitudinal biomarker data using M-estimation. The authors evaluate several logistic functions and loss functions, introduce what they call the modified Stannard function, use bootstrapping to quantify uncertainty, order biomarkers by estimated inflection points, and classify clinical status using kernel density estimates of DPS distributions with a Bayesian classifier. On ADNI test data, the best configuration (modified Stannard with logistic loss) is reported to achieve an average normalized MAE of 0.991 and a multiclass AUC of 0.934; on NACC data the corresponding values are 1.182 and 0.929. The paper also claims to outperform most state-of-the-art results in predicting biomarker values and classifying clinical status.

Significance. If the results are validated under an appropriate protocol, the work would make a useful contribution: robust M-estimation for disease progression modeling, joint fitting of multiple biomarkers, bootstrap-based uncertainty quantification, and cross-cohort evaluation are all valuable components, and the comparison with the analogous Jedynak model under the same protocol is a legitimate like-for-like assessment. The temporal ordering of biomarkers is consistent with prior literature, which lends credibility to the fitted curves. However, two load-bearing issues compromise the current claims: the modified Stannard function is mathematically a reparameterization of Richards' function, so the claimed novelty is inaccurate; and the comparison with TADPOLE and other state-of-the-art methods is not apples-to-apples because the test DPSs are estimated from each test subject's full longitudinal record, including the visits whose values are later 'predicted.' The paper's central contribution is therefore better described as a robust, jointly fitted extension of an existing parametric model rather than a new functional form with state-of-the-art forecasting performance.

major comments (3)
  1. [Section 4.6 and Section 2.3] The claimed state-of-the-art comparison in Section 4.6 is not supported by the evaluation protocol. In Section 2.3, for each test subject the subject-specific DPS parameters (alpha_i, beta_i) are estimated by minimizing Eq. (2) over all available biomarker values and visits for that subject, including the same visits whose biomarker values are subsequently predicted. The TADPOLE official evaluation, by contrast, requires predictions to be made from a fixed forecast date using only data available up to that date. The reported ADAS-13 MAE of 3.93 and AUC of 0.937 are therefore not comparable to the cited TADPOLE results (MAE 4.70, AUC 0.931). The authors should either rerun the evaluation under the official TADPOLE forecast protocol or remove the state-of-the-art comparison and revise the abstract and conclusion accordingly.
  2. [Table 1 and Section 1] The 'modified Stannard' function is not a new family of growth functions. Its formula, g(s) = [1 + (1/gamma) exp(-(b/gamma)(s-c))]^{-gamma}, becomes the Richards function after the reparameterization r = 1/gamma and b_r = b/gamma: [1 + r exp(-b_r(s-c))]^{-1/r}. Consequently, the claimed four-fold contribution of introducing a novel logistic function is incorrect, and the small BIC differences between Richards and modified Stannard in Table 5 are numerical artifacts of the optimization rather than evidence of a genuinely more flexible model. The novelty claim should be removed or the contribution reframed around the robust estimation and joint fitting components.
  3. [Sections 4.4 and 4.5] The test-set NMAE and AUC are not forecasting metrics in the usual sense. Because the test DPSs are estimated from the complete longitudinal record of each test subject, the reported errors measure the quality of a per-subject trajectory fit, not the accuracy of predictions made from an earlier time point. The comparison with the Jedynak model in Table 6 is fair as a like-for-like trajectory-shape comparison, and this is a legitimate evaluation target, but the manuscript should consistently describe the results as trajectory-modeling and trajectory-based classification performance, not as state-of-the-art biomarker prediction. This distinction is essential for readers comparing the results with TADPOLE and other longitudinal forecasting benchmarks.
minor comments (5)
  1. [Section 3.2] The definition of BIC uses E(Lopt)_train, while Sections 3.3 and 3.4 describe selecting Lopt using the validation loss; please clarify whether the reported BIC is computed from the training loss at the validation-selected iteration and how this avoids optimistic model selection.
  2. [Figure 5] The 16 by 16 probability matrix in Figure 5 is very dense and difficult to read at print size; enlarging the figure or presenting the ordering probabilities in a supplementary table would improve accessibility.
  3. [Table 7] The columns 'Inflection point (median)' and 'Test MAE (mean)' in Table 7 should state their units and clarify that the MAE values are averaged over the 100 bootstrap runs.
  4. [Section 3.1.3] The 3-month matching rule for MRI and clinical visits is reasonable, but the manuscript should report how many MRI visits in NACC were assigned missing clinical status as a consequence, since this affects the effective sample size for the classification experiments.
  5. [Section 5] The statement that the method could be applied to biomarkers with non-monotonic behavior 'as long as suitable functions are used' is vague; a concrete example or a reference to a suitable function family would make the claim more informative.

Circularity Check

1 steps flagged · score 6.0 of 10

The paper's test-set biomarker 'prediction' is a per-subject self-fit residual, because Eq. (2) estimates each test subject's DPS from the same values that are then scored.

  1. fitted input called prediction [Section 2.3, Eq. (2); applied in Section 4.4 / Table 6; compared in Section 4.6]
    "Age mapping part of the proposed algorithm is applied to estimate the subject-specific parameters using Equation (2) based on the values of those biomarkers of the test subject that have available estimated biomarker-specific parameters in the fitted model. Next, biomarker values are predicted as f (si,j;θk) using the estimated test DPSs."

    Equation (2) estimates the test subject's α_i, β_i by minimizing the robust loss over all of that subject's visits and biomarker values. Those same y_i,j,k values are then plugged into MAE = |y_i,j,k − f(s_i,j;θ_k)| to obtain the reported test NMAEs (0.991 for ADNI; 1.182 for ADNI-to-NACC) and the ADAS-13 MAE of 3.93. Thus the 'predicted' biomarker values are fitted values of a per-subject alignment, not forecasts of unseen measurements. Section 4.6 compares these with TADPOLE forecasting results (MAE 4.70, AUC 0.931), but TADPOLE uses data only up to a fixed forecast date, whereas the proposed evaluation uses the full longitudinal record of each test subject, including the target values.

full rationale

The core model-fitting derivation is not circular: biomarker parameters θ are optimized on training subjects via Eq. (1), the bootstrap/BIC model selection is self-contained, and the modified Stannard function is an independent modeling contribution rather than a renaming of an input. No load-bearing self-citation chain or imported uniqueness theorem was found. The circularity is confined to the evaluation protocol behind the paper's headline prediction claims. In Section 2.3, each test subject's DPS parameters (α_i, β_i) are estimated from that subject's own observed biomarker values via Eq. (2), and the same values are then used to compute MAE/NMAE against f(s_i,j;θ_k). This makes the 'test NMAE' an in-sample residual of a two-parameter subject alignment, not an out-of-sample prediction of biomarker values. The subsequent comparison with TADPOLE forecasting results in Section 4.6 is therefore not apples-to-apples: TADPOLE scores are true forecasts from a cutoff date, while the proposed numbers have access to the entire test trajectory. The classification AUC is also computed on test DPSs estimated from the full test record, so the 'diagnostic predictive performance' wording overstates out-of-sample prediction, though this is more a temporal-leakage issue than a definitional circularity. Overall, the central modeling contribution retains independent content, but the prediction claim partially reduces to a self-fit, giving a partial circularity score of 6.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The model rests on strong structural assumptions: a one-dimensional monotone disease process, a linear age-to-stage mapping, homoscedastic Gaussian noise, and several post-hoc data filtering choices. The modified Stannard curve is a reparameterization of Richards, so the curve family adds no new degrees of freedom. The KDE bandwidth and time-gap threshold are free choices that affect the reported performance.

free parameters (3)
  • KDE bandwidth w = not reported
    Used in kernel density estimation for clinical status classification (Section 2.4); the selection procedure (cross-validation, rule of thumb, or manual) is not described, and the classifier's AUC depends on it.
  • Time gap threshold = 3 months
    In Section 3.1.3, the threshold for excluding measurements matched to cognitive visits is set to three months 'based on the data statistics'. This post hoc choice affects which visits enter the analysis.
  • Early stopping iteration range (Lmin, Lmax) = 10, 50
    In Section 3.4, Lmin=10 and Lmax=50 are set empirically; the validation loss minimum was observed within this range, but these values are hand-chosen and affect model selection.
assumptions (5)
  • domain assumption Each biomarker follows a monotone S-shaped (logistic) function of the DPS with fixed parameters.
    Stated in Section 2.1 and Table 1; the entire fitting procedure optimizes these functions. Violations (non-monotone or non-sigmoid dynamics) would bias estimates.
  • domain assumption The DPS of a subject is a linear function of age with subject-specific slope and intercept.
    Defined as s_i,j = alpha_i t_i,j + beta_i in Section 2.1; this alignment is inherited from Jedynak et al. and is used for all subjects and visits.
  • domain assumption Additive white Gaussian noise with per-biomarker standard deviation sigma_k.
    Assumed in Section 2.1 (y = f + sigma epsilon); the M-estimation scale factors and loss functions are calibrated against the normal distribution (Table 2).
  • domain assumption Complete monotonicity of biomarker trajectories over the modeled disease range.
    The logistic functions used are monotone and bounded; if a biomarker (e.g., ventricular volume) follows a different shape, the inflection point ordering may be misleading. The paper notes some MRI biomarkers are noisy.
  • domain assumption The residual linear regression on controls corrects for cohort/software and head size differences.
    Used in Section 3.1.5 for MRI normalization; assumes a linear relationship between volumes and ICV in cognitively normal subjects and that the same correction applies to patients.

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Pith. "Pith review of Robust parametric modeling of Alzheimer's disease progression." pith.science (2026). https://pith.science/paper/TKS62RFQ

@misc{pith2026190805338,
  author       = {Pith},
  title        = {Pith review of: Robust parametric modeling of Alzheimer's disease progression},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TKS62RFQ}},
  note         = {Machine review of arXiv:1908.05338}
}
read the original abstract

Quantitative characterization of disease progression using longitudinal data can provide long-term predictions for the pathological stages of individuals. This work studies the robust modeling of Alzheimer's disease progression using parametric methods. The proposed method linearly maps the individual's age to a disease progression score (DPS) and jointly fits constrained generalized logistic functions to the longitudinal dynamics of biomarkers as functions of the DPS using M-estimation. Robustness of the estimates is quantified using bootstrapping via Monte Carlo resampling, and the estimated inflection points of the fitted functions are used to temporally order the modeled biomarkers in the disease course. Kernel density estimation is applied to the obtained DPSs for clinical status classification using a Bayesian classifier. Different M-estimators and logistic functions, including a novel type proposed in this study, called modified Stannard, are evaluated on the data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) for robust modeling of volumetric MRI and PET biomarkers, CSF measurements, as well as cognitive tests. The results show that the modified Stannard function fitted using the logistic loss achieves the best modeling performance with an average normalized MAE of 0.991 across all biomarkers and bootstraps. Applied to the ADNI test set, this model achieves a multiclass AUC of 0.934 in clinical status classification. The obtained results for the proposed model outperform almost all state-of-the-art results in predicting biomarker values and classifying clinical status. Finally, the experiments show that the proposed model, trained using abundant ADNI data, generalizes well to data from the National Alzheimer's Coordinating Center (NACC) with an average normalized MAE of 1.182 and a multiclass AUC of 0.929.

Figures

Figures reproduced from arXiv: 1908.05338 by the authors.

Figure 1
Figure 1. An illustration of the AD progression modeling method proposed by [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. An illustration of how the proposed method (red curves) tackles the existing biomarker curve-fitting problems using simulated data [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Estimated curves per bootstrap (in gray) for the ADNI biomarkers using the modified Stannard function and the logistic loss. The average [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: The average of the normalized curves of the ADNI biomarkers across 100 bootstraps. [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: Temporal ordering of the ADNI biomarkers in the disease [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Estimated class-conditional likelihoods using the DPSs ob [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: Estimated curves per bootstrap (in gray) for the NACC biomarkers using the modified Stannard function and the logistic loss. The average [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.