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Modelling the temporal evolution of plasma p-tau217, amyloid PET, tau PET and cognition.

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Paper

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The authors' code

Stan · 72 lines · 2.5 KB · no license

  1. // --- DO NOT EDIT THIS FILE ----
  3. // This file is extracted (tangled) from 'src/stan-runs.org'
  4. // and modifications to this file will be overwritten
  8. // Using STAN for a PIB fit
  9. // B[1]- B[5] are the parameters of the target function, two columns
  10. // y ~ Gaussian(f(age + offset), sigma)
  11. // Add covariates
  12. // The only difference from 18d5 is that we have 4 covariates
  13. functions{
  14. real ghyper(real b1, real b2, real b3, real k, real x) {
  15. return(b1 + b2*(x+2) + .5*(b3-b2)*(x + sqrt(x^2 + k^2)));
  16. }
  17. }
  18. data {
  19. int<lower=0> N; // number of observations
  20. int<lower=0> M; // number of persons (subjects)
  21. int<lower=0> P; // number of variables
  22. real y[N]; // observed values
  23. int outcome[N]; // is each Y a pointer to pib or tau
  24. real age[N]; // age values
  25. matrix [N,P] x; // covariates
  26. int id[N]; // the id index, 1,2 etc
  27. real tau; // SD of the bivariate t random effects
  28. real dft; // degrees of freedom of the bivariate t
  29. int adrc[N]; // indicator of ADRC (it's int but multiplied by real)
  30. }
  31. parameters {
  32. real<lower=0> B[5,2]; // parameters of the logistic
  33. real<lower=0> sigma[2]; // residual std
  34. matrix[M,2] alpha; // per subject intercepts
  35. matrix[P,2] beta;
  36. real rho;
  37. real adrc_shift; // how much earlier are ADRC subjects?
  38. }
  39. transformed parameters {
  40. matrix[N,2] lin; // linear predictors
  41. vector[N] tage;
  42. vector[N] yhat;
  43. matrix[2,2] Sigma;
  44. row_vector[2] zero;
  45. Sigma[1,1] = tau*tau;
  46. Sigma[2,2] = tau*tau;
  47. Sigma[1,2] = rho*(tau*tau);
  48. Sigma[2,1] = rho*(tau*tau);
  50. zero = rep_row_vector(0,2);
  51. lin = x*beta; // ADRC shift curve same for PiB and tau
  52. for (i in 1:N) { // ...................
  53. tage[i] = (age[i] + alpha[id[i],outcome[i]] + lin[i, outcome[i]] + adrc_shift * adrc[i])/10 - B[4,outcome[i]];
  54. yhat[i] = ghyper(B[1,outcome[i]], B[2, outcome[i]], B[3,outcome[i]],
  55. B[5, outcome[i]], tage[i]);
  56. }
  57. }
  58. model {
  59. for (k in 1:2){
  60. B[,k] ~ normal(0, 50); //vague prior, sd of 50, all our values are < 10
  61. beta[,k] ~ normal(0,50); //vague again, all values are < 20
  62. }
  63. sigma ~ normal(0, 1); // the value is near .04, so this is no constraint
  64. rho ~ beta(2,1);
  65. for (j in 1:M) {
  66. alpha[j,] ~ multi_student_t(dft, zero, Sigma);
  67. }
  68. for (i in 1:N) {
  69. y[i] ~ normal(yhat[i], sigma[outcome[i]]);
  70. }
  71. adrc_shift ~ normal(0, 50); // <---- Model the common ADRC shift
  72. }

aft-model.stan at commit 5d4ca79, no license · at the source

Overview

Authors: Petrice M Cogswell1, Emily S Lundt2, Terry M Therneau2, Mingzhao Hu2, Michael E Griswold3, Heather J Wiste2, Mary M Machulda4, Nikki H Stricker4, Joel B Braunstein5, Tim West5, Philip B Verghese5, Jonathan Graff-Radford6, Alicia Algeciras-Schimnich7, Val J Lowe1, Christopher G Schwarz1, Matthew L Senjem1,8, Jeffrey L Gunter1, David S Knopman6, Prashanthi Vemuri1, Ronald C Petersen2,6, Clifford R Jack1
ORCID iDs: Petrice M Cogswell, Jonathan Graff-Radford, Alicia Algeciras-Schimnich, Christopher G Schwarz, David S Knopman, Prashanthi Vemuri, Clifford R Jack
  1. Department of Radiology, Mayo Clinic, Rochester, MN 55905, USA
  2. Department of Quantitative Health Sciences, Mayo Clinic, Rochester, MN 55905, USA
  3. Department of Data Science, University of Mississippi Medical Center, Jackson, MS 39216, USA
  4. Department of Psychiatry and Psychology, Mayo Clinic, Rochester, MN 55905, USA
  5. C2N Diagnostics, St. Louis, MO 63110, USA
  6. Department of Neurology, Mayo Clinic, Rochester, MN 55905, USA
  7. Department of Laboratory Medicine and Pathology, Mayo Clinic, Rochester, MN 55905, USA
  8. Department of Information Technology, Mayo Clinic, Rochester, MN 55905, USA
Institutions: Mayo Clinic (United States); University of Mississippi Medical Center (United States); C2N Diagnostics (United States) (United States)
Journal: Brain : a journal of neurology, volume 149, issue 9, pages 3002-3014
Dates: received 9 August 2025; accepted 25 January 2026; published online 25 February 2026; in print September 2026
Type: Research article · Language: English
License: CC BY-NC
Identifiers: DOI 10.1093/brain/awag075 · PMID 41738322 · PMCID PMC13548868 · OpenAlex W7131361358
Open access: hybrid, a free copy (OpenAlex)
Status: code verified
Categories: other (modality), PET / SPECT (modality), human (organism), Alzheimer's / dementia (population)
Methods: Preprocessing, fMRI & imaging
Keywords: Alzheimer’s disease, temporal modelling, plasma p-tau, amyloid-β PET, tau PET, cognitive decline
MeSH: Alzheimer Disease*, Cognition*, tau Proteins*, Aged, Aged, 80 and over, Amyloid beta-Peptides, Biomarkers, Cognitive Dysfunction, Cohort Studies, Disease Progression, Female, Humans, Male, Positron-Emission Tomography (* major topic)
Topic: Dementia and Cognitive Impairment Research (Psychiatry and Mental health, Medicine), according to OpenAlex
Funding: NIH (U01 AG006786, P50 AG016574, R37 AG011378, RO1 AG041851, R01 NS097495, R01 AG056366, 5R01AG069052-03)
Citations: cited by 1 paper (Europe PMC); 67 references in the paper

Abstract

Associations of Alzheimer’s disease biomarker progression with cognitive decline are important to inform patient prognosis. Of particular interest is how newly available plasma biomarkers evolve relative to cognitive decline. The goals of this work are to measure how much earlier versus later an individual’s progression on plasma and PET Alzheimer’s disease biomarkers is associated with earlier versus later cognitive progression and to estimate the average timeline of progression of these processes in the population.

In this cohort study of 2369 Mayo Clinic Study of Aging (MCSA) and 1591 Alzheimer’s Disease Neuroimaging Initiative (ADNI) participants, we fit non-linear mixed-effects models to estimate how much earlier versus later each individual progresses on plasma phosphorylated tau (p-tau)217, amyloid PET, tau PET and auditory verbal learning test (AVLT) sum of trials relative to the population mean (individual adjustment), the associations of these individual adjustments among biomarker pairs and how covariates affect the timing of biomarker progression. The association of individual adjustments implies mechanistic associations and the amount of variability in cognitive decline accounted for by each biomarker. By applying cut-off points, we also estimated the relative timing that these biomarkers become abnormal in the population.

Associations of individual adjustments were moderate between all biomarkers and AVLT (R = 0.38–0.47) in the MCSA and stronger (R = 0.74–0.81) in ADNI; plasma p-tau217 accounted for 16% of the variability in timing of AVLT decline in the MCSA and 64% in ADNI. APOE ɛ4 carriership was associated with earlier biomarker progression. AVLT became abnormal after the biomarkers up to age 90, after which AVLT was estimated to become abnormal prior to tau biomarkers.

The association of the timing of plasma and PET Alzheimer’s disease biomarker progression with cognitive decline was modest in the MCSA population-based sample and stronger in the Alzheimer’s disease-enriched ADNI cohort. The timing of plasma p-tau217 progression explained a similar degree of variability in AVLT progression as amyloid PET, supporting its utility as a marker of disease progression. The estimated temporal ordering of biomarkers and cognitive abnormality was as anticipated (amyloid, tau, cognition) up to the age of 90, beyond which AVLT was estimated to become abnormal prior to tau biomarkers, likely related to the effects of non-Alzheimer’s disease co-pathologies.

Reproduced under the paper's license (CC BY-NC), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above.

therneau/aftmodel

License: none: the authors keep all their rights
State: the link answers, verified on 26 September 2026
Evidence: files inventoried
Commit: 5d4ca79dcfcfcd76d7da202734891ff9829d4e37, 25 March 2025
Languages: R (3), Stan (2)
Size: 10 files, 5 scripts
Software Heritage: not archived
Found in: “Data availability”
Holds: README
Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Stan (5 files), tidyverse (1 file)
Availability: 1 check, the latest on 26 September 2026: the link answers
  • 26 September 2026: the link answers
6 files
At the source: github.com/Therneau/AFTmodel/fourmarkers

The paper's code and data availability statement is in the Data section.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 5 scripts, each with its path and the digest of its content;
  • no match between paragraphs and code yet;
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Data availability

MRI, PET and other data from the Mayo Clinic Study of Aging are available to qualified academic and industry researchers by request to the MCSA Executive Committee (https://www.mayo.edu/research/centers-programs/alzheimers-disease-research-center/research-activities/mayo-clinic-study-aging/for-researchers/data-sharing-resources). The code is available at github.com/Therneau/AFTmodel/fourmarkers. The PET and MRI measurement pipeline is available at https://www.nitrc.org/projects/mcalt/.

Reproduced under the paper's license (CC BY-NC), from the paper cited above.

Versions

The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.

Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 21 authors, 6 keywords, 14 MeSH terms, 1 funder, 66 references.

Cite

This paper

Cogswell, P. M., Lundt, E. S., Therneau, T. M., Hu, M., Griswold, M. E., Wiste, H. J., Machulda, M. M., Stricker, N. H., Braunstein, J. B., West, T., Verghese, P. B., Graff-Radford, J., Algeciras-Schimnich, A., Lowe, V. J., Schwarz, C. G., Senjem, M. L., Gunter, J. L., Knopman, D. S., Vemuri, P., . . . Jack, C. R. (2026). Modelling the temporal evolution of plasma p-tau217, amyloid PET, tau PET and cognition. Brain : a journal of neurology, 149(9), 3002-3014. https://doi.org/10.1093/brain/awag075

BibTeX

@article{cogswell2026modelling,
author = {Cogswell, Petrice M and Lundt, Emily S and Therneau, Terry M and Hu, Mingzhao and Griswold, Michael E and Wiste, Heather J and Machulda, Mary M and Stricker, Nikki H and Braunstein, Joel B and West, Tim and Verghese, Philip B and Graff-Radford, Jonathan and Algeciras-Schimnich, Alicia and Lowe, Val J and Schwarz, Christopher G and Senjem, Matthew L and Gunter, Jeffrey L and Knopman, David S and Vemuri, Prashanthi and Petersen, Ronald C and Jack, Clifford R},
title = {{Modelling the temporal evolution of plasma p-tau217, amyloid PET, tau PET and cognition}},
journal = {Brain : a journal of neurology},
year = {2026},
month = sep,
volume = {149},
number = {9},
pages = {3002--3014},
publisher = {Oxford University Press},
issn = {0006-8950},
doi = {10.1093/brain/awag075},
url = {https://doi.org/10.1093/brain/awag075},
pmid = {41738322},
pmcid = {PMC13548868}
}

RIS

TY - JOUR
AU - Cogswell, Petrice M
AU - Lundt, Emily S
AU - Therneau, Terry M
AU - Hu, Mingzhao
AU - Griswold, Michael E
AU - Wiste, Heather J
AU - Machulda, Mary M
AU - Stricker, Nikki H
AU - Braunstein, Joel B
AU - West, Tim
AU - Verghese, Philip B
AU - Graff-Radford, Jonathan
AU - Algeciras-Schimnich, Alicia
AU - Lowe, Val J
AU - Schwarz, Christopher G
AU - Senjem, Matthew L
AU - Gunter, Jeffrey L
AU - Knopman, David S
AU - Vemuri, Prashanthi
AU - Petersen, Ronald C
AU - Jack, Clifford R
TI - Modelling the temporal evolution of plasma p-tau217, amyloid PET, tau PET and cognition
T2 - Brain : a journal of neurology
J2 - Brain
PY - 2026
DA - 2026/09/01
VL - 149
IS - 9
SP - 3002
EP - 3014
SN - 0006-8950
PB - Oxford University Press
DO - 10.1093/brain/awag075
UR - https://doi.org/10.1093/brain/awag075
LA - en
ER -

CSL-JSON

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