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@article{alonso2016information,
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@article{parast2024statistical,
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@article{gilbert2024four,
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@article{brothers2015ethical,
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@article{zhou2023landmark,
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@article{alonso2008evaluating,
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  year={2008},
  publisher={SAGE Publications Sage UK: London, England}
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@article{roberts2021incorporating,
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  journal={Statistics in Medicine},
  volume={40},
  number={29},
  pages={6605--6618},
  year={2021},
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}

@article{schaeffer2005long,
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@article{temple1999surrogate,
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@article{sachs2022understanding,
  title={Understanding medicare’s aduhelm coverage decision},
  author={Sachs, Rachel},
  journal={Health Affairs Forefront},
  year={2022}
}

@article{dunn2021approval,
  title={Approval of aducanumab for Alzheimer disease—the FDA’s perspective},
  author={Dunn, Billy and Stein, Peter and Cavazzoni, Patrizia},
  journal={JAMA {I}nternal {M}edicine},
  volume={181},
  number={10},
  pages={1276--1278},
  year={2021},
  publisher={American Medical Association}
}

@article{fillit2021aducanumab,
  title={Aducanumab and the FDA—where are we now?},
  author={Fillit, Howard and Green, Allan},
  journal={Nature Reviews Neurology},
  volume={17},
  number={3},
  pages={129--130},
  year={2021},
  publisher={Nature Publishing Group UK London}
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@article{alexander2021revisiting,
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  author={Alexander, G Caleb and Knopman, David S and Emerson, Scott S and Ovbiagele, Bruce and Kryscio, Richard J and Perlmutter, Joel S and Kesselheim, Aaron S},
  journal={The New England journal of medicine},
  volume={385},
  number={9},
  pages={769--771},
  year={2021}
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@article{sevigny2016antibody,
  title={The antibody aducanumab reduces A$\beta$ plaques in Alzheimer’s disease},
  author={Sevigny, Jeff and Chiao, Ping and Bussi{\`e}re, Thierry and Weinreb, Paul H and Williams, Leslie and Maier, Marcel and Dunstan, Robert and Salloway, Stephen and Chen, Tianle and Ling, Yan and others},
  journal={Nature},
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@misc{biogen,
	Author = {Biogen\null},
	Howpublished = {\url{https://investors.biogen.com/news-releases/news-release-details/biogen-realign-resources-alzheimers-disease-franchise}},
	Title = {Biogen to Realign Resources for Alzheimer's Disease Franchise},
	Year = {2024}}


@misc{nytimes,
	Author = {Belluck, Pam},
	Title = {Medicare Officially Limits Coverage of Aduhelm to Patients in Clinical Trials},
	Howpublished = {\url{https://www.nytimes.com/2022/04/07/health/aduhelm-medicare-alzheimers.html}},
	Note = {Published in the New York Times},
	Year = {2022}
}

@article{kowey2024antiarrhythmic,
  title={Antiarrhythmic drug therapy: where do we go from here?},
  author={Kowey, Peter R and Naccarelli, Gerald V},
  journal={Circulation},
  volume={149},
  number={11},
  pages={801--803},
  year={2024},
  publisher={Am Heart Assoc}
}


@misc{stocks2,
	Author = {Alison Frankel},
	Howpublished = {\url{https://www.reuters.com/legal/government/column-biogen-its-investors-both-want-us-appeals-court-clarify-class-2024-10-02/}},
	Title = {Biogen and its investors both want US appeals court to clarify class certification},
	Note = {Published in Reuters},
	Year = {2022}}

@misc{stocks,
	Author = {Julie Steenhuysen and Deena Beasley},
	Howpublished = {\url{https://www.reuters.com/business/healthcare-pharmaceuticals/us-fda-set-rule-controversial-biogen-alzheimers-drug-2021-06-07/}},
	Title = {U.S. approval of Biogen Alzheimer's drug sends shares soaring, hailed as ``big day" for patients},
	Note = {Published in Reuters},
	Year = {2021}}

@misc{FDA_approved,
	Author = {FDA\null},
	Howpublished = {\url{https://www.fda.gov/drugs/development-resources/table-surrogate-endpoints-were-basis-drug-approval-or-licensure}},
	Title = {Table of Surrogate Endpoints That Were the Basis of Drug Approval or Licensure},
	Year = {2022}}

	@misc{CRAN,
	Author = {{C}{R}{A}{N}\null},
	Howpublished = {\url{https://cran.r-project.org}},
	Title = {The Comprehensive R Archive Network},
	Year = {2024}}

@misc{FDA_program,
	Author = {FDA\null},
	Howpublished = {\url{https://www.fda.gov/patients/fast-track-breakthrough-therapy-accelerated-approval-priority-review/accelerated-approval}},
	Title = {Fast Track, Breakthrough Therapy, Accelerated Approval, Priority Review: Accelerated Approval},
	Year = {2024}}

@article{croce2024lower,
  title={Lower socioeconomic status may help explain racial disparities in asthma and atopic dermatitis prevalence: A mediation analysis},
  author={Croce, Emily A and Parast, Layla and Bhavnani, Darlene and Matsui, Elizabeth C},
  journal={Journal of Allergy and Clinical Immunology},
  volume={153},
  number={4},
  pages={1140--1147},
  year={2024},
  publisher={Elsevier}
}

@misc{FDA_drug,
	Author = {{FDA}},
	Howpublished = {\url{https://www.fda.gov/news-events/press-announcements/fda-approves-jardiance-reduce-cardiovascular-death-adults-type-2-diabetes}},
	Title = {FDA Approves Novel, Dual-Targeted Treatment for Type 2 Diabetes},
	Year = {2016}}

@misc{parast2022statistical,
  title={Statistical Challenges in the Identification, Validation, and Use of Surrogate Markers},
  author={Parast, Layla and Gilbert, Peter and Wu, Lang},
  year={2022},
  Howpublished = {\url{https://www.birs.ca/cmo-workshops/2022/22w5184/report22w5184.pdf}}
}

@misc{Lily2014,
	Author = {Lilly\null},
	Howpublished = {\url{https://investor.lilly.com/news-releases/news-release-details/fda-approves-jardiancer-empagliflozin-tablets-adults-type-2}},
	Title = {FDA approves Jardiance (empagliflozin) tablets for adults with type 2 diabetes},
	Year = {2014}}



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@article{burzykowski2001validation,
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@article{shafie2023incorporating,
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@article{wang2023higher,
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@article{yeap2022testosterone,
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@misc{NDEP,
	Author = {NDEP\null},
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@misc{DPPOS,
	Author = {DPPOS\null},
	Howpublished = {\url{ https://www.niddkrepository.org/studies/dppos/}},
	Title = {Diabetes Prevention Program Outcomes Study},
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@article{parast2022using,
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  author={Parast, Layla and Cai, Tianxi and Tian, Lu},
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  volume={42},
  number={1},
  pages={68--88},
  year={2023},
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	@misc{DPPdata,
	Author = {DPP},
	Howpublished = {{ https://repository.niddk.nih.gov/studies/dpp/}},
	Title = {Diabetes Prevention Program},
	Year = {2013}}

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	Date-Modified = {2013-08-03 17:49:07 -0400},
	Institution = {Statistics and Probability Letters},
	Title = {A Note on Margin-based Loss Functions in Classification},
	Year = {2004}}

@article{Lin02supportvector,
	Author = {Yi Lin},
	Date-Added = {2013-08-03 17:49:07 -0400},
	Date-Modified = {2013-08-03 17:49:07 -0400},
	Journal = {Data Mining and Knowledge Discovery},
	Pages = {259--275},
	Title = {Support vector machines and the Bayes rule in classification},
	Volume = {6},
	Year = {2002}}

@article{Koltchinskii2002,
	Abstract = {We prove new probabilistic upper bounds on generalization error of complex classifiers that are combinations of simple classifiers. Such combinations could be implemented by neural networks or by voting methods of combining the classifiers, such as boosting and bagging. The bounds are in terms of the empirical distribution of the margin of the combined classifier. They are based on the methods of the theory of Gaussian and empirical processes (comparison inequalities, symmetrization method, concentration inequalities) and they improve previous results of Bartlett (1998) on bounding the generalization error of neural networks in terms of l\_1-norms of the weights of neurons and of Schapire, Freund, Bartlett and Lee (1998) on bounding the generalization error of boosting. We also obtain rates of convergence in Levy distance of empirical margin distribution to the true margin distribution uniformly over the classes of classifiers and prove the optimality of these rates.},
	Archiveprefix = {arXiv},
	Author = {Koltchinskii, Vladimir and Panchenko, Dmitry},
	Comment = {published = 2004-05-18T02:49:35Z, updated = 2004-05-18T02:49:35Z, 35 pages, 1 figure},
	Date-Added = {2013-08-03 17:49:07 -0400},
	Date-Modified = {2013-08-13 09:39:17 -0400},
	Eprint = {math/0405343v1},
	Journal = {Ann. Statist.},
	Month = may,
	Number = {1},
	Pages = {1-50},
	Primaryclass = {math.PR},
	Title = {{Empirical margin distributions and bounding the generalization error of combined classifiers}},
	Url = {http://arxiv.org/abs/math/0405343v1; http://arxiv.org/pdf/math/0405343v1},
	Volume = {30},
	X-Fetchedfrom = {arXiv.org},
	Year = {2002},
	Bdsk-Url-1 = {http://arxiv.org/abs/math/0405343v1;%20http://arxiv.org/pdf/math/0405343v1}}

@book{RefWorks:1634,
	Added-At = {2012-12-09T12:44:18.000+0100},
	Author = {Hastie, T. and Tibshirani, R. and Friedman, J.},
	Biburl = {http://www.bibsonomy.org/bibtex/20cd6d6683b38e7b5a15ee550266b5b9c/jbmere},
	Date-Added = {2013-08-03 17:49:07 -0400},
	Date-Modified = {2013-08-03 17:49:07 -0400},
	Interhash = {39bdf0a76d889fa39deb5d1ac793ff4e},
	Intrahash = {0cd6d6683b38e7b5a15ee550266b5b9c},
	Keywords = {imported},
	Publisher = {Springer, New York},
	Title = {{The Elements of Statistical Learning}},
	X-Fetchedfrom = {Bibsonomy},
	Year = 2009}

@misc{Zhu09multi-classadaboost,
	Author = {Ji Zhu and Hui Zou and Saharon Rosset and Trevor Hastie},
	Date-Added = {2013-08-03 17:49:07 -0400},
	Date-Modified = {2013-08-03 17:49:07 -0400},
	Title = {Multi-class AdaBoost},
	Year = {2009}}


@ARTICLE{Arulampalam-particlefilter,
  author={Arulampalam, M.S. and Maskell, S. and Gordon, N. and Clapp, T.},
  journal={IEEE Transactions on Signal Processing},
  title={A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking},
  year={2002},
  volume={50},
  number={2},
  pages={174-188},
  keywords={Tutorial;Particle filters;Nonlinear dynamical systems;Costs;Signal processing;Bayesian methods;Particle tracking;Kalman filters;Filtering;Monte Carlo methods},
  doi={10.1109/78.978374}}

@book{Amari-GeomInfo,
author = {Amari, Shun-ichi},
title = {Information Geometry and Its Applications},
year = {2016},
isbn = {4431559779},
publisher = {Springer Publishing Company, Incorporated},
edition = {1st}
}

@misc{Alves-kparametric,
      title={k-parametric Dynamic Generalized Linear Models: a sequential approach via Information Geometry},
      author={Mariane Branco Alves and Helio S. Migon and Raíra Marotta and dos Santos, Junior, Silvaneo Vieira},
      year={2024},
      eprint={2201.05387},
      archivePrefix={arXiv},
      primaryClass={stat.ME}
}

@book{West-DLM,
  added-at = {2009-10-28T04:42:52.000+0100},
  author = {West, Mike and Harrison, Jeff},
  biburl = {https://www.bibsonomy.org/bibtex/291bc168235af168280eb3558ca6dcdbc/jwbowers},
  citeulike-article-id = {111604},
  date-added = {2007-09-03 22:45:16 -0500},
  date-modified = {2007-09-03 22:45:16 -0500},
  howpublished = {Hardcover},
  interhash = {7a4066d39c9fa325dfddacb1264c79e9},
  intrahash = {91bc168235af168280eb3558ca6dcdbc},
  isbn = {0387947256},
  keywords = {bayesian statistics},
  month = {February},
  opturl = {http://www.amazon.fr/exec/obidos/ASIN/0387947256/citeulike04-21},
  publisher = {Springer-Verlag},
  timestamp = {2009-10-28T04:43:02.000+0100},
  title = {Bayesian Forecasting and Dynamic Models (Springer Series in Statistics)},
  year = 1997
}

@article{alves-transferfunction,
author = {Alves, Mariane and Gamerman, Dani and Ferreira, Marco},
year = {2010},
month = {04},
pages = {03-40},
title = {Transfer functions in dynamic generalized linear models},
volume = {10},
journal = {Statistical Modelling - STAT MODEL},
doi = {10.1177/1471082X0801000102}
}

@article{WestHarrMigon,
author = { Mike   West  and  P.   Jeff   Harrison  and  Helio S.   Migon },
title = {Dynamic Generalized Linear Models and Bayesian Forecasting},
journal = {Journal of the American Statistical Association},
volume = {80},
number = {389},
pages = {73-83},
year  = {1985},
publisher = {Taylor \& Francis},
doi = {10.1080/01621459.1985.10477131},

URL = {
        https://www.tandfonline.com/doi/abs/10.1080/01621459.1985.10477131

},
eprint = {
        https://www.tandfonline.com/doi/pdf/10.1080/01621459.1985.10477131

}

}

@article{Kalman_filter_origins,
    Author = {Kalman, Rudolph Emil},
    Title = {A New Approach to Linear Filtering and Prediction Problems},
    Journal = {Transactions of the ASME--Journal of Basic Engineering},
    Volume = {82},
    Number = {Series D},
    Pages = {35--45},
    Year = {1960}
}
@article{Parast2025Tutorial,
author = {Parast, Layla},
title = {Surrogate Marker Evaluation: A Tutorial Using R},
journal = {Statistics in Medicine},
volume = {44},
number = {10-12},
pages = {e70048},
keywords = {biomarker, censoring, implementation, non-parametric, surrogate, treatment effect},
doi = {https://doi.org/10.1002/sim.70048},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.70048},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.70048},
abstract = {ABSTRACT The practice of using a surrogate marker to replace a primary outcome in clinical studies has become widespread. Typically, the primary outcome requires long-term patient follow-up, is expensive, or is invasive or burdensome for patients to measure, while the surrogate marker is not (or less so). Of course, a surrogate marker must be validated before it should be used to make a decision about the effectiveness of a treatment. There has been a tremendous amount of statistical and clinical research focused on evaluating and validating surrogate markers over the past 35 years. Although there is ongoing debate over the optimal evaluation method, the development of new approaches and insights has greatly enriched the field. In this tutorial, we describe available statistical frameworks for evaluating a surrogate marker and specifically focus on the practical implementation of the proportion of treatment effect explained framework. We consider both uncensored and censored outcomes, parametric and non-parametric estimation, evaluating multiple surrogates, heterogeneity in the utility of the surrogate marker, surrogate evaluation from a prediction perspective, and the surrogate paradox. We include R code to implement these procedures with a follow-along R markdown. We close with a discussion on open problems in this research area, particularly in terms of using the surrogate marker to test for treatment in a future study, which is the ultimate goal of surrogate marker evaluation.},
year = {2025}
}

@article{Musch2009Visual,
title = {Visual Field Progression in the Collaborative Initial Glaucoma Treatment Study: The Impact of Treatment and Other Baseline Factors},
journal = {Ophthalmology},
volume = {116},
number = {2},
pages = {200-207.e1},
year = {2009},
issn = {0161-6420},
doi = {https://doi.org/10.1016/j.ophtha.2008.08.051},
url = {https://www.sciencedirect.com/science/article/pii/S0161642008008762},
author = {David C. Musch and Brenda W. Gillespie and Paul R. Lichter and Leslie M. Niziol and Nancy K. Janz},
abstract = {Purpose
To evaluate factors associated with visual field (VF) progression, using all available follow-up through 9 years after treatment initiation, in the Collaborative Initial Glaucoma Treatment Study (CIGTS).
Design
Longitudinal follow-up of participants enrolled in a randomized clinical trial.
Participants
Six hundred seven newly diagnosed glaucoma patients.
Methods
In a randomized clinical trial, 607 subjects with newly diagnosed open-angle glaucoma initially were treated with either medication or trabeculectomy. After treatment initiation and early follow-up, subjects were evaluated clinically at 6-month intervals. Study participants in both arms of the CIGTS were treated aggressively in an effort to reduce intraocular pressure (IOP) to a level at or below a predetermined, eye-specific target pressure. Visual field progression was analyzed using repeated measures models.
Main Outcome Measures
Visual field progression, measured by Humphrey 24-2 full-threshold testing and assessed by the change in the mean deviation (MD), and an indicator of substantial worsening of the VF (MD decrease of ≥3 dB from baseline), assessed at each follow-up visit.
Results
Follow-up indicated minimal change from baseline in each initial treatment group's average MD. However, at the 8-year follow-up examination, substantial worsening (≥3 dB) of MD from baseline was found in 21.3% and 25.5% of the initial surgery and initial medicine groups, respectively. The effect of initial treatment on subsequent VF loss was modified by time (P<0.0001), baseline MD (P = 0.03), and diabetes (P = 0.01). Initial surgery led to less VF progression than initial medicine in subjects with advanced VF loss at baseline, whereas subjects with diabetes had more VF loss over time if treated initially with surgery.
Conclusions
The CIGTS intervention protocol led to a lowering of IOP that persisted over time in both treatment groups. Progression in VF loss was seen in a subset, increasing to more than 20% of the subjects. The findings regarding initial surgery being beneficial for subjects with more advanced VF loss at presentation, but detrimental for patients with diabetes, are noteworthy and warrant independent confirmation.
Financial Disclosure(s)
The author(s) have no proprietary or commercial interest in any materials discussed in this article.}
}


@article{Blackledge1994Prostate,
author = {Blackledge, George R. P. and Lowery, Kathryn},
title = {Role of prostate-specific antigen as a predictor of outcome in prostate cancer},
journal = {The Prostate},
volume = {25},
number = {S1},
pages = {34-38},
keywords = {antiandrogen, Casodex®, castration},
doi = {https://doi.org/10.1002/pros.2990250710},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/pros.2990250710},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/pros.2990250710},
abstract = {Abstract Prostate-specific antigen (PSA) has been shown over the past few years to be a useful and sensitive marker for prostate cancer. During Phase III studies of the non-steroidal antiandrogen, Casodex®, in which different doses were compared with castration (either surgical or medical), serum PSA was measured on a regular basis. Attention was focused on the change in serum PSA from baseline after 3 months Casodex treatment and also on the number of patients receiving Casodex whose PSA returned to the normal range. Data from trials comparing Casodex, 50 mg/day, with castration showed a clear shortfall for Casodex compared with castration, in terms of percentage fall in PSA at 3 months, and also in the number of patients whose PSA fell into the normal range after 3 months. Subsequent analysis showed, however, that the PSA level was related to outcome in terms of time to progression. These data allowed the use of PSA to determine dose selection in a subsequent trial comparing Casodex, 100 mg/day or 150 mg/day, with castration. At the time of dose selection, changes in PSA showed a statistically significant difference between Casodex, 100 mg/day, and castration, but no significant difference between Casodex, 150 mg/day, and castration, either for the change in PSA at 3 months or for the proportion of patients whose PSA had fallen into the normal range. The idea that serum PSA levels can predict outcome in prostate cancer and that they are correlated with other measures of outcome, such as time to progression, is supported by these data. A decrease in PSA is not a true surrogate endpoint in that it cannot predict the outcome for an individual patient with complete accuracy, but it does correlate well with other measures of outcome, such as time to progression, for patient populations. © 1994 Wiley-Liss, Inc.},
year = {1994}
}
@article {Jacobson1991AIDS,
	author = {Jacobson, M. A. and Bacchetti, P. and Kolokathis, A. and Chaisson, R. E. and Szabo, S. and Polsky, B. and Valainis, G. T. and Mildvan, D. and Abrams, D. and Wilber, J.},
	title = {Surrogate markers for survival in patients with AIDS and AIDS related complex treated with zidovudine.},
	volume = {302},
	number = {6768},
	pages = {73--78},
	year = {1991},
	doi = {10.1136/bmj.302.6768.73},
	publisher = {BMJ Publishing Group Ltd},
	abstract = {OBJECTIVE--To determine whether early effects of zidovudine treatment on CD4+ lymphocyte count and concentrations of beta 2 microglobulin, neopterin, or HIV p24 antigen or antibody are correlated with survival in patients with AIDS or AIDS related complex. DESIGN--Retrospective study of changes in laboratory markers and survival. SETTING--Multicentre trial at university hospital clinics. SUBJECTS--90 Patients with AIDS or AIDS related complex. INTERVENTION--Patients started zidovudine 200 mg orally every four hours. Fifty six of the patients died a median 17 months after starting zidovudine; the remaining 34 patients were followed up for a median 25.5 months. MAIN OUTCOME MEASURES--Changes in CD4+ lymphocyte count and serum concentrations of p24 antigen and antibody, beta 2 microglobulin, and neopterin; survival of the patient. RESULTS--The pretreatment characteristics that independently predicted poor survival were determined using a multivariate proportional hazards model: a diagnosis of AIDS (v AIDS related complex), age over 45 years, and the logarithm of serum neopterin concentration. When these baseline characteristics were controlled for the logarithm of CD4+ lymphocyte count at weeks 8-12 of treatment (p = 0.007) and an increase in serum beta 2 microglobulin concentration at weeks 8-12 (p = 0.05) also independently correlated with survival. In the 38 patients with a better pretreatment prognosis, 24 month survival estimated by the product-limit method was 88\% for those with a good response on both surrogate markers during early treatment compared with only 50\% for those with a poor response on either marker. In the 38 with a worse pretreatment prognosis, 24 month survival was estimated to be 49\% for those with a good response on both surrogate markers compared with only 18\% for those with a poor response on either. CONCLUSION--These data suggest that CD4+ lymphocyte count at 8-12 weeks and, perhaps, change in serum beta 2 microglobulin concentration could be surrogate end points for clinical outcome in trials of antiretroviral drugs for patients with HIV disease.},
	issn = {0959-8138},
	URL = {https://www.bmj.com/content/302/6768/73},
	eprint = {https://www.bmj.com/content/302/6768/73.full.pdf},
	journal = {BMJ}
}

@techreport{Athey2019Index,
 title = "The Surrogate Index: Combining Short-Term Proxies to Estimate Long-Term Treatment Effects More Rapidly and Precisely",
 author = "Athey, Susan and Chetty, Raj and Imbens, Guido W and Kang, Hyunseung",
 institution = "National Bureau of Economic Research",
 type = "Working Paper",
 series = "Working Paper Series",
 number = "26463",
 year = "2019",
 month = "November",
 doi = {10.3386/w26463},
 URL = "http://www.nber.org/papers/w26463",
 abstract = {A common challenge in estimating the impact of interventions (e.g., job training programs, educational programs) is that many outcomes of interest (e.g., lifetime earnings or other labor market outcomes) are observed with a long delay. In biomedical settings this is often addressed by using short-term outcomes as so-called “surrogates” for the outcome of interest, e.g., tumor size as a surrogate for mortality in cancer studies. We build on this literature by combining multiple, possibly qualitatively distinct, short-term outcomes (e.g., short-run earnings and employment indicators) systematically into a “surrogate index.” Under the Prentice surrogacy assumption, which requires that the primary outcome is independent of the treatment conditional on the surrogates, we show that the average treatment effect on the surrogate index equals the treatment effect on the long-term outcome. We also relate the surrogacy assumption to a set of structural, causal assumptions. We then characterize the bias that arises from violations of each of the key assumptions, and we provide simple methods to validate these assumptions using additional observed outcomes. We apply our method to analyze the long-term impacts of a multi-site job training experiment in California. Rather than waiting a full nine years to directly observe the long-term impact, we show that it is possible to use short-term (the first six quarters) outcomes as surrogates. One could have estimated the program’s long-term impacts on mean employment rates using the employment rates observed in the first six quarters, with a 35% reduction in standard errors.},
}

@article{Chetty2014Education,
Author = {Chetty, Raj and Friedman, John N. and Rockoff, Jonah E.},
Title = {Measuring the Impacts of Teachers II: Teacher Value-Added and Student Outcomes in Adulthood},
Journal = {American Economic Review},
Volume = {104},
Number = {9},
Year = {2014},
Month = {September},
Pages = {2633–79},
DOI = {10.1257/aer.104.9.2633},
URL = {https://www.aeaweb.org/articles?id=10.1257/aer.104.9.2633}}

@article{Roberts2022Longitudinal,
    author = {Roberts, Emily K. and Elliott, Michael R. and Taylor, Jeremy M. G.},
    title = {Solutions for Surrogacy Validation with Longitudinal Outcomes for a Gene Therapy},
    journal = {Biometrics},
    volume = {79},
    number = {3},
    pages = {1840-1852},
    year = {2022},
    month = {07},
    abstract = {Valid surrogate endpoints S can be used as a substitute for a true outcome of interest T to measure treatment efficacy in a clinical trial. We propose a causal inference approach to validate a surrogate by incorporating longitudinal measurements of the true outcomes using a mixed modeling approach, and we define models and quantities for validation that may vary across the study period using principal surrogacy criteria. We consider a surrogate-dependent treatment efficacy curve that allows us to validate the surrogate at different time points. We extend these methods to accommodate a delayed-start treatment design where all patients eventually receive the treatment. Not all parameters are identified in the general setting. We apply a Bayesian approach for estimation and inference, utilizing more informative prior distributions for selected parameters. We consider the sensitivity of these prior assumptions as well as assumptions of independence among certain counterfactual quantities conditional on pretreatment covariates to improve identifiability. We examine the frequentist properties (bias of point and variance estimates, credible interval coverage) of a Bayesian imputation method. Our work is motivated by a clinical trial of a gene therapy where the functional outcomes are measured repeatedly throughout the trial.},
    issn = {0006-341X},
    doi = {10.1111/biom.13720},
    url = {https://doi.org/10.1111/biom.13720},
    eprint = {https://academic.oup.com/biometrics/article-pdf/79/3/1840/56035442/biometrics_79_3_1840.pdf},
}

@article{Agniel2024Survival,
    author = {Agniel, Denis and Parast, Layla},
    title = {Robust evaluation of longitudinal surrogate markers with censored data},
    journal = {Journal of the Royal Statistical Society Series B: Statistical Methodology},
    volume = {87},
    number = {3},
    pages = {891-907},
    year = {2024},
    month = {12},
    abstract = {The development of statistical methods to evaluate surrogate markers is an active area of research. In many clinical settings, the surrogate marker is not simply a single measurement but is instead a longitudinal trajectory of measurements over time, e.g. fasting plasma glucose measured every 6 months for 3 years. In general, available methods developed for the single-surrogate setting cannot accommodate a longitudinal surrogate marker. Furthermore, many of the methods have not been developed for use with primary outcomes that are time-to-event outcomes and/or subject to censoring. In this paper, we propose robust methods to evaluate a longitudinal surrogate marker in a censored time-to-event outcome setting. Specifically, we propose a method to define and estimate the proportion of the treatment effect on a censored primary outcome that is explained by the treatment effect on a longitudinal surrogate marker measured up to time t0. We accommodate both potential censoring of the primary outcome and of the surrogate marker. A simulation study demonstrates a good finite-sample performance of our proposed methods. We illustrate our procedures by examining repeated measures of fasting plasma glucose, a surrogate marker for diabetes diagnosis, using data from the diabetes prevention programme.}
}

@article{Agniel2020Longitudinal,
    author = {Agniel, Denis and Parast, Layla},
    title = {Evaluation of Longitudinal Surrogate Markers},
    journal = {Biometrics},
    volume = {77},
    number = {2},
    pages = {477-489},
    year = {2020},
    month = {06},
    abstract = {The use of surrogate markers to examine the effectiveness of a treatment has the potential to decrease study length and identify effective treatments more quickly. Most available methods to investigate the usefulness of a surrogate marker involve restrictive parametric assumptions and tend to focus on settings where the surrogate is measured at a single point in time. However, in many clinical settings, the potential surrogate marker is often measured repeatedly over time, and thus, the surrogate marker information is a trajectory of measurements. In addition, it is often difficult in practice to correctly specify the relationship between a treatment, primary outcome, and surrogate marker trajectory. In this paper, we propose a model-free definition for the proportion of the treatment effect on the primary outcome that is explained by the treatment effect on the longitudinal surrogate markers. We propose three novel flexible methods to estimate this proportion, develop the asymptotic properties of our estimators, and investigate the robustness of the estimators under multiple settings via a simulation study. We apply our proposed procedures to an AIDS clinical trial dataset to examine a trajectory of CD4 counts as a potential surrogate.},
    issn = {0006-341X},
    doi = {10.1111/biom.13310},
    url = {https://doi.org/10.1111/biom.13310},
    eprint = {https://academic.oup.com/biometrics/article-pdf/77/2/477/54382058/biometrics_77_2_477.pdf},
}
@article{VanderWeele2016Mediation,
    author = {VanderWeele, Tyler J. and Tchetgen Tchetgen, Eric J.},
    title = {Mediation Analysis with time Varying Exposures and Mediators},
    journal = {Journal of the Royal Statistical Society Series B: Statistical Methodology},
    volume = {79},
    number = {3},
    pages = {917-938},
    year = {2016},
    month = {06},
    abstract = {We consider causal mediation analysis when exposures and mediators vary over time. We give non-parametric identification results, discuss parametric implementation and also provide a weighting approach to direct and indirect effects based on combining the results of two marginal structural models. We also discuss how our results give rise to a causal interpretation of the effect estimates produced from longitudinal structural equation models. When there are time varying confounders affected by prior exposure and a mediator, natural direct and indirect effects are not identified. However, we define a randomized interventional analogue of natural direct and indirect effects that are identified in this setting. The formula that identifies these effects we refer to as the ‘mediational g-formula’. When there is no mediation, the mediational g-formula reduces to Robins's regular g-formula for longitudinal data. When there are no time varying confounders affected by prior exposure and mediator values, then the mediational g-formula reduces to a longitudinal version of Pearl's mediation formula. However, the mediational g-formula itself can accommodate both mediation and time varying confounders and constitutes a general approach to mediation analysis with time varying exposures and mediators.},
    issn = {1369-7412},
    doi = {10.1111/rssb.12194},
    url = {https://doi.org/10.1111/rssb.12194},
    eprint = {https://academic.oup.com/jrsssb/article-pdf/79/3/917/49214890/jrsssb_79_3_917.pdf},
}


@article{Diaz2023Mediation,
url = {https://doi.org/10.1515/jci-2022-0077},
title = {Efficient and flexible mediation analysis with time-varying mediators, treatments, and confounders},
author = {Iván Díaz and Nicholas Williams and Kara E. Rudolph},
pages = {20220077},
volume = {11},
number = {1},
journal = {Journal of Causal Inference},
doi = {doi:10.1515/jci-2022-0077},
year = {2023},
lastchecked = {2025-09-19}
}


@article{Parast2024Small,
    author = {Parast, Layla and Cai, Tianxi and Tian, Lu},
    title = {A rank-based approach to evaluate a surrogate marker in a small sample setting},
    journal = {Biometrics},
    volume = {80},
    number = {1},
    pages = {ujad035},
    year = {2024},
    month = {02},
    abstract = {In clinical studies of chronic diseases, the effectiveness of an intervention is often assessed using “high cost” outcomes that require long-term patient follow-up and/or are invasive to obtain. While much progress has been made in the development of statistical methods to identify surrogate markers, that is, measurements that could replace such costly outcomes, they are generally not applicable to studies with a small sample size. These methods either rely on nonparametric smoothing which requires a relatively large sample size or rely on strict model assumptions that are unlikely to hold in practice and empirically difficult to verify with a small sample size. In this paper, we develop a novel rank-based nonparametric approach to evaluate a surrogate marker in a small sample size setting. The method developed in this paper is motivated by a small study of children with nonalcoholic fatty liver disease (NAFLD), a diagnosis for a range of liver conditions in individuals without significant history of alcohol intake. Specifically, we examine whether change in alanine aminotransferase (ALT; measured in blood) is a surrogate marker for change in NAFLD activity score (obtained by biopsy) in a trial, which compared Vitamin E (\$n=50\$) versus placebo (\$n=46\$) among children with NAFLD.},
    issn = {0006-341X},
    doi = {10.1093/biomtc/ujad035},
    url = {https://doi.org/10.1093/biomtc/ujad035},
    eprint = {https://academic.oup.com/biometrics/article-pdf/80/1/ujad035/56741252/ujad035.pdf},
}

@article{Alves2025Econometrics,
author = {Alves, Mariane B. and Migon, Helio S. and Menezes, André F. B. and Pinheiro, Eduardo G. and dos Santos Jr., Silvaneo V.},
title = {Dynamic Econometric Models: A State-Space Formulation},
journal = {Journal of Forecasting},
volume = {n/a},
number = {n/a},
pages = {},
year = 2025,
keywords = {discount factor, nonlinear dynamic models, Phillips curve, sequential inference, stochastic volatility, transfer function},
doi = {https://doi.org/10.1002/for.70017},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/for.70017},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/for.70017},
abstract = {ABSTRACT In the area of econometrics, the investigation and characterization of processes that retain memory for the past are often of interest. This work overcomes collinearity problems that arise in distributed lag formulations by modeling these effects as structural elements within nonlinear dynamic models using transfer functions. Our main contribution lies in performing sequential Bayesian inference for nonlinear dynamic models, providing an efficient computational solution based on analytical approximations. The scalability offered by the proposed sequential method is particularly relevant in the econometric context, where long time series or multiple levels of disaggregation are often encountered. The proposed models incorporate stochastic volatility, achieved through the use of discount factors. An extensive simulation investigation validates the inferential approximation. The results of the proposed sequential and analytical approximation are compared with the inference obtained through Hamiltonian Monte Carlo in a particular application to real-world consumption data. The results show that the sequential approach produces results that are largely comparable while requiring a significantly shorter amount of computing time. Using the proposed Bayesian state-space framework and a thorough examination of the Phillips curve, a case study is developed focusing on the relationship between inflation and the output gap in the Brazilian scenario. We conclude with a substantial contribution, based on an innovative approach that preserves Bayesian sequential inference and offers a joint model for inflation and the output gap, with dynamic predictive structures assigned to the means, precisions, and correlation between both economic indicators.}
}

@article{Auger2021Ecology,
author = {Auger-Méthé, Marie and Newman, Ken and Cole, Diana and Empacher, Fanny and Gryba, Rowenna and King, Aaron A. and Leos-Barajas, Vianey and Mills Flemming, Joanna and Nielsen, Anders and Petris, Giovanni and Thomas, Len},
title = {A guide to state–space modeling of ecological time series},
journal = {Ecological Monographs},
volume = {91},
number = {4},
pages = {e01470},
keywords = {Bayesian, diagnostic, fitting procedure, frequentist, model selection, state–space model, time series},
doi = {https://doi.org/10.1002/ecm.1470},
url = {https://esajournals.onlinelibrary.wiley.com/doi/abs/10.1002/ecm.1470},
eprint = {https://esajournals.onlinelibrary.wiley.com/doi/pdf/10.1002/ecm.1470},
abstract = {Abstract State–space models (SSMs) are an important modeling framework for analyzing ecological time series. These hierarchical models are commonly used to model population dynamics, animal movement, and capture–recapture data, and are now increasingly being used to model other ecological processes. SSMs are popular because they are flexible and they model the natural variation in ecological processes separately from observation error. Their flexibility allows ecologists to model continuous, count, binary, and categorical data with linear or nonlinear processes that evolve in discrete or continuous time. Modeling the two sources of stochasticity separately allows researchers to differentiate between biological variation and imprecision in the sampling methodology, and generally provides better estimates of the ecological quantities of interest than if only one source of stochasticity is directly modeled. Since the introduction of SSMs, a broad range of fitting procedures have been proposed. However, the variety and complexity of these procedures can limit the ability of ecologists to formulate and fit their own SSMs. We provide the knowledge for ecologists to create SSMs that are robust to common, and often hidden, estimation problems, and the model selection and validation tools that can help them assess how well their models fit their data. We present a review of SSMs that will provide a strong foundation to ecologists interested in learning about SSMs, introduce new tools to veteran SSM users, and highlight promising research directions for statisticians interested in ecological applications. The review is accompanied by an in-depth tutorial that demonstrates how SSMs can be fitted and validated in R. Together, the review and tutorial present an introduction to SSMs that will help ecologists to formulate, fit, and validate their models.},
year = {2021}
}

@article{hsu2015surrogate,
  title={Surrogate markers for time-varying treatments and outcomes},
  author={Hsu, Jesse Y and Kennedy, Edward H and Roy, Jason A and Stephens-Shields, Alisa J and Small, Dylan S and Joffe, Marshall M},
  journal={Clinical Trials},
  volume={12},
  number={4},
  pages={309--316},
  year={2015},
  publisher={SAGE Publications Sage UK: London, England}
}


@article{chakraborty2014dynamic,
  title={Dynamic treatment regimes},
  author={Chakraborty, Bibhas and Murphy, Susan A},
  journal={Annual review of statistics and its application},
  volume={1},
  number={1},
  pages={447--464},
  year={2014},
  publisher={Annual Reviews}
}



@article{Prashad2025Epidemiology,
title = {State-space modelling for infectious disease surveillance data: Stochastic simulation techniques and structural change detection},
journal = {Infectious Disease Modelling},
volume = {10},
number = {4},
pages = {1507-1532},
year = {2025},
issn = {2468-0427},
doi = {https://doi.org/10.1016/j.idm.2025.05.005},
url = {https://www.sciencedirect.com/science/article/pii/S2468042725000375},
author = {Christopher D. Prashad},
keywords = {State-space modelling, Nonlinear dynamic regression, Stochastic simulation, Structural change detection, Rao-blackwellized particle filter, Infectious disease surveillance data},
abstract = {We present an exploration of advanced stochastic simulation techniques for state-space models, with a specific focus on their applications in infectious disease modelling. Utilizing COVID-19 surveillance data from the province of Ontario, Canada, we employ Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) methods to detect structural changes and pre-dict future trends in case counts. Our approach begins with the application of a Kalman smoothing technique, integrated with MCMC for state sampling within local level and seasonal models, alongside Bayesian inference for non-linear dynamic regression models. We then assess the effectiveness of various priors, including normal, Student's t, Laplace, and horseshoe distributions, in capturing abrupt changes within the data using a Rao-Blackwellized par-ticle filter. Our findings highlight the superior performance of the horseshoe prior in identifying change points and adapting to complex data structures, offering valuable insights for real-time monitoring and forecasting in public health. This study emphasizes the efficacy of state-space models, particu-larly when enhanced with sophisticated prior distributions, in providing a nuanced understanding of infectious disease transmission.}
}

@article{Chetverikov_Wilhelm_Kim_2021, title={AN ADAPTIVE TEST OF STOCHASTIC MONOTONICITY}, volume={37}, DOI={10.1017/S0266466620000225}, number={3}, journal={Econometric Theory}, author={Chetverikov, Denis and Wilhelm, Daniel and Kim, Dongwoo}, year={2021}, pages={495–536}} <div></div>

@article{SHIMODAIRA2000227,
title = {Improving predictive inference under covariate shift by weighting the log-likelihood function},
journal = {Journal of Statistical Planning and Inference},
volume = {90},
number = {2},
pages = {227-244},
year = {2000},
issn = {0378-3758},
doi = {https://doi.org/10.1016/S0378-3758(00)00115-4},
url = {https://www.sciencedirect.com/science/article/pii/S0378375800001154},
author = {Hidetoshi Shimodaira},
keywords = {Akaike information criterion, Design of experiments, Importance sampling, Kullback–Leibler divergence, Misspecification, Sample surveys, Weighted least squares},
abstract = {A class of predictive densities is derived by weighting the observed samples in maximizing the log-likelihood function. This approach is effective in cases such as sample surveys or design of experiments, where the observed covariate follows a different distribution than that in the whole population. Under misspecification of the parametric model, the optimal choice of the weight function is asymptotically shown to be the ratio of the density function of the covariate in the population to that in the observations. This is the pseudo-maximum likelihood estimation of sample surveys. The optimality is defined by the expected Kullback–Leibler loss, and the optimal weight is obtained by considering the importance sampling identity. Under correct specification of the model, however, the ordinary maximum likelihood estimate (i.e. the uniform weight) is shown to be optimal asymptotically. For moderate sample size, the situation is in between the two extreme cases, and the weight function is selected by minimizing a variant of the information criterion derived as an estimate of the expected loss. The method is also applied to a weighted version of the Bayesian predictive density. Numerical examples as well as Monte-Carlo simulations are shown for polynomial regression. A connection with the robust parametric estimation is discussed.}
}

@article{Steingrimsson2022,
    author = {Steingrimsson, Jon A and Gatsonis, Constantine and Li, Bing and Dahabreh, Issa J},
    title = {Transporting a Prediction Model for Use in a New Target Population},
    journal = {American Journal of Epidemiology},
    volume = {192},
    number = {2},
    pages = {296-304},
    year = {2022},
    month = {07},
    abstract = {We considered methods for transporting a prediction model for use in a new target population, both when outcome and covariate data for model development are available from a source population that has a different covariate distribution compared with the target population and when covariate data (but not outcome data) are available from the target population. We discuss how to tailor the prediction model to account for differences in the data distribution between the source population and the target population. We also discuss how to assess the model’s performance (e.g., by estimating the mean squared prediction error) in the target population. We provide identifiability results for measures of model performance in the target population for a potentially misspecified prediction model under a sampling design where the source and the target population samples are obtained separately. We introduce the concept of prediction error modifiers that can be used to reason about tailoring measures of model performance to the target population. We illustrate the methods in simulated data and apply them to transport a prediction model for lung cancer diagnosis from the National Lung Screening Trial to the nationally representative target population of trial-eligible individuals in the National Health and Nutrition Examination Survey.},
    issn = {0002-9262},
    doi = {10.1093/aje/kwac128},
    url = {https://doi.org/10.1093/aje/kwac128},
    eprint = {https://academic.oup.com/aje/article-pdf/192/2/296/57195526/kwac128.pdf},
}

@article{Wager2016,
author = {Stefan Wager  and Wenfei Du  and Jonathan Taylor  and Robert J. Tibshirani },
title = {High-dimensional regression adjustments in randomized experiments},
journal = {Proceedings of the National Academy of Sciences},
volume = {113},
number = {45},
pages = {12673-12678},
year = {2016},
doi = {10.1073/pnas.1614732113},
URL = {https://www.pnas.org/doi/abs/10.1073/pnas.1614732113},
eprint = {https://www.pnas.org/doi/pdf/10.1073/pnas.1614732113},
abstract = {As datasets get larger and more complex, there is a growing interest in using machine-learning methods to enhance scientific analysis. In many settings, considerable work is required to make standard machine-learning methods useful for specific scientific applications. We find, however, that in the case of treatment effect estimation with randomized experiments, regression adjustments via machine-learning methods designed to minimize test set error directly induce efficient estimates of the average treatment effect. Thus, machine-learning methods can be used out of the box for this task, without any special-case adjustments. We study the problem of treatment effect estimation in randomized experiments with high-dimensional covariate information and show that essentially any risk-consistent regression adjustment can be used to obtain efficient estimates of the average treatment effect. Our results considerably extend the range of settings where high-dimensional regression adjustments are guaranteed to provide valid inference about the population average treatment effect. We then propose cross-estimation, a simple method for obtaining finite-sample–unbiased treatment effect estimates that leverages high-dimensional regression adjustments. Our method can be used when the regression model is estimated using the lasso, the elastic net, subset selection, etc. Finally, we extend our analysis to allow for adaptive specification search via cross-validation and flexible nonparametric regression adjustments with machine-learning methods such as random forests or neural networks.}}

@article{Sugiyama2008,
  author  = {Sugiyama, Masashi and Suzuki, Taiji and Nakajima, Shinichi and Kashima, Hisashi and von B{\"u}nau, Paul and Kawanabe, Motoaki},
  title   = {Direct importance estimation for covariate shift adaptation},
  journal = {Annals of the Institute of Statistical Mathematics},
  year    = {2008},
  volume  = {60},
  number  = {4},
  pages   = {699--746},
  doi     = {10.1007/s10463-008-0197-x},
  url     = {https://doi.org/10.1007/s10463-008-0197-x}
}



@article{SUGIYAMA2011183,
title = {Direct density-ratio estimation with dimensionality reduction via least-squares hetero-distributional subspace search},
journal = {Neural Networks},
volume = {24},
number = {2},
pages = {183-198},
year = {2011},
issn = {0893-6080},
doi = {https://doi.org/10.1016/j.neunet.2010.10.005},
url = {https://www.sciencedirect.com/science/article/pii/S0893608010001917},
author = {Masashi Sugiyama and Makoto Yamada and Paul {von Bünau} and Taiji Suzuki and Takafumi Kanamori and Motoaki Kawanabe},
keywords = {Density-ratio estimation, Dimensionality reduction, Unconstrained least-squares importance fitting},
abstract = {Methods for directly estimating the ratio of two probability density functions have been actively explored recently since they can be used for various data processing tasks such as non-stationarity adaptation, outlier detection, and feature selection. In this paper, we develop a new method which incorporates dimensionality reduction into a direct density-ratio estimation procedure. Our key idea is to find a low-dimensional subspace in which densities are significantly different and perform density-ratio estimation only in this subspace. The proposed method, D3-LHSS (Direct Density-ratio estimation with Dimensionality reduction via Least-squares Hetero-distributional Subspace Search), is shown to overcome the limitation of baseline methods.}
}

@inproceedings{Izbicki2014,
author = {Izbicki, Rafael and Lee, Ann and Schafer, Chad},
year = {2014},
month = {04},
pages = {},
title = {High-Dimensional Density Ratio Estimation with Extensions to Approximate Likelihood Computation},
journal = {Proceedings of the International Conference on Artificial Intelligence and Statistics, AISTATS}
}

@misc{santos2026causalframeworkevaluatingjointly,
      title={A Causal Framework for Evaluating Jointly Longitudinal Outcomes and Surrogate Markers: A State-Space Approach},
      author={Silvaneo V. dos Santos Jr. and Layla Parast},
      year={2026},
      eprint={2604.12882},
      archivePrefix={arXiv},
      primaryClass={stat.ME},
      url={https://arxiv.org/abs/2604.12882},
}
