About

Martin Timothy Wells is the Charles A. Alexander Professor of Statistical Sciences at Cornell University and a Professor of Social Statistics in the ILR School. He joined the Cornell faculty in 1987 and holds additional appointments as Professor of Biostatistics and Epidemiology at Weill Medical School, as well as an elected member of the Cornell Law School faculty. His teaching encompasses statistical methodology across a broad range of fields including agriculture, biology, epidemiology, finance, law, medicine, nutrition, social science, and veterinary medicine, with graduate courses in statistics. His research focuses on statistical modeling, Bayesian inference, hierarchical regression approaches, and applications in bioinformatics, epidemiology, law, and social sciences. Wells has contributed extensively to the academic literature with numerous publications in reputable journals, emphasizing the development of statistical methods and their application to real-world problems.

Research topics

• Political Science
• Medicine
• Sociology
• Internal medicine
• Endocrinology
• Medical education
• Microbiology
• Biochemistry
• Psychology
• Criminology
• Biology
• Nursing
• Law
• Pediatrics
• Physical therapy
• Immunology

Selected publications

• A Milestone-Based Framework for Characterizing Time-Varying Treatment Effects in Immunotherapy Trials

  arXiv (Cornell University) · 2026-04-27

  preprintOpen accessSenior author

  Immune checkpoint inhibitor--based therapies often produce heterogeneous survival responses, including early risk, delayed treatment benefit, and durable long-term survival in a subset of patients. In these settings, conventional summary measures such as the hazard ratio may not adequately describe how treatment effects evolve over follow-up. We propose a milestone-based framework that separates long-term survival beyond a clinically meaningful time point from earlier outcomes and provides a practical way to characterize patient heterogeneity in treatment response. The framework summarizes treatment differences through milestone survival probabilities and, among patients who do not reach the milestone, characterizes short-term treatment ordering over time using a tau-based summary that helps identify hazard reversal. We illustrate the approach using reconstructed individual-level data from three landmark phase III trials: CheckMate~067, CheckMate~227, and CLEAR. Across these examples, the framework captures patterns that are difficult to summarize with conventional measures, including settings in which early disadvantage coexists with later durable benefit. It also helps clarify when treatment benefit begins to emerge and how short-term and long-term effects differ within the same trial. This approach provides a clinically interpretable and statistically principled way to evaluate heterogeneous and time-varying treatment effects in oncology trials with nonproportional hazards.

  PublisherDOI

• BLOG: Bayesian longitudinal omics with group constraints

  Statistical Applications in Genetics and Molecular Biology · 2026-01-01

  articleOpen accessSenior author

  Abstract Clinical investigators are increasingly interested in discovering computational biomarkers from short-term longitudinal omics datasets. This work focuses on Bayesian regression and variable selection for longitudinal omics datasets, which can estimate posterior evidence for each candidate biomarker and control false discovery using evidence thresholds. In our univariate approach, Zellner’s g -prior is used with two different options of the tuning parameter g : <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:mi>g</m:mi> <m:mo>=</m:mo> <m:msqrt> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msqrt> </m:math> $g=\sqrt{n}$ and a g that minimizes Stein’s unbiased risk estimate (SURE). Bayes factors are used to rank metabolites by evidence, and their mapping to posterior model probabilities under prior odds can provide local posterior null probabilities whose average over the rejection set defines a Bayesian analogue of the global FDR. In the multivariate approach, we use Bayesian group lasso with a spike and slab prior for group variable selection. In both approaches, we use the first difference (Δ) scale of longitudinal predictor and the response. These methods work together to enhance our understanding of biomarker identification, improving inference and prediction. We compare our method against commonly used linear mixed effect models on simulated data and real data from a Tuberculosis (TB) study on metabolite biomarker selection. With an automated selection of hyperparameters, the Zellner’s g -prior approach correctly identifies target metabolites with high specificity and sensitivity across various simulation and real data scenarios. The multivariate Bayesian group lasso spike and slab approach also correctly selects target metabolites across various simulation scenarios.

  PublisherOA PDFDOI

• A Milestone-Based Framework for Characterizing Time-Varying Treatment Effects in Immunotherapy Trials

  ArXiv.org · 2026-04-27

  articleOpen accessSenior author

  Immune checkpoint inhibitor--based therapies often produce heterogeneous survival responses, including early risk, delayed treatment benefit, and durable long-term survival in a subset of patients. In these settings, conventional summary measures such as the hazard ratio may not adequately describe how treatment effects evolve over follow-up. We propose a milestone-based framework that separates long-term survival beyond a clinically meaningful time point from earlier outcomes and provides a practical way to characterize patient heterogeneity in treatment response. The framework summarizes treatment differences through milestone survival probabilities and, among patients who do not reach the milestone, characterizes short-term treatment ordering over time using a tau-based summary that helps identify hazard reversal. We illustrate the approach using reconstructed individual-level data from three landmark phase III trials: CheckMate~067, CheckMate~227, and CLEAR. Across these examples, the framework captures patterns that are difficult to summarize with conventional measures, including settings in which early disadvantage coexists with later durable benefit. It also helps clarify when treatment benefit begins to emerge and how short-term and long-term effects differ within the same trial. This approach provides a clinically interpretable and statistically principled way to evaluate heterogeneous and time-varying treatment effects in oncology trials with nonproportional hazards.

  PublisherOA PDF

• SEMMS with Random Effects: A Mixed-Model Extension for Variable Selection in Clustered and Longitudinal Data

  arXiv (Cornell University) · 2026-03-16

  preprintOpen accessSenior author

  SEMMS (Scalable Empirical-Bayes Model for Marker Selection) is a variable-selection procedure for generalized linear models that uses a three-component normal mixture prior on regression coefficients. In its original form, SEMMS assumes that all observations are independent. Many real-world datasets, however, arise from repeated-measures or clustered designs in which observations within the same subject are correlated. Ignoring this correlation inflates the apparent residual variance and can severely degrade variable-selection performance. We extend SEMMS to accommodate random intercepts, random slopes, or both, via an alternating coordinate-ascent algorithm. After each round of fixed-effect variable selection, the subject-level best linear unbiased predictors (BLUPs) are updated with \texttt{lmer} (Gaussian) or \texttt{glmer} (non-Gaussian); the fixed-effect step then operates on the random-effect-adjusted response. We describe the algorithm, evaluate its performance in three Gaussian simulation studies spanning a range of signal strengths, random-effect magnitudes, and sample/predictor-space regimes, and present a semi-synthetic real-data example. We further extend the framework to non-Gaussian families (Poisson, binomial) via an IRLS working-response adaptation: at each outer iteration the fixed-effects step uses the RE-adjusted working response computed from the current \texttt{glmer} fitted values rather than the raw response. When the fixed-effect signal is strong relative to the random-effect variance, both the original and extended procedures perform comparably. When the random-effect variance dominates -- the scenario most likely to cause plain SEMMS to fail -- the mixed-model extension recovers the exact true predictor set in 93\% of simulated datasets (Gaussian), 61\% (Poisson), and 65\% (binomial), compared with 1\%, 45\%, and 39\% for plain SEMMS respectively.

  PublisherDOI

• SEMMS with Random Effects: A Mixed-Model Extension for Variable Selection in Clustered and Longitudinal Data

  ArXiv.org · 2026-03-16

  articleOpen accessSenior author

  SEMMS (Scalable Empirical-Bayes Model for Marker Selection) is a variable-selection procedure for generalized linear models that uses a three-component normal mixture prior on regression coefficients. In its original form, SEMMS assumes that all observations are independent. Many real-world datasets, however, arise from repeated-measures or clustered designs in which observations within the same subject are correlated. Ignoring this correlation inflates the apparent residual variance and can severely degrade variable-selection performance. We extend SEMMS to accommodate random intercepts, random slopes, or both, via an alternating coordinate-ascent algorithm. After each round of fixed-effect variable selection, the subject-level best linear unbiased predictors (BLUPs) are updated with \texttt{lmer} (Gaussian) or \texttt{glmer} (non-Gaussian); the fixed-effect step then operates on the random-effect-adjusted response. We describe the algorithm, evaluate its performance in three Gaussian simulation studies spanning a range of signal strengths, random-effect magnitudes, and sample/predictor-space regimes, and present a semi-synthetic real-data example. We further extend the framework to non-Gaussian families (Poisson, binomial) via an IRLS working-response adaptation: at each outer iteration the fixed-effects step uses the RE-adjusted working response computed from the current \texttt{glmer} fitted values rather than the raw response. When the fixed-effect signal is strong relative to the random-effect variance, both the original and extended procedures perform comparably. When the random-effect variance dominates -- the scenario most likely to cause plain SEMMS to fail -- the mixed-model extension recovers the exact true predictor set in 93\% of simulated datasets (Gaussian), 61\% (Poisson), and 65\% (binomial), compared with 1\%, 45\%, and 39\% for plain SEMMS respectively.

  PublisherOA PDF

• Is There an AI Bubble? Robust Date-Stamping for Periods of Exuberance

  arXiv (Cornell University) · 2026-04-13

  preprintOpen accessSenior author

  The recent surge in valuations among AI related firms has renewed concerns that markets may be entering a new phase of speculative exuberance, especially in the technology and semiconductor sectors at the center of the AI investment wave. This paper develops a practical econometric framework for detecting, date-stamping, and drawing inference on the origination and collapse of bubble episodes when prices evolve under persistent, time-varying volatility. Standard bubble tests are typically derived under homoskedasticity or weak heteroskedasticity and may therefore yield misleading inference in more general settings. We extend right-tailed Dickey-Fuller unit root tests to autoregressive models with highly persistent mean and volatility dynamics, delivering a stochastic-volatility-robust ADF (SV-ADF) test that accommodates persistent variance without imposing strict parametric structure. Building on a moderate-deviation asymptotic theory, the SV-ADF yields nuisance-parameter-free procedures with distinct critical values for origination and collapse, producing more stable alarms and fewer transient false positives around volatility spikes. We establish consistency of the date-stamping estimator and show that it remains asymptotically tractable. Monte Carlo simulations document strong power and substantial gains over homoskedastic (PWY) procedures when volatility dynamics are pronounced. An empirical analysis of AI-exposed equities, including the "Magnificent Seven" and leading semiconductor firms, finds pervasive exuberance with substantial heterogeneity in timing, intensity, and duration. The evidence points to especially strong bubble dynamics for Alphabet and TSMC in the current cycle, while Tesla and Nvidia exhibited pronounced explosive episodes in earlier phases of the AI-driven market cycle.

  PublisherDOI

• Is There an AI Bubble? Robust Date-Stamping for Periods of Exuberance

  ArXiv.org · 2026-04-13

  articleOpen accessSenior author

  The recent surge in valuations among AI related firms has renewed concerns that markets may be entering a new phase of speculative exuberance, especially in the technology and semiconductor sectors at the center of the AI investment wave. This paper develops a practical econometric framework for detecting, date-stamping, and drawing inference on the origination and collapse of bubble episodes when prices evolve under persistent, time-varying volatility. Standard bubble tests are typically derived under homoskedasticity or weak heteroskedasticity and may therefore yield misleading inference in more general settings. We extend right-tailed Dickey-Fuller unit root tests to autoregressive models with highly persistent mean and volatility dynamics, delivering a stochastic-volatility-robust ADF (SV-ADF) test that accommodates persistent variance without imposing strict parametric structure. Building on a moderate-deviation asymptotic theory, the SV-ADF yields nuisance-parameter-free procedures with distinct critical values for origination and collapse, producing more stable alarms and fewer transient false positives around volatility spikes. We establish consistency of the date-stamping estimator and show that it remains asymptotically tractable. Monte Carlo simulations document strong power and substantial gains over homoskedastic (PWY) procedures when volatility dynamics are pronounced. An empirical analysis of AI-exposed equities, including the "Magnificent Seven" and leading semiconductor firms, finds pervasive exuberance with substantial heterogeneity in timing, intensity, and duration. The evidence points to especially strong bubble dynamics for Alphabet and TSMC in the current cycle, while Tesla and Nvidia exhibited pronounced explosive episodes in earlier phases of the AI-driven market cycle.

  PublisherOA PDF

• An Assessment of Racial Disparities in Pretrial Decision‐Making Using Misclassification Models

  Journal of Empirical Legal Studies · 2026-04-16

  preprintOpen accessSenior author

  ABSTRACT Pretrial risk assessment tools are used in jurisdictions across the country to assess the likelihood of “pretrial failure,” the event where defendants either fail to appear (FTA) for court or reoffend. Judicial officers, in turn, use these assessments to determine whether to release or detain defendants during trial. While algorithmic risk assessment tools were designed to predict pretrial failure with greater accuracy relative to judges, there is still concern that both risk assessment recommendations and pretrial decisions are biased against minority groups. We use the Virginia Pretrial Risk Assessment Instrument (VPRAI) as a case study to investigate the accuracy and fairness of risk assessment algorithms and judicial decisions. In this paper, we develop methods to investigate the association between risk factors and pretrial failure, while simultaneously estimating misclassification rates of pretrial risk assessments and of judicial decisions as a function of defendant race. This approach adds to a growing literature that makes use of outcome misclassification methods to answer questions about fairness in pretrial decision‐making. We give a detailed simulation study for our proposed methodology and apply these methods to data from the Virginia Department of Criminal Justice Services. We estimate that the VPRAI algorithm has near‐perfect specificity, but its sensitivity differs by defendant race. Judicial decisions also display evidence of bias; we estimate wrongful detention rates of 39.7% and 51.4% among white and Black defendants, respectively.

  PublisherOA PDFDOI

• e3SIM software and demo files

  Open MIND · 2026-01-01

  other

• Quantum Cognition Machine Learning for Forecasting Chromosomal Instability

  ArXiv.org · 2025-06-02

  preprintOpen access

  The accurate prediction of chromosomal instability from the morphology of circulating tumor cells (CTCs) enables real-time detection of CTCs with high metastatic potential in the context of liquid biopsy diagnostics. However, it presents a significant challenge due to the high dimensionality and complexity of single-cell digital pathology data. Here, we introduce the application of Quantum Cognition Machine Learning (QCML), a quantum-inspired computational framework, to estimate morphology-predicted chromosomal instability in CTCs from patients with metastatic breast cancer. QCML leverages quantum mechanical principles to represent data as state vectors in a Hilbert space, enabling context-aware feature modeling, dimensionality reduction, and enhanced generalization without requiring curated feature selection. QCML outperforms conventional machine learning methods when tested on out of sample verification CTCs, achieving higher accuracy in identifying predicted large-scale state transitions (pLST) status from CTC-derived morphology features. These preliminary findings support the application of QCML as a novel machine learning tool with superior performance in high-dimensional, low-sample-size biomedical contexts. QCML enables the simulation of cognition-like learning for the identification of biologically meaningful prediction of chromosomal instability from CTC morphology, offering a novel tool for CTC classification in liquid biopsy.

  PublisherOA PDFDOI

Frequent coauthors

• Theodore Eisenberg

  60 shared

• Dominique Fourdrinier

  Normandie Université

  60 shared

• William E. Strawderman

  Rutgers Sexual and Reproductive Health and Rights

  35 shared

• Mary E. Charlson

  Cornell University

  33 shared

• Dabao Zhang

  23 shared

• Janey C. Peterson

  Presbyterian Hospital

  22 shared

• Patricia A. Cassano

  22 shared

• Sumanta Basu

  Cornell University

  20 shared

Education

• PhD, Mathematics

  University of California Santa Barbara

  1987