About

Kevin Leder joined the University of Minnesota in 2011 and is a Professor and Director of Graduate Studies in the Department of Industrial and Systems Engineering. His research focuses on large deviations and rare event simulation algorithms for stochastic models that arise in operations research and statistics, including queueing networks, random matrices, and reflecting diffusions. Additionally, he extensively works on mathematical modeling of cancer, utilizing classical models of population genetics to investigate tumor evolution and applying optimization techniques to understand and improve cancer therapies. Professor Leder's academic background includes a PhD in Applied Mathematics from Brown University, where he was supervised by Paul Dupuis and Hui Wang. His prior post-doctoral research was conducted at Harvard University and Columbia University, working with Franziska Michor and Jose Blanchet, respectively. His work has been published in high-quality journals and supported by grants from NSF, Fulbright Foundation, and NCI. He has received notable awards such as the NSF CAREER Award and the Fulbright Scholar Award, and is a member of professional societies including INFORMS and SIAM.

Research topics

• Biology
• Bioinformatics
• Mathematical analysis
• Statistical physics
• Pharmacology
• Physics
• Genetics
• Statistics
• Mathematics
• Computational biology
• Demography

Selected publications

• Exact site frequency spectra of neutrally evolving tumors: A transition between power laws reveals a signature of cell viability

  Theoretical Population Biology · 30 citations

  • Mathematics
  • Statistics
  • Statistical physics

  The site frequency spectrum (SFS) is a popular summary statistic of genomic data. While the SFS of a constant-sized population undergoing neutral mutations has been extensively studied in population genetics, the rapidly growing amount of cancer genomic data has attracted interest in the spectrum of an exponentially growing population. Recent theoretical results have generally dealt with special or limiting cases, such as considering only cells with an infinite line of descent, assuming deterministic tumor growth, or taking large-time or large-population limits. In this work, we derive exact expressions for the expected SFS of a cell population that evolves according to a stochastic branching process, first for cells with an infinite line of descent and then for the total population, evaluated either at a fixed time (fixed-time spectrum) or at the stochastic time at which the population reaches a certain size (fixed-size spectrum). We find that while the rate of mutation scales the SFS of the total population linearly, the rates of cell birth and cell death change the shape of the spectrum at the small-frequency end, inducing a transition between a 1/j2 power-law spectrum and a 1/j spectrum as cell viability decreases. We show that this insight can in principle be used to estimate the ratio between the rate of cell death and cell birth, as well as the mutation rate, using the site frequency spectrum alone. Although the discussion is framed in terms of tumor dynamics, our results apply to any exponentially growing population of individuals undergoing neutral mutations.

  DOI

• Investigational CRISPR-Cas9-edited T cells for metastatic colorectal cancer treatment: Clinical insights for future development

  Molecular Therapy Oncology · 2026-02-16

  articleOpen accessSenior author
  PublisherDOI

• A statistical framework for detecting therapy-induced resistance from drug screens

  npj Systems Biology and Applications · 2025-08-06 · 2 citations

  articleOpen accessSenior author

  Resistance to therapy remains a significant challenge in cancer treatment, often due to the presence of a stem-like cell population that drives tumor recurrence post-treatment. Moreover, many anticancer therapies induce plasticity, converting initially drug-sensitive cells to a more resistant state, e.g. through epigenetic processes and de-differentiation programs. Understanding the balance between therapeutic anti-tumor effects and induced resistance is critical for identifying treatment strategies. In this study, we present a robust statistical framework leveraging multi-type branching process models to characterize the evolutionary dynamics of tumor cell populations. This approach enables the detection and quantification of therapy-induced resistance using high-throughput drug screening data involving total cell counts, without requiring information on subpopulation counts. The framework is validated using both simulated (in silico) and recent experimental (in vitro) datasets, demonstrating its ability to generate meaningful predictions.

  PublisherOA PDFDOI

• Limit theorems for the site frequency spectrum of neutral mutations in an exponentially growing population

  Stochastic Processes and their Applications · 2025-01-11 · 2 citations

  articleOpen access
  PublisherOA PDFDOI

• Parameter Estimation in Recurrent Tumor Evolution with Finite Carrying Capacity

  ArXiv.org · 2025-10-01

  preprintOpen access1st authorCorresponding

  In this work, we investigate the population dynamics of tumor cells under therapeutic pressure. Although drug treatment initially induces a reduction in tumor burden, treatment failure frequently occurs over time due to the emergence of drug resistance, ultimately leading to cancer recurrence. To model this process, we employ a two-type branching process with state-dependent growth rates. The model assumes an initial tumor population composed predominantly of drug-sensitive cells, with a small subpopulation of resistant cells. Sensitive cells may acquire resistance through mutation, which is coupled to a change in cellular fitness. Furthermore, the growth rates of resistant cells are modulated by the overall tumor burden. Using stochastic differential equation techniques, we establish a functional law of large numbers for the scaled populations of sensitive cells, resistant cells, and the initial resistant clone. We then define the stochastic recurrence time as the first time the total tumor population regrows to its initial size following treatment. For this recurrence time, as well as for measures of clonal diversity and the size of the largest resistant clone at recurrence, we derive corresponding law of large number limits. These asymptotic results provide a theoretical foundation for constructing statistically consistent estimators for key biological parameters, including the cellular growth rates, the mutation rate, and the initial fraction of resistant cells.

  PublisherOA PDFDOI

• Clonal Diversity at Early Cancer Recurrence

  Bulletin of Mathematical Biology · 2025-01-01

  preprintOpen access1st author
  PublisherOA PDFDOI

• Early Circulating Tumor DNA Kinetics as a Dynamic Biomarker of Cancer Treatment Response

  JCO Clinical Cancer Informatics · 2025-03-01 · 8 citations

  articleOpen access

  PURPOSE: Circulating tumor DNA (ctDNA) assays are promising tools for the prediction of cancer treatment response. Here, we build a framework for the design of ctDNA biomarkers of therapy response that incorporate variations in ctDNA dynamics driven by specific treatment mechanisms. These biomarkers are based on novel proposals for ctDNA sampling protocols, consisting of frequent sampling within a compact time window surrounding therapy initiation-which we hypothesize to hold valuable prognostic information on longer-term treatment response. METHODS: We develop mathematical models of ctDNA kinetics driven by tumor response to several therapy classes and use them to simulate randomized virtual patient cohorts to test candidate biomarkers. RESULTS: Using this approach, we propose specific biomarkers, on the basis of ctDNA longitudinal features, for targeted therapy and radiation therapy. We evaluate and demonstrate the efficacy of these biomarkers in predicting treatment response within a randomized virtual patient cohort data set. CONCLUSION: This study highlights a need for tailoring ctDNA sampling protocols and interpretation methodology to specific biologic mechanisms of therapy response, and it provides a novel modeling and simulation framework for doing so. In addition, it highlights the potential of ctDNA assays for making early, rapid predictions of treatment response within the first days or weeks of treatment and generates hypotheses for further clinical testing.

  PublisherDOI

• Relapse prediction in multiple myeloma patients treated with isatuximab, carfilzomib, and dexamethasone

  medRxiv · 2024-05-03

  preprintOpen access

  Abstract Multiple myeloma (MM) patients experience repeated cycles of treatment response and relapse, yet despite close monitoring of disease status through M protein measurements, no standard model exists for relapse prediction in MM. We investigate the feasibility of predicting relapse using a hierarchical Bayesian model of subpopulation dynamics by training and testing the model on 229 patients from the IKEMA trial. After observing between 11 and 18 treatment cycles, the model predicted relapse within six cycles with an average sensitivity between 60 and 80 %, and an average specificity between 60 and 90 %. A model of linear extrapolation is preferable when patients have been observed for less than 6 cycles, but for longer observation windows the hierarchical Bayesian model is preferred. Including available baseline and longitudinal covariate information did not improve predictive accuracy. A survival analysis showed that two model parameters separated patients into groups with significantly different PFS ( p < 0.001). Statement of Significance Currently, no standard model exists for relapse prediction in multiple myeloma. A personalized model of M protein development could guide the frequency of follow-up measurements, reduce uncertainty for patients, and give clinicians more time to choose the best subsequent treatment for each patient. Furthermore, models that predict relapse are required to study the effect of changing treatment in advance of relapse rather than in response to it. Our work addresses this need by developing a hierarchical Bayesian model of subpopulation dynamics for prediction of future M protein values. We validate the model on a patient cohort treated with state-of-theart CD38 inhibitor therapy and show that it can accurately predict relapse within the next six treatment cycles, highlighting the promise of mathematical modeling in multiple myeloma and for personalized medicine in general. Declaration of Interests F.S. received honorarium from Sanofi, Janssen, BMS, Oncopeptides, Abbvie, GSK, and Pfizer. The authors declare that they have no other conflicts of interest.

  PublisherOA PDFDOI

• Parameter estimation from single patient, single time-point sequencing data of recurrent tumors

  Journal of Mathematical Biology · 2024-10-09 · 3 citations

  article1st authorCorresponding
  PublisherDOI

• Parameter Estimation from Single Patient, Single Time-Point Sequencing Data of Recurrent Tumors

  arXiv (Cornell University) · 2024-03-19

  preprintOpen access1st authorCorresponding

  In this study, we develop consistent estimators for key parameters that govern the dynamics of tumor cell populations when subjected to pharmacological treatments. While these treatments often lead to an initial reduction in the abundance of drug-sensitive cells, a population of drug-resistant cells frequently emerges over time, resulting in cancer recurrence. Samples from recurrent tumors present as an invaluable data source that can offer crucial insights into the ability of cancer cells to adapt and withstand treatment interventions. To effectively utilize the data obtained from recurrent tumors, we derive several large number limit theorems, specifically focusing on the metrics that quantify the clonal diversity of cancer cell populations at the time of cancer recurrence. These theorems then serve as the foundation for constructing our estimators. A distinguishing feature of our approach is that our estimators only require a single time-point sequencing data from a single tumor, thereby enhancing the practicality of our approach and enabling the understanding of cancer recurrence at the individual level.

  PublisherOA PDFDOI

Recent grants

• New Mathematical Models for Optimal Anti-Cancer Therapy

  NSF · $277k · 2014–2018

• CAREER: Rare Events in Cancer Evolution

  NSF · $500k · 2016–2022

Frequent coauthors

• Jasmine Foo

  Twin Cities Orthopedics

  69 shared

• Kathleen M. Storey

  Lafayette College

  19 shared

• Franziska Michor

  Harvard University

  17 shared

• Einar Bjarki Gunnarsson

  13 shared

• Marc D. Ryser

  Duke University

  13 shared

• José Blanchet

  12 shared

• Hamidreza Badri

  Netflix (United States)

  10 shared

• Yoichi Watanabe

  Toyokawa City Hospital

  10 shared

Awards & honors

• Fulbright Scholar Award to visit University of Oslo in Norwa…
• Best Publication Prize, INFORMS Simulation Society (2010)
• NSF CAREER Award (2016)