Short Course Program

Four half day and three full day Short Course proposals have been selected for presentation just before the International Biometric Conference begins.  All Short Courses will take place on Sunday, 10 July 2022.  These courses are taught by experienced professionals who are experts in their fields, so you do not want to miss out! We will provide additional information about these courses over the next few months! Stay tuned. 

Full day courses

Pseudo Observation in Survival Analysis

Per Kragh Anderson & Henrik Ravn

COURSE INFORMATION

Abstract
Pseudo observations (PO) have since their appearance in the biostatistical literature in 2003 been an active research field in survival analysis. PO now appear in SAS procedures, R packages, RCT protocols and textbooks.

The basic idea is that a random variable f(T) that is incompletely observed due to censoring is replaced by its PO for regression analysis of E(f(T)|Z) where T is the survival time and Z covariates. Here, the PO is obtained from an estimator of the marginal mean E(f(T)) that takes the censored data properly into account, such as the Kaplan-Meier estimator for P(T>t)=E(I(T>t)). Thereby, censoring is dealt with ‘once and for all’ and standard generalized estimating equations may be used with the PO as response variable

In the course, we will first give a brief recap of basic survival analysis, including the Kaplan-Meier estimator, the Cox model, and basics on competing risks and recurrent events. We will next introduce the PO and explain how they can be used for analysis of ‘marginal’ parameters in survival analysis. We will explain this in detail and show how the analysis may be performed using the R software. We will also briefly discuss the mathematical properties of PO methods.

Prerequisites 
The course will be at an intermediate level with emphasis on hands-on practicals and interpretation of analysis results.

Participants should be statisticians with a basic knowledge of ‘standard’ survival analysis, such as the Kaplan-Meier estimator, the Cox regression model and competing risks cumulative incidence function. Fundamental R knowledge is required, including how to install and apply new packages

Learning Objectives
Knowledge. Participants should know what pseudo observations (PO) are and how they may be used for specific modeling purposes in survival analysis. This includes both practical knowledge about how to use pseudo observations when analyzing a given data set and theoretical knowledge about their mathematical properties.

Skills. Through exercises, participants will be able to compute and analyze PO using existing R packages.

Competences. Participants should be able to recognize analysis situations in which the use of PO may be beneficial and, subsequently, know how to carry out the analysis in practice.

Laptop
Required, with R version 4.0.4 or later installed.

About the Instructors

Henrik Ravn is statistician at Novo Nordisk A/S, Copenhagen, Denmark. He graduated with an MSc in Theoretical Statistics in 1992 from University of Aarhus, Denmark and completed a PhD in Biostatistics in 2002 from the University of Copenhagen, Denmark. He joined Novo Nordisk in late 2015 after more than 22 years of experience from biostatistical and epidemiological research, at Statens Serum Institut, Denmark, with a main focus of analysis of survival data. As external lecturer for more than 10 years at Biostatistics, University of Copenhagen he has been teaching at numerous PhD-courses in biostatistics. Majority of courses were taught in English. This also included courses in Italy (Residential Summer Course in Epidemiology, Centro Studi, Florence, Italy), Guinea-Bissau, Tanzania and Ghana for local researchers and statisticians. Recent courses include a four days course in Survival Analysis in Clinical Trials for Danish Society for Biopharmaceutical Statistics (with Per K. Andersen) held three times (2017, 2018 and 2019).

Per Kragh Andersen is professor of biostatistics at the Department of Public Health, University of Copenhagen, Denmark since 1998. He graduated in mathematical statistics from University of Copenhagen in 1978, got his PhD in 1982 and a DrMSc degree in 1997. From 1993 to 2002 he worked half time as chief statistician at Danish Epidemiology Science Center (concurrently with the position as associate professor/professor at Univ. Copenhagen). He is an author or co-author of more than 100 papers on statistical methodology and more than 200 papers in the medical literature. His research has concentrated on survival analysis and he is a co-author of the 1993 Springer book ‘Statistical Models Based on Counting Processes’. He has taught numerous courses both nationally and internationally both for students with a mathematical background and for students in medicine or public health, including both more than 20 appearances at the Florence summer course in epidemiology and the four days course in Survival Analysis in Clinical Trials for Danish Society for Biopharmaceutical Statistics (with Henrik Ravn).

Bayesian Methods for Missing Covariates in Longitudinal Studies

Nicole Erler & Emmanuel Lesaffre

COURSE INFORMATION

Abstract
Missing values commonly complicate the analysis of observational data. It is well known that “ignoring” the missing values (i.e., complete case analyses) usually leads to biased results. Multiple imputation (MI) is considered to be the “gold standard” to alleviate this problem. MI, developed at the beginning of the Computer Age, is based on Bayesian ideas. In complex settings, e.g. involving non-linear associations or multi-level data, the assumptions of the commonly used MI algorithms are, however, often violated, leading to possibly biased results.

Thanks to the current computational power, a fully Bayesian approach to incomplete data, allowing us to simultaneously estimate parameters of interest and impute missing values, is now feasible. This approach is theoretically valid and superior to MI in complex settings, such as with longitudinal studies. Highly complex non-standard missing data models can relatively easily be implemented. Freely available software such as the R package JointAI greatly facilitates the model specification.

In this course, the essentials of imputation will be briefly reviewed as also the essential Bayesian concepts. The course focuses on the Bayesian approach to missing values in covariates in multi-level and longitudinal studies. Practical sessions will be organized to show the capabilities of the R package JointAI.

Prerequisites
General knowledge of statistical methods such as (generalized) linear regression, (generalized) linear mixed models. Some experience in the use of R, including packages like lme4 and nlme. A basic knowledge of Bayesian methods is required.

Learning Objectives
  • Obtain a general understanding of the impact and the handling of data sets plagued with incomplete data
  • To understand the Bayesian approach to missing data issues
  • Understand the difficulties of standard (Bayesian) imputation methods in complex data structures, with a focus on longitudinal data and multi-level data and especially with missing values in covariates
  • Fit Bayesian models on data sets with incomplete data using the R package JointAI

Laptop
Laptop is strongly recommended and necessary to actively follow the practical exercises.


About the Instructors


Dr. Nicole Erler obtained her PhD in Biostatistics on the topic of Bayesian Imputation of Missing Covariates. She is teaching on the topic of Missing Data in Clinical Research and Using R for Statistics in Medical Research at the Netherlands Institute of Health Sciences, and provided a 1-day workshop on Multiple Imputation of Missing Data in Simple and More Complex Settings at the 2019 meeting of the section on Methods & Evaluation of the German Psychological Society. She is author and maintainer of the R package JointAI that performs fully Bayesian analysis of incomplete data.

Prof. emeritus Emmanuel Lesaffre is the author of the Wiley book Bayesian Biostatistics (2012), and leading editor of the Chapman and Hall book Bayesian Methods in Pharmaceutical Research. He has taught courses on Bayesian methods in clinical studies on Master level at the University of Hasselt and KU Leuven both in Belgium, Erasmus MC (Rotterdam, the Netherlands) and that for more than 25 years. He has also taught short course on Bayesian methods at various universities abroad and clinical research institutes.

Network Modeling for High-Dimensional Data

Carel F. Peeters & Wessel N. van Wieringen

COURSE INFORMATION

Abstract
Networks are ubiquitous in modern science. Network extraction has become, for many fields, a popular
approach to explore a complex of interrelations between entities of interest. The entities in which we take
interest are molecular features stemming from omics studies. A challenge with omics-data is that they are often high-dimensional, i.e., the number of features exceeds the number of observations.

We approach network extraction for high-dimensional data as a problem in penalized graphical
modeling. Graphical models utilize graphs to express conditional (in)dependence relations between random
variables. Penalization then ensures that these models are estimable from high-dimensional data. We use, in
contrast to popular L1 approaches, an L2-approach to penalization.

In this course we first show why L2-based network extraction may be preferred over its L1-based analogue. We will then focus on the following situations of interest:
  1. Extracting a single network from steady-state data;
  2. Simultaneously extracting multiple networks from multiple related data sets and/or data consisting of distinct (disease) subclasses;
  3. Extracting networks from time-course data.
Importantly, for each of these situations we will explore methodology to analyze and exploit the networks in
order to enhance their practical value. Hence, the course revolves around (i) estimating graphical models, and (ii) translating these models into tangible information and practical consequences for the medical collaborator.

Prerequisites
The course is intended to be challenging,  but will not be overly difficult. It will be oriented towards all (applied) statisticians with an interest in reverse-engineering and analyzing networks from high-dimensional omics data. We expect participants to have a working knowledge of (i) linear algebra, (ii) penalization methods, and (iii) the R platform and language. Knowledge of network science is not required: basic network concepts will be introduced during the course.

Learning Objectives
Participants will become familiar with basic concepts from network science and current approaches for the extraction of networks from high-dimensional data. Participants will also gain hands-on experience with the extraction, visualization and basic analysis of molecular networks. Moreover, we believe the course will support participants in envisioning how network-information can be of clinical interest.
Textbook
No textbook is required. Recommended reading will consist of articles. Especially:

  • Bilgrau, A.E., Peeters, C.F.W., et al. (2020). Targeted fused ridge estimation of inverse covariance matrices from multiple high-dimensional data classes. Journal of Machine Learning Research, 21(26): 1-52.
  • Friedman, J., Hastie, T., & Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3): 432-441.
  • Miok, V., Wilting, S.M., & van Wieringen, W.N. (2016). Ridge estimation of the VAR(1) model and its time series chain graph from multivariate time-course omics data. Biometrical Journal, 59(1): 172-191.
  • van Wieringen, W.N., & Peeters, C.F.W. (2016). Ridge estimation of inverse covariance matrices from high-dimensional data. Computational Statistics & Data Analysis, 103(November): 284-303.

Laptop
We require the participants to bring a laptop with the latest version of R installed. Moreover, we expect the participants to have the latest version of the R packages rags2ridges and ragt2ridges. Preferably, the participants will also have RStudio installed. 


About the Instructors


Carel F.W. Peeters is an associate professor of Statistical Learning at the Division of Mathematical & Statistical Methods of Wageningen University & Research. He specializes in multivariate and high-dimensional statistical learning. Current interest lies with the network-integration of omics data and representation learning. For more information, see his personal website.

Latest course taught:
  • Statistics for Data Scientists
  • Focusing on the interface between statistics and machine learning
  • Taught in English
  • Audience: Master students in Applied Data Science

Wessel N. van Wieringen is an associate professor of Molecular Biostatistics at the Department of Mathematics of the VU University Amsterdam and at the Statistics for Omics Research Group in the Department of Epidemiology & Data Science, VU University medical center Amsterdam, the Netherlands. His research facilitates the deduction of the biological tangible conclusions (w.r.t. the dys/functioning of the cell) from omics data. This requires a.o. 1) the formulation of multivariate statistical models (e.g. graphical models) describing cellular processes, 2) the estimation of model parameters from the (highdimensional)
data, 3) understanding the models' limitations in their capacity to explain observed data from dysregulated processes, and 4) re-iterating the previous three steps to improve the models.

Latest courses taught:
  • 1) Advanced biostatistics and 2) High-dimensional data analysis
  • Focusing on 1) biomedical applications of Markov model and 2) regularized learning.
  • Taught in 1) Dutch and 2) English
  • Audience: 1) bachelor students of Medical Natural Sciences 2) master students in Statistical Science

Half day courses

Time to Event Outcome with Statistical Learning

Malka Gorfine

COURSE INFORMATION

Abstract
Machine learning of time-to-event outcome methods take advantage of recent development of machine learning and optimization to learn the association structure between survival times and covariates in a flexible manner. This course will cover contemporary methodologies for machine learning with time-to-event outcomes that either compete or complement with traditional survival methods. This includes techniques for high dimensional data, as well as methods appropriate for huge number of observations. Participants will learn about the most effective machine learning of time-to-event outcome techniques. Additionally, they will learn about not only the theoretical underpinnings of learning in survival analysis, but also gain the practical know-how needed to quickly and powerfully apply these techniques to modern datasets such as electronic health records (EHR). Topics include: a brief review of existing conventional time-to-event methods (non-parametric, semi-parametric and parametric models); performance evaluation metrics; regularized time-to-event regression methods; survival trees ensemble (bagging, random forest, boosting) and neural networks.

Prerequisites
The course targeted Master/PhD students and statisticians working on the development of statistical methodology. Prior knowledge of basic survival analysis is highly recommended, but not a must. The course will start with basic definitions and common notation in survival analysis. Proofs will be omitted.

Learning Objectives
Participants will learn about the most effective machine learning of survival outcome techniques. Additionally, they will learn about not only the theoretical underpinnings of learning in survival analysis, but also gain the practical know-how needed to quickly and powerfully apply these techniques to modern datasets. A concise description of the relevant software packages will be provided.

About the Instructor

Malka Gorfine, Prof. of statistics at Tel Aviv University, Israel.  Their main research area, for many years, is survival analysis. Malka has published many papers in this topic in top-tier journals, including JASA, Biometrika, Biometrics, Annals of Statistics, Biostatistics, SMMR, Statistics in Medicine and more.  They have recently served as a Co-Editor of Biometrics.

Malka is currently teaching various courses, including a variety topics of survival analysis, and has been for many years. They are very experienced in teaching and typically gets very high scores from students. Typically Malka teaches in Hebrew, but is also experienced in lecturing in English. In the year 2013, they provided a 4-hour pre-conference course in English, at the 7th Meeting of the Eastern Mediterranean Region of the International Biometrics Society (EMR-IBS): “Survival Analysis - Beyond the Cox Model”.  Visit Malka's home page in which more details can be found: http://www.tau.ac.il/~gorfinem/

Analysis of Interval-Censored Time-to-event Data: Methods and Applications

Professor, Jianguo (Tony) Sun & Professor, Ding-Geng (Din) Chen

COURSE INFORMATION

Abstract
Interval-censored time-to-event data are common generated in biomedical research in estimating the treatment effectiveness and studying patient survivals in cancer, infectious disease, such as, COVID-19, HIV/AIDS, TB, etc. This course is timely to analyze time-to infection data from current COVID-10 pandemic for current public health recommendations.

This short course is then designed to provide a thorough presentation of statistical analyses of interval-censored time-to-event data with detailed illustrations using real data arising from clinical studies. Specifically, we will start with an overview of data structure from right-censored, left-censored to interval-censored data and then discuss the associated statistical survival models to analyze these data with Cox proportional hazards regression, linear transformation modes and their extensions and development. We will focus on the modeling of interval-censored data since it is the most general and includes the right-censored/left-censored data. Commonly used statistical procedures will then be discussed with the most recent development in methods and software implementations in R/SAS. The specific topics to be discussed include 1) Biases inherent in the common practice of imputing interval-censored time-to-event data, 2) Nonparametric estimation of a survival function, 3) Nonparametric treatment comparisons, 4) Semiparametric regression analysis, 5) Analysis of multivariate interval-censored failure time data, 6) Variable selection of interval-censored data.

Prerequisites
  1. Master-level statistical training is preferred, but not necessary since we start the short course with an overview of survival data analysis for the first part of the short course. In this part, we will review the commonly used parametric regressions, such as Weibull model, and the Cox proportional hazards regression.
  2. Knowledge on survival data analysis is preferable, but not necessary. The knowledge of survival analysis will benefit more in the second part of this short course since we will discuss the recent development of survival models in analysis interval-censored time-to-event data.
  3. Knowledge on R/SAS will be helpful, but not necessary. With the software knowledge, the participants can readily use the program code in this short course to analyze their own data.

Learning Objectives
At the conclusion of this short course, participants will be able to understand:
  1. Data structures associated with interval-censored time-to-event data which are generated from biomedical research and public health applications.
  2. Common parametric and nonparametric survival models to analyze the interval-censored time-to-event data.
  3. Recent development in survival methods to better analyze interval-censored time-to-event data.
  4. Recent development in software in R packages and SAS procedures for interval-censored data analysis.
At the conclusion of this short course, we expect the participants to use the knowledge learned from this short course to analyze their own research projects which generated interval-censored time-to-event data.

About the Instructors

Jianguo Sun (Tony) Sun received his Ph.D. in Statistics from the University of Waterloo in 1992 and he is currently a professor at the University of Missouri. Professor Sun has been working on failure time data analysis and longitudinal data analysis for over 20 years, especially on various statistical problems in AIDS studies. He has published many papers and in particular, wrote a book Statistical Analysis of Interval-censored Failure Time Data published by Springer in 2006. In addition, he has given many invited presentations of his work in both academics and industry and as co-editor with Professors Ding-Geng (Din) Chen and Karl E. Peace on book "Interval-Censored Time-to-event Data: Methods and Applications" published by CRC in 2012.

Ding-Geng (Din) Chen received his Ph.D. in Statistics from the University of Guelph (Canada) in 1995 and he is now the Wallace Kuralt Distinguished professor at the University of North Carolina at Chapel Hill. He was a professor in biostatistics at the University of Rochester Medical Center and the Karl E. Peace endowed eminent scholar chair in biostatistics from the Jiann-Ping Hsu College of Public Health at the Georgia Southern University. Professor Chen is also a senior biostatistics consultant for biopharmaceuticals and government agencies with extensive expertise in clinical trials and bioinformatics. He has more than 200 referred professional publications and co-authored/co-edited 33 books on clinical trials, meta-analysis, causal inference and bigdata science.

Estimand-aligned Statistical Analyses of Clinical Trials

Tobias Mutze & Frank Bretz

COURSE INFORMATION

Abstract
Defining the scientific questions of interest in a clinical trial is crucial to align its design, conduct, analysis, and interpretation. With the recent release of an addendum to the E9 guideline on 'Statistical principles in clinical trials' by the International Council of Harmonization (ICH), regulatory agencies require statistical analyses to be aligned with the target estimand(s) which precisely describe the treatment effect(s) of interest that a clinical trial should address.

For a given estimand, an aligned method of analysis, or estimator, should be implemented that is able to provide an estimate on which reliable interpretation can be based and which includes the handling of post-randomization events, missing data and sensitivity analyses. Many statistical analysis procedures are available for different types of data, although it is often unclear which estimands these imply.

In this course, we first briefly introduce the ICH E9 addendum on estimands. We then discuss how to identify and implement analyses approaches as well as sensitivity analyses that are aligned with a chosen estimand for different types of endpoints (continuous, binary, time-to-event, recurrent events) in longitudinal clinical trial settings. We illustrate the methods with real case studies and provide code examples to facilitate implementation in practice.

Prerequisites
The participants should have basic knowledge of the fundamentals of statistics including experience with common data types (continuous, binary, time-to-event, recurrent events) as well as the associated models and estimation methods, such as maximum likelihood, multiple imputation, logistic regression, and Cox models. Knowledge in causal inference is a plus, but not mandated. Moreover, participants are expected to have basic knowledge of clinical trial methodology and should be familiar with concepts and terms such as bias, randomization, and blinding.

The difficulty level of the course is intermediate, at a second-year graduate course level. The focus will not be on the theoretical derivations and properties of the statistical methods, but on their application in clinical trial settings.

Learning Objectives
The difficulty level of the course is intermediate, at a second-year graduate course level. The learning objectives are four-fold:
  1. to identify an appropriate primary analysis method that targets the estimand of interest, fully aligned with the ICH E9 addendum;
  2. to understand how to change assumptions made for the primary analysis using appropriate sensitivity analyses;
  3. to implement appropriate analyses and sensitivity analyses in practical settings; and
  4. to get an overview of basic functionality in SAS and R to design and analyze clinical trials.

Textbook
This course is based on a 1.5 day course developed and presented internally at our company. No textbook is recommended or required, but it is recommended to be familiar with ICH E9 addendum.

About the Instructors

Dr. Tobias Mütze is a statistical methodologist at Novartis in Basel, Switzerland, and works primarily on late phase studies. His current research interests are adaptive clinical trial designs, recurrent event modelling, estimands, and more recently missing data methodology. He received his PhD in the area of biostatistics from the University of Göttingen, Germany, and holds a BSc and a MSc in mathematics. Tobias Mütze was awarded the Bernd Streitberg Award and the Gustav Adolf Lienert Award from the German Region of the International Biometric Society.

Dr. Frank Bretz is a Distinguished Quantitative Research Scientist at Novartis. He has supported the methodological development in various areas of biostatistics, including dose finding, multiple comparisons, and adaptive designs. Frank is currently holding Adjunct professorial positions at the Hannover Medical School (Germany) and the Medical University of Vienna (Austria). He was a core member of the ICH E9(R1) working group on “Estimands and sensitivity analysis in clinical trials”. He has authored or co-authored more than 150 articles in peer-reviewed journals and five books. Frank is an Executive Board member of the International Biometric Society, a recipient of the Susanne-Dahms-Medal from the German Region and a Fellow of the American Statistical Association.

Mathematical Modelling of Real-World Infectious Disease Epidemics - An R Based Hands-On Short Course

Ashok Krishnamurthy

COURSE INFORMATION

Abstract
Mathematical modelling of infectious diseases is an interdisciplinary area of increasing interest. In this short course we will describe and illustrate participants an understanding of infectious diseases and their value for public health. The course will be based on our real-world experience of tracking the spatial spread of
  • measles in pre-vaccine England and Wales (1944-1966),
  • Ebola in the Democratic Republic of Congo (2018-2020), and
  • SARS-CoV-2 in Nigeria and the Czech Republic (2020-2021) using integro-differential equations.

Objectives: By the end of the short course participants will be able to:
  • know how to build a compartment model of epidemiology (for ex: SIR, SEIR, SEIRD, SVEIRD etc.) to track the spatial spread of an infectious disease outbreak.
  • adopt the two basic ingredients for spatiotemporal tracking of infectious diseases via Bayesian data assimilation methods; (1) a mathematical model (to reproduce the process of interest) (2) incorporate observations (incidence, prevalence, recovery, and death data) to update epidemic state estimates
  • apply ideas to a realistic scenario involving tracking COVID-19 in a particular country.
This interactive short course will be delivered using real-world data and practical simulation exercises using the free, open-source software R. No prior detailed knowledge of modelling infectious diseases or epidemiology is required.

Prerequisites
This short course assumes a basic understanding of compartmental models of epidemiology. We will primarily be using R program and the RStudio IDE. Some amount of programming will be involved (students with complementary skills will be encouraged to form teams) and basic understanding from Calculus, Linear Algebra and Introductory Statistics may be beneficial.

Learning Objectives
Registered participants will be asked to watch pre-recorded lectures (a walkthrough of installing open-source tools or packages), download and install the relevant R packages, and then participate in a hands-on half-day (four hour) synchronous short course where Dr. Krishnamurthy will offer practical advice on using the R program and Geospatial tools to generate spatio-temporal disease maps.

Objectives: By the end of the short course participants will be able to:
  • know how to build a compartment model of epidemiology (for ex: SIR, SEIR, SEIRD, SVEIRD etc.) to track the spatial spread of an infectious disease outbreak.
  • adopt the two basic ingredients for spatiotemporal tracking of infectious diseases via Bayesian data assimilation methods; (1) a mathematical model (to reproduce the process of interest) (2) incorporate observations (incidence, prevalence, recovery, and death data) to update epidemic state estimates
  • apply ideas to a realistic scenario involving tracking COVID-19 in a particular country.
Target Audience: This short course will be designed for early-career data scientists, epidemiologists, biostatisticians, and graduate students. The workshop is open to IBC 2022 delegates only. Preferred workshop duration: 1/2 day (four hours).

Laptop
Recommended participants bring a laptop with R and RStudio pre-installed

About the Instructor

Dr. Ashok Krishnamurthy is the instructor for this short course. Dr. Krishnamurthy is working on several projects including the application of mathematical models to track the spatial spread of Ebola in the Democratic Republic of Congo and tracking COVID-19 in Nigeria, and the Czech Republic. Currently finishing up a project on the spatial tracking of measles in pre-vaccine England and Wales. Recent presentations on this topic by Dr. Krishnamurthy include:

Krishnamurthy, A. (2020). Spatiotemporal transmission dynamics of COVID-19 in Nigeria (Online Presentation - Invited). 13th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2020) (December 19, 2020).

Krishnamurthy, A. (2020). Application of the Spatial SVEIRD model to the Ebola outbreak in Congo (Oral Presentation – Abstract Accepted after Peer-Review of 700+ submissions). 30th International Biometric Conference (IBC 2020, August 21, 2020) (in-person conference canceled - moved to a virtual conference). (Link for my 12-minute presentation can be found here)

Krishnamurthy, A. (2020). Spatiotemporal transmission dynamics of COVID-19 in Spain (Online Presentation). CAIMS - PIMS Coronavirus Modelling Conference (June 22-24, 2020). https://www.pims.math.ca/scientific-event/200622-cpcmc

Krishnamurthy, A. (2020). Application of the Spatial SEIRD model to the COVID-19 outbreak in Spain (Online Presentation – Invited Talk). Advancing knowledge about spatial modeling, infectious diseases, environment, and health (June 8-12, 2020), Toronto, ON, Canada. http://www.fields.utoronto.ca/activities/19-20/modeling-infectious-diseases

Dr. Krishnamurthy is scheduled to present a similar workshop/mini-course at the 2021 Annual Meeting of the Canadian Mathematical Society (virtual) to be held in June of this year and the World Congress of Epidemiology (virtual) to be held in September 2021. Dr. Krishnamurthy assiduously promotes the discipline of mathematics, statistics, data science, and computing among his students and creates high-impact learning opportunities.