Variable selection with a biased sample using tilted knockoffs

Presented by Qian Zhao, University of Massachusetts, Amherst

Wednesday, April 3, 2024
4:00 PM-5:00 PM ET
AUST 163
Webex Meeting Link
Coffee will be served at 3:30 pm in the Noether Lounge (AUST 326)

Researchers in biomedical studies often work with biased samples that are not selected uniformly at random from the population of interest. One example is a case-control study, where cases are over-sampled to study risk factors of rare diseases. While these designs are motivated by specific scientific questions, it is often of interest to use them to pursue secondary lines of investigations. In these cases, the biased sample can lead to spurious association between an exposure and an outcome when both of them affect the case-control status. This phenomenon is known in the causal inference literature as collider bias. While tests of independence under biased sampling are available, these methods typically do not apply when the number of variables is large.

In this work, we are interested in using the knockoff framework to select important variables among very many with replicability guarantees. We show that the standard model-X knockoffs fail to control FDR in the presence of biased sampling. We show that by tilting the population distribution with the selection probability and constructing knockoff variables according to this tilted distribution, the knockoff filter would control the FDR. We apply the tilted knockoff method to identify genetic underpinning of endophenotypes in a case-control study.

Speaker Bio:

Qian Zhao is an Assistant Professor in Statistics at the University of Massachusetts, Amherst. Prior to joining UMASS, she was a postdoctoral researcher in the department of Biomedical Data Science at Stanford University. Her research focuses on developing statistical theory and methods to achieve valid inference for high-dimensional problems, where the number of variables is large or comparable to the number of observations. She is passionate about data science education, and using data science to achieve positive social impacts.

Change Point Detection for High-dimensional Time Series Models With Local Dynamics

Presented by Abolfazl Safikhani, Department of Statistics, George Mason University

Friday, April 5 2024
10:00 AM-11:00 AM ET
AUST 202
Webex Meeting Link
Coffee will be served at 9:30 am in the Noether Lounge (AUST 326)

Sequential monitoring of multivariate time series to find sudden changes in the data generating process is a canonical problem in statistics and signal processing. Most developed detection algorithms work under two main assumptions: (a) there are no cross-correlations between time series components, and (b) observations between two change points follow a stationary model with fixed parameters. Both of these assumptions are unrealistic in real data applications. Failing to include cross-correlations and dynamic/non-stationary structures may lead to over-fitting and/or inaccurate change point identification in such algorithms. In this talk, first a general modeling framework is introduced to include local dynamic structures and cross-correlations in multivariate time series. Then, a novel sequential detection algorithm is proposed to estimate the location of change points while also estimating all model parameters, including cross-covariance parameters. Theoretical properties are established under mild conditions including controlling the false positive rate, detection power calculation, and localization error bounds. Finally, empirical performance of the proposed method is investigated through various simulation settings, comparison with several competing methods, and real data examples including paper production data. This is a joint work with Yuhan Tian and Kamran Paynabar.

Speaker Bio:

Dr. Safikhani is currently an assistant professor in the department of statistics at George Mason University. He received his PhD from the department of statistics and probability, Michigan State University. Prior to GMU, he has held positions at Columbia University and University of Florida. His main research interests include network modeling, high-dimensional statistics, spatio-temporal models, change point detection, and applications in urban planning, neuroscience, and smart cities. He has published in top-tier statistical journals and machine learning conferences including JASA, Technometrics, JCGS, EJS, EJP, IEEE-TSP, and NeurIPS and his research has been supported by NSF. He is currently an Associate Editor of Statistica Sinica and Data Science in Science.

Advances in the use of the multivariate contaminated normal distribution in model-based clustering

Presented by Antonio Punzo, Department of Economics and Business, University of Catania

Wednesday, April 10 2024
4:00 PM-5:00 PM ET
AUST 163
Webex Meeting Link
Coffee will be served at 3:30 pm in the Noether Lounge (AUST 326)

The multivariate contaminated normal (MCN) distribution represents a simple elliptical heavy-tailed generalization of the multivariate normal (MN) distribution aiming at handling and detecting mild outliers, sometimes also referred to as ‘bad’ points in the literature about the MCN. Advantageously, the two additional parameters have an interpretation of practical interest as a proportion of good observations and degree of contamination. In the talk, I will present a review of the uses of MCN distribution, and of some of its extensions, in clustering based on mixture models.

Speaker Bio:

Antonio Punzo attained his Ph.D. in Methodological and Applied Statistics from the University of Milano-Bicocca, Milan, Italy. Currently, he holds the position of Full Professor of Statistics within the Department of Economics and Business at the University of Catania, Catania, Italy. Notably, he has authored numerous articles, primarily focusing on clustering and classification using mixture models, which have been published in prestigious journals and book chapters. Additionally, he serves as an Associate Editor for esteemed publications including the Journal of Classification, Statistical Methods & Applications, Biometrical Journal, and Italian Journal of Applied Statistics.

In Defense Of Unrestricted Spatial Regression

Presented by Dr. Dale Zimmerman, University Of Iowa

Friday, 04/12/2024, 11am ET
In-Person: AUST 202
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Spatial regression is commonly used in the environmental, social, and other sciences to study relationships between spatially referenced data and other variables, and to predict variables at locations where they are not observed. Spatial confounding, i.e., collinearity between fixed effects and random effects in a spatial regression model, can adversely affect estimates of the fixed effects, and it has been argued that something ought to be done to “fix” it. Restricted spatial regression methods have been proposed as a remedy for spatial confounding. Such methods replace inference for the fixed effects of the original spatial regression model with inference for those effects under a model in which the random effects are restricted to a subspace orthogonal to the column space of the fixed effects model matrix; thus, they “deconfound” the two types of effects. We prove, however, using classical linear model theory, that frequentist inference for the fixed effects of a deconfounded linear model is generally inferior to that for the fixed effects of the original spatial linear model; in fact, it is even inferior to inference for the corresponding nonspatial model (i.e., inference based on ordinary least squares). We show further that deconfounding also leads to inferior predictive inferences. Based on these results, we argue against the use of restricted spatial regression, in favor of plain old (unrestricted) spatial regression. This is joint work with Jay Ver Hoef of NOAA National Marine Mammal Laboratory and was published in 2022 in The American Statistician.

Dr. Dale L. Zimmerman is Professor of Statistics and Actuarial Science and Department of Biostatistics at the University of Iowa. He received his Ph.D. in Statistics from Iowa State University in 1986. He is a Fellow of the American Statistical Association and the Institute for Mathematical Statistics. In 2007, he received the Distinguished Achievement Award from the Section on Statistics and the Environment of the American Statistical Association. His research interests include spatial statistics, longitudinal data analysis, multivariate analysis, mixed linear models, environmental statistics, and sports statistics. He has authored or co-authored five books and more than 90 articles in journals such as: Biometrics; Biometrika; Journal of the Royal Statistical Society (Series B); Applied Statistics; Test; Journal of Statistical Computation and Simulation; Journal of Statistical Planning and Inference; Journal of Computational and Graphical Statistics; Statistics in Medicine; Environmetrics; Journal of Agricultural, Biological, and Environmental Statistics; The American Statistician; Technometrics; Probability and Statistics Letters; and Mathematical Geology. At the University of Iowa, he teaches courses in spatial and environmental statistics, linear models, experimental design, and sports statistics. He has supervised the doctoral thesis research of 16 Ph.D. students. He has given 86 invited presentations and many more contributed presentations at conferences and universities.

Some Reflections on Rosenbaum and Rubin’s Propensity Score Paper

Presented by Roderick J. Little
Richard D. Remington Distinguished University Professor of Biostatistics
Department of Biostatistics, University of Michigan

Wednesday, April 24, 2024
4:00 PM-5:00 PM ET
AUST 163
Webex Meeting Link
Coffee will be served at 3:30 pm in the Noether Lounge (AUST 326)

Rosenbaum and Rubin’s paper is highly cited because the basic idea is simple and insightful, and it has applications to important practical problems in treatment comparisons with observational data, and selection bias and nonresponse in surveys. I discuss several issues related to the method, including use of the propensity score for weighting or prediction, and two robust methods that use the propensity score as a covariate and can be more efficient that weighting when the weights are highly variable, namely Penalized Spline of Propensity Prediction (PSPP) and Penalized Spline of Propensity for Treatment Comparisons (PENCOMP). Approaches to addressing highly variable weights are discussed, including omitting variables in the propensity model that are unrelated to outcomes, and redefining the estimand.

Keywords: confounding by indication, nonresponse modeling, penalized spline of propensity, robust causal inference.

Speaker Bio:

Roderick J. Little is Richard D. Remington Distinguished University Professor of Biostatistics at the University of Michigan, where he also holds appointments in the Department of Statistics and the Institute for Social Research. He chaired the Biostatistics Department at Michigan for 11 years. He has over 250 publications, notably on methods for the analysis of data with missing values and model-based survey inference, and the application of statistics to diverse scientific areas, including medicine, demography, economics, psychiatry, aging and the environment. Little is an elected member of the International Statistical Institute, a Fellow of the American Statistical Association and the American Academy of Arts and Sciences, and a member of the National Academy of Medicine. In 2005, Little was awarded the American Statistical Association’s Wilks Medal for research contributions, and he gave the President’s Invited Address at the Joint Statistical Meetings. He was the COPSS Fisher Lecturer at the 2012 Joint Statistics Meetings.

Robert Makuch is a Professor in the Department of Biostatistics at the Yale School of Public Health and Director of the Regulatory Affairs Track. A graduate of the University of Connecticut (BA), University of Washington (MA – mathematics), and Yale University (MPhil, PhD), Professor Makuch worked at the National Cancer Institute (NCI) and the World Health Organization’s International Agency for Research on Cancer early in his career. He also worked for six months at the National Cancer Research Center in Tokyo, Japan.

He also was heavily involved in HIV research from the mid 80’s through the early-mid 90’s. He participated on the data monitoring committee for the original AZT vs. placebo randomized clinical trial in AIDS patients, and served on numerous committees for the NCI and the National Institute of Allergy and Infectious Diseases. He also worked closely with the Food and Drug Administration (FDA), developing and implementing more than 200 HIV studies. He also served as a Special Government Employee (SGE) to the FDA. He returned to Yale in 1986, and has worked extensively on methodologic issues in clinical trials and large population-based studies since. Another area of current interest involves detection of rare adverse drug events, especially in the post-marketing environment.

These areas of methodologic research evolved as a result of his continued interest (since the mid 1980s) in regulatory affairs science. In addition, Makuch developed a regulatory affairs track at YSPH for graduate and post-doctoral level students, and over the past 10 years has been the leader of more than 25 training programs for senior delegations of the Chinese Food and Drug Administration. His areas of medical application include cancer, HIV, arthritis, and cardiovascular disease.

In 2003, Makuch received the American Statistical Association Fellow Award for his numerous contributions to the field. In 2008, Makuch was received a Distinguished Alumni Award from the University of Connecticut. In 2012, Makuch was nominated to serve on the University of Connecticut Dean’s Advisory Board for the College of Liberal Arts and Sciences. He also has been a decades-long member of Phi Beta Kappa. He also developed a 5-year biostatistics training program in Japan, in collaboration with the Japanese government. His primary research interests continue to be methodologic issues in the design, conduct, analysis, and interpretation of clinical and large-population/epidemiologic studies. Design and sample size considerations for Phase IV studies is another active research area, in which a new class of hybrid designs has been proposed for scientific and regulatory purposes to detect rare adverse events.