A Summer School of Mathematics for Data Science at the Department of Mathematics

When: 11-15 July 2022

Where: University of Trento, Povo (Trento), Italy

The school will be held exclusively in presence in Trento. In case of impediments due to the COVID-19 pandemic, the school will run remotely on the same dates.

Accomodation

In terms of accommodation in Trento during the time of the summer school, you may want to consider:

Outline

The course aims to introduce the key concepts and state-of-art methods for causal inference from randomized experiments and observational studies under the potential outcome framework. We will first introduce the basic concepts of the potential outcome framework and the essential role of the treatment assignment mechanism. Then, we will cover different situations corresponding to different assumptions concerning the assignment mechanism. We will discuss the design and analysis of experimental designs and the design and analysis of observational studies with regular assignment mechanisms where the unconfoundedness assumption is assumed to hold. We will introduce irregular assignment mechanisms discussing strategies to deal with experimental studies with noncompliance. We will also introduce the principal stratification framework. Finally, we will cover some advanced topics: regression discontinuity designs, differences-in-differences methods, and synthetic control methods. We will present example and real case studies from many disciplines, including economics, social sciences, epidemiology and biomedical sciences. We will use R for the practical sessions.

Lecturers

Alessandra Mattei
Prof.

Alessandra Mattei
University of Florence
Bio Alessandra Mattei is Associate Professor of Statistics in the Department of Statistics, Computer Science, Applications at the University of Florence (Italy). She received her PhD and postdoc training in statistics from the University of Florence. She currently serves as Guest co-Editor for a special issue of Statistical Methods and Applications and as associate editor for the Biometrical Journal and Statistical Methods and Applications. She has been co-editor of the Proceedings of BAYSM 2016 and Guest co-Editor for a special issue of the Journal of Royal Statistical Society - Series A (published in 2020), for which she also served as associate editor from 2015 to 2018. Alessandra Mattei's main research interest is causal inference from experimental and observational studies. Her methodological research is focused on developing methods for the design and analysis of causal studies with irregular treatment assignment rules, causal studies with post-treatment confounded variables (principal stratification and mediation), and causal studies with complex data structures. She is also interested in missing data problems and Bayesian inference methods. Her empirical research includes studies in social sciences, public policy, public health, environmental health, and biomedical sciences. She has published in peer-reviewed journals, including Annals of Applied Statistics, Biometrics, Biostatistics, Journal of the American Statistical Association, Journal of Business & Economic Statistics, Journal of the Royal Statistical Society (Series A, B, C).
Veronica Ballerini
Prof.

Veronica Ballerini
University of Florence
Bio Veronica Ballerini is research fellow at the Department of Statistics, Data Science, Applications "G. Parenti" of the University of Florence. After graduating in Economics, she obtained her PhD in Economic Statistics at Sapienza University of Rome in 2021, with a thesis on Bayesian inference and computational methods for population size estimation problems. Just before completing her PhD, she joined the research team of Prof. Fabrizia Mealli, including causal inference among her main research interests. She is a Teaching Assistant for the "Causal Inference and Policy Evaluation" course of the Master's program in Statistics and Data Science. Her current research activities include the formalization and the implementation of Bayesian models for estimating causal effects in experiments with noncompliance in both clinical trials and social frameworks.

Schedule

  • 11 July 2022
    • Material
    • 14.00-15.30: Introduction to the potential outcome approach
      1. Potential Outcomes and causal effects
      2. The role of the assignment mechanism in causal inference
    • 16.00-17.30: Design and analysis of randomized experiments (I)
      1. Randomized Experiments
      2. Fisher’s exact p-value approach and Neyman’s repeated sampling approach to completely randomized experiments
  • 12 July 2022
    • Material
    • 09.30-11.00: Design and analysis of randomized experiments (II)
      1. Regression analysis in completely randomized experiments
    • 11.30-13.00: Design and analysis of randomized experiments (III)
      1. Bayesian model-based imputation approach in completely randomized studies
      2. Stratified and pairwise randomized experiments
    • 14.30-15.45: Practical session on the design and analysis of randomized experiments (I)
      1. Fisher’s exact p-value approach and Neyman’s repeated sampling approach to completely randomized experiments
    • 16:15-17:30: Practical session on the design and analysis of randomized experiments (II)
      1. Regression analysis and Bayesian model-based imputation approach
  • 13 July 2022
    • Material
    • 09.30-11.00: Design and analysis of observational studies under unconfoundedness (I)
      1. The role of the propensity score in the design and analysis of observational studies
      2. Designing observational studies: matching, subclassification, weighting, trimming
    • 11.30-13.00: Design and analysis of observational studies under unconfoun- dedness (II)
      1. Analysis of observational studies: stratification, weighting estimators, matching estimators, methods based on the outcome models and regression
    • 14.30-15.45: Practical session on the design of observational studies under unconfoundedness
    • 16.15-17.30: Practical session on the analysis of of observational studies under unconfoundedness
  • 14 July 2022
    • Material
    • 09.30-11.00: Design and analysis of observational studies under unconfoun- dedness (III)
      1. Analysis of observational studies: Combined methods (Bias corrected estimators, doubly robust estimators)
      2. Sensitivity analysis
      3. Enhancing causal inference with machine learning in high dimensional settings and heterogeneous effects
    • 11.30-13.00: Experimental studies with non compliance
      1. Instrumental variable (IV) analysis
      2. Bayesian IV analysis: relaxing some of the assumptions
      3. Point, partial, weak identification of causal effects
      4. The role of covariates
    • 14.30-15.45: Theory and practice of experimental studies with post-treatment complications (I)
    • 16.15-17.30: Theory and practice of experimental studies with post-treatment complications (II)
  • 15 July 2022
    • Material
    • 09.30-11.00: Miscellanea
      1. Regression discontinuity designs
      2. Difference in difference, synthetic controls and beyond
    • 11.30-13.00: Case study: “Evaluating causal effects on time-to-event outcomes in clinical trials in the presence of treatment discontinuation due to adverse events”

The summer school will start with a lunch at 12:30pm on Monday 11th of July and will finish with a lunch on Friday 15th of July. All morning and afternoon lectures will be delivered in two slots.

Readings

  • Lecture notes (with additional references) will be provided in class.
  • Athey, S. and G. W. Imbens (2017). The state of applied econometrics - causality and policy evaluation. Journal of Economic Perspectives, 31(2), 3-32
  • Athey, S. and G. W. Imbens (2017). Chapter 3 - The econometrics of randomized experiments. Handbook of Economic Field Experiments 1, 73-140
  • Bargagli Stoffi F., Dominici F. and Mealli F. (2021) From controlled to undisciplined data: estimating causal effects in the era of data science using a potential outcome framework. Harvard Data Science Review, 3(3)
  • Ding, P. and Li, F. (2018). Causal inference: a missing data perspective. Statistical Science. 33(2), 214-237
  • Imbens G.W., Rubin D.B. (2015). Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction. Cambridge University Press
  • Li, F, Mealli, F. (2014). A conversation with Donald B. Rubin. Statistical Science. 29(3), 439-457
  • Mattei, A. Mealli F., Nodehi A. (2021) Design and Analysis of Experiments. In: Zimmermann K.F. (eds) Handbook of Labor, Human Resources and Population Economics. Springer
  • Mealli, F., B. Pacini, and D. B. Rubin (2011). Statistical inference for causal effects. In Kenett R. and Salini S. (Eds.) Modern Analysis of Customer Surveys: with Applications Using R, Wiley, 171-192
  • Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology 66, 688-701
  • Rubin, D. B. (1976). Inference and missing data. Biometrika 63, 581-592
  • Rubin, D. B. (1978). Bayesian inference for causal effects: The role of randomization. Annals of Statistics. 6 34-58

Registration

  • The ideal participant of this school is a PhD or a Master student with background in Mathematics, Probability, Statistics or Data Science. However the application is open to everyone.

  • The course will be delivered in English.

  • There are no school fees.

  • Attendance is limited to 30 people. Registration is compulsory. Limited resources are available to support the local expenses of some of the participating students. To register (and possibly apply for support) follow this webapps.unitn.it/form/it/Web/Application/convegni/SSCI2022: you will be asked some information about yourself and standard documentation (CV) and a motivation letter if you apply for financial support. To receive full consideration please submit your application no later than 15 June 2022.

  • For further information, please contact Prof. Veronica Vinciotti