**Statistics 186**

Spring,
2024

Causal
Inference concerns the very difficult, challenging problem of addressing
questions such as, "Would vaccinating children 16 and younger against
COVID 19 lead to fewer deaths among public school teachers?" and
"Would providing Harvard students access to a mobile health application
designed to help them manage school stress, lead to improved school
performance?" This class will include 4 modules. The first module
introduces the nuanced world of causal inference along with a fundamental tool:
the language of potential outcomes. The second module covers
randomized experiments and how data from randomized experiments can be used to
make causal statements. The third module introduces the rather tricky
problem of using observational (non-randomized) data to attempt to make causal
statements. The final module introduces a new and challenging area
in which the goal is to make causal inference about the effect of sequences of
treatments.

**Professor**: Susan Murphy (samurphy@g.harvard.edu).

**Class
Times**: MW 4:30 pm-5:45 pm (EST) at the
Science Center, room TBD. No class 2/19,
3/11, 3/13.

**TF**: Nathan Cheng (ncheng@g.harvard.edu )

**Sections
and Office Hours**:

Susan Murphy’s Office Hours: 5pm-6pm EST on Thursday in 2.335 SEC except
for 3/14.

Nathan Cheng’s Office Hours: TBD

**Course
Webpage**: https://canvas.harvard.edu/courses/127531

**Book**: Imbens,
G., & Rubin, D. (2015). __Causal Inference for Statistics, Social, and Biomedical
Sciences: An Introduction__. Cambridge: Cambridge University Press.
doi:10.1017/CBO9781139025751. No purchase is necessary; you can download pdf copies of the
book chapters from the “Library Reserves” section of the Stat 186 Canvas site. You can also purchase the hard copy or an Adobe e-book at the Harvard Coop Bookstore.

**Other Papers**: Scientific papers may be assigned.

**Recommended Texts**: Hernán MA, Robins JM (2020). Causal Inference:
What If. Boca Raton: Chapman & Hall/CRC. See https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/

**Prerequisites**: Stat110, Stat111, Stat139.
Probability and statistical inference are needed extensively, and
statistical linear models are often used.

**Computing
and Simulation**: Some homework problems will mainly involve
statistical reasoning and probability whereas other homework problems will
require programming in R*. *Students may
use other software programs such as Python and Matlab, but we will only provide
support for R. I recommend RStudio as an interface for R. Both R and RStudio are freely
available. You are welcome to use
generative AI (ChatGPT, Bard, etc) for assistance in coding.

**Typical
Class:**

4:30pm: Ensure
that you have turned in the Quiz on Canvas

4:30pm: Sit
with your assigned group

4:30-5:00pm: 30 Min. Lecture

5:00-5:10pm: Breakout with your group
(Discuss quiz and questions posed in Lecture)

5:10-5:20pm: Class Discussion (one of
the groups leads the discussion)

5:20-5:45pm: 25 Min. Lecture

**Topics
Covered**:

__Module
1____:
[Potential Outcomes, Assignment Mechanisms]__

Tentative
Dates:__ __1/22, 1/24, 1/29

*This module provides the crucial
underpinning for this entire course.
This unit will assist you in thinking critically about statements made
in everyday life about cause and effect. We provide a language for
investigating causality—this language will help you translate statements such
as “Students who walk at least 10,000 steps per day are less likely to be
stressed” into mathematical statements and then if needed reframe these
statements to enhance precision. This
then allows us to be precise in how we use data to investigate causality.*

__Assigned
Reading Material__: Chapters 1 & 3 of Imbens and Rubin

__Module
2____:
[Randomized Experiments and Associated Data Analyses]__

*Much of our course focuses on Module 2;
Module 2 will help you understand why randomized experiments facilitate causal
inference and also this module will help you understand how to reason about and
conduct causal inference with experimental data. This Module provides first hints about how
you might be able to conduct causal inference when you have observational data
instead of experimental data.*

*1. *__Classical
Randomized Experiments __

Dates: 1/29, 1/31

*This section concerns experimental
settings in which we determine the assignment mechanism, that is the
probability distribution of the randomized treatment assignment. We will learn about some of the pros and cons
of different approaches to randomization.*

__Assigned
Reading Material__: Chapter 4 of Imbens and Rubin.

__Other
interesting material__: “Statistical Properties of Randomization in
Clinical Trials” by Lachin, “Properties of Simple Randomization in Clinical
Trials” by Lachin and “Randomization in Clinical Trials: Conclusions and
Recommendations” by Lachin, Matts and Wei.
These papers are under Files on Canvas.

2.
__Fisher's Approach to Causal Reasoning about
Treatment Effects for the Population of N Individuals in the Sample__

Tentative Dates: 1/31, 2/05, 2/07

*This
section concerns finite sample inference.
In this section you will learn about how you can conduct causal
inference about the N units (individuals) in the experiment (finite sample
inference). Randomization tests are
crucial tools*.

__Assigned
Reading Material__: Chapter 5 of Imbens and Rubin; Section 5.1 is
critical but very dense. I suggest reading
Section 5.1 again and again as you go through the other sections so that you
gradually began to understand Section 5.1.

__Other
interesting material__: “Statistical Properties of Randomization in
Clinical Trials” by Lachin, “Properties of Simple Randomization in Clinical
Trials” by Lachin and “Randomization in Clinical Trials: Conclusions and
Recommendations” by Lachin, Matts and Wei.
These papers are under Files on Canvas.

3.
__Neyman's Approach to Causal Reasoning about
Treatment Effects for the Population of N Units in the Sample and it's
Extension to using the Sample to Conduct Causal Inference about Treatment
Effects in a Large Population.__

Tentative Dates:
02/12, 02/14, 02/21

*Often we
aim to use the sample of N units (individuals) to inform decisions about a
larger population (should we provide the new take-home chemotherapy to all
adolescents recovering from leukemia as opposed to the current take-home
chemotherapy?). You will learn why this
causal inference both requires more assumptions and at the same is less
restrictive than finite sample causal inference. You will learn first statistical approaches
to conducting this type of causal inference.*

__Assigned
Reading Material__: Chapter 6 of Imbens and Rubin

4.
__Using Regression to Conduct Causal Inference__.

Tentative Dates:
02/26, 02/28, 03/04

*Regression
is one of the earliest and continues to be one of the most common tools used to
conduct causal inference. In regression we often add outside knowledge about
the form of the mean of the outcome conditional on covariates. In this section you will learn how you can
use covariates to improve your ability to detect and conduct inference about
causal effects. You will learn about the
consequences of miss-specifying the regression.*

__Assigned
Reading Material__: Chapter 7 of Imbens and Rubin; additional reading
material may be assigned.

__Module
3____:
[Observational Studies]__

*In many areas of science, experiments are
unethical, for example, we might be interested in the causal effect of parental
divorce on children’s elementary school performance. Or for monetary or societal reasons, data
from experiments is not available. These are all settings in which the
“assignment mechanism” is unknown. In
this module you will learn about first approaches to conducting causal
inference in these thorny problems. *

1.
__Unconfounded
Treatment Assignment__.

Tentative
Dates*: * 4 classes TBD

*In this section you will learn about the
critical role the propensity score plays in conducting causal inference, in
particular for use in settings in which science along with high quality
observational data can be harnessed to explain the assignment mechanism.*

__Assigned
Reading Material:__
Chapter 12 of Imbens and Rubin; additional reading material may be assigned.

2.
__Estimating the Propensity Score__.

Tentative Dates: 2 classes TBD

*In the analysis of observational data with
propensity scores you will need to estimate the propensity score. You will learn about methods for doing this and,
how to think about estimation when the goal is to reduce confounding as opposed
to fitting a good model.*

__Assigned Reading Material__.
Chapter 13 Imbens and Rubin; additional reading material may be assigned.

3.
__Using the Propensity Score to Conduct Causal
Inference in Observational Studies__.

Tentative Dates: 4 classes TBD

*Here we discuss how to use
the propensity score via stratification/blocking in causal inference. If time permits, we will discuss a second
approach, namely propensity score weighting.*

__Assigned
Reading Material__: Chapter 17 Imbens and Rubin; additional reading
material may be assigned.

__Module
4____:
[Dynamic Treatment Regimes & Sequential Experimentation]__

Tentative Date: 3 classes TBD

*This is causal inference on
steroids!! In this module you will learn about how to reason about potential
outcomes when treatments are sequential. When treatments are sequential, it is
easy for the analysis method to accidentally introduce confounding even though
the treatments are randomized.*

__Assigned
Reading Material__: MRTs for Developing Digital
Interventions. This paper is written for behavioral scientists.

**Grading**: Course grades will be based on a weighted average of homework
scores (30%), quizzes (20%), participation (10%) and a final exam on a date to
be determined (40%). Additional information about each of these components is
below. The course is letter-graded by default,
but you have my permission to switch to SAT/UNSAT grading if you prefer. If you
are considering SAT/UNSAT you should discuss it with your advisor, and check whether
it would count for what you want it to count for. A grade of SAT corresponds to
a letter grade of C- or above.

**Quizzes**: Assigned Readings are listed above in
each section. To
help with various circumstances (expected or unexpected), your lowest three (3)
quizzes will be dropped. Monday’s Quiz
is available on Canvas starting at 4:30pm EST on Sunday and closing at 4:30pm
EST on Monday at the beginning of class: similarly, Wednesday’s Quiz is
available on Canvas starting at 4:30pm EST on Tuesday and closing at 4:30pm EST
on Wednesday at the beginning of class. Once you start the quiz, __you have 10
minutes__ to complete the quiz. *Collaboration on Quizzes is not permitted.
Use of generative AI is not permitted.*

**Homework**: Problem sets will be assigned on every other Thursday 4pm via
Canvas and will be due two weeks later on the following Thursday at 4pmEST in Canvas. The first assignment
will appear in Canvas at 4pm on 1/25 and is due in Canvas at 4pm on 2/08.

Homework must be submitted via the
Canvas course website; no submissions on paper or by email will be accepted. Your submission must be a single PDF file,
no more than 20 MB in size, except that computer code can be uploaded in a separate
supplementary file if that is more convenient for you (i.e., a .R or .Rmd file with your R code).
The outputs from your code,
e.g., plots and summary statistics, must still be in your main PDF file. Your homework can be typeset, written using a tablet, or
scanned from handwritten work, but must be clear and easily legible (not blurry
or faint), and correctly rotated (e.g., not upside down). Always check your
submission: download it after uploading it in Canvas, and make sure that it is
the correct file and that it got uploaded successfully.

Late homework submissions are not
accepted. To help with various circumstances (expected or unexpected), your
lowest two homework scores will be dropped.

Unless otherwise specified, please show
your work, simplify fully, and give clear, careful justifications for your answers
(using *words and sentences* to explain
your logic, not just formulas).

**Homework
Collaboration Policy**: Beginning the first week, every other week
students are randomly divided into collaborative groups of people on Thursdays
at 4pm. This is your discussion +
homework group for next two weeks. Each
student individually submits their homework solution with a list of who was in
their assigned collaboration group. *You
must write up your solutions yourself and in your own words*. Copying
someone else's solution or a solution from generative AI, or just making
trivial changes to other’s solutions, including a generative AI solution for
the sake of not copying verbatim, is not acceptable. For
example, in problems where you must make up a story or example, two students
should not have the exact same answer, or almost the same answer except one has
an example with dogs chasing cats and the other has an example with cats
chasing mice, with the same structure and the same numbers. I highly recommend starting problem sets
early enough so that you have time to work hard on the problems on your own
first, before discussing them with your group.

Using generative AI tools such as
ChatGPT to help with homework is allowed, but not recommended. In my own testing of ChatGPT (with GPT-4), it
could do some Stat 186 problems correctly but also made many mistakes. It could
be a useful tool for suggesting ideas (and to chat about the material with or
compare answers with) but it is error-prone. Furthermore, working hard on the
homework problems is crucial for learning the material and preparing for the
final, so even if ChatGPT did excellent work on the Stat 186 homeworks, relying
on it too much would likely be harmful for overall understanding and for
performance on the exam. In any case,
your solutions must reflect your own understanding of the material, explained
in your own way, rather than being copied from any other source.

**Participation**: Active participation is expected, through attending class
(Mondays and Wednesdays), completing quizzes and engaging in discussions. Stat 186
is a challenging course covering subtle concepts, so let's all try to help
create a supportive, collaborative community.

**Final**: The Final is TBD. You
can bring two 8.5 by 11 sheets of notes (using both back and front) with you to
the final. Otherwise the final is closed book, no internet access and no
computer access.

**Accommodations**: Students needing academic adjustments or
accommodations because of a documented disability must present their Faculty Letter
from the Accessible Education Office
(AEO) and
speak with the professor by the end of the second week of the term, (fill in
specific date). Failure to do so may result in the Course Head's inability to
respond in a timely manner. All discussions will remain confidential, although
Faculty are invited to contact AEO to discuss appropriate implementation.

**Where to get tech help**: The Academic Resources
Center has resources. For tech help you can chat with Nathan to
see if he can help and/or you can call the HUIT help desk.