• Methods for estimating causal effects: how to answer the question of "What is the effect of A on B?"
• Randomized designs
• Alternative designs when randomization is infeasible: matching methods, propensity scores, regression discontinuity, and instrumental variables.
• Broad spectrum of applications: health sciences, genetic studies, mental health, econometrics, public policy, education, …

• For a woman older >50 yrs, should she be getting regular screening for breast cancer?
• Do citizens of Los Angeles die because of air polution?
• What is the effect of heavy adolescent marijuana use on adult outcomes (e.g., earnings at age 40)?
• How much mortality and other burden was due to tobacco industry's misconduct?
• Does the Head Start program improve educational and health outcomes for children?
• Does a "healthy marriage" intervention improve relationship quality?
• How does the type of school affect a child's achievements later in life?
• …

• Are parents more conservative than their children because they are older?
• Is there an effect of gender in this regression?

What's the diffference between the two? (Intervention).

A causal question is a problem with a manipulable intervention.

• Important (and hot) topic right now
• Comparative effectiveness
• Debates regarding study design: "efficacy" versus "effectiveness"; observational versus randomized experiments
• Analytic challenges on modern study designs: community-level interventions (highway billboards, vaccination, new program…); matched-pair cluster-randomized trials (Wu et al., 2014, Biometrics)

• Be able to formalize causal effect discussions
• Understand key elements of causal inference
• Use causal diagrams as tools to formulate, investigate and analyze causal questions.

• What is the effect of some "treatment" \(T\) on an outcome \(Y\)?
  • Effect of a cause rather than cause of an effect
  • \(T\) must be a particular "intervention": something we can imagine giving or withholding
  • e.g. smoking a pack a day on lung cancer, Good Behavior Game on children's behavior and academic achievement

• Subjects (units), at a particular place and time
• Treatments/interventions to compare (e.g., \(T=0\) for standard, \(T=1\) for new)

• Potential outcomes, e.g., \(Y_i(1), Y_i(0)\) are the outcomes that would be observed on the same subjects if assigned new, or alternatively, if assigned standard treatment

• Causal Effect (definition): comparisions of potential outcomes for the same subject or same groups of subjects.

Help us be very clear about the effects we are estimating. (data table with observed and unobserved potential outcomes.)

• The entity to whic we apply or withhold the treatment
• e.g., individuals, schools, communities
• At a particular point in time
  • Me today and me tomorrow are two differen units
• Example: adolescents, elderly people

• The "intervention" that we could apply or withhold
  • Not "being male" or "being black"
  • Think of specific intervention that could happen
  • Example: Body mass index (BMI); heavy druge use during adolescence; trained nurses in a clinic to help manage the care for elderly people
• Defined in reference to some control condition of interest (!)
  • Defining control could be more difficult than the treatment
  • No treatment? Existing standard treatment?
  • Example: no or light drug use?

• The potential outcomes that could be observed for each unit
  • \(Y(T=1)=Y(1)\): the outcome that could be observed if a unit gets the treatment
  • \(Y(T=0)=Y(0)\): the outcome that could be observed if a unit gets the control
• For example, your headache pain in two hours if you ake an aspirin; your headache pain in two hours if not taking the aspirin
• Example: earnings if are heavy drug user (\(Y_i(1)\)); earnings if not (\(Y_i(0)\))
• Causal effects are comparisons of these potential outcomes

• Replication
• The Stable Unit Treatment Value Assumption (SUTVA)
• The assignment mechanism

• Need to have multiple units, some getting treatment and some getting control
• The number of potential outcomes grows

• No interference between units: treatment assignment of one unit does not affect potential outcomes of another unit
  • Agricultural experiments
  • Drug use of one individual does not affect earnings of other individuals
• Only one version of each treatment
  • Lumping all "heavy" druge use together; estimating effect of any "heavy drug use"

• Process that determines which treatment unit receives
• Randomized experiments: Known (nice!) assignment mechanism
• Observational studies: have to posit an assignment mechanism (determine/model why some individuals become heavy drug users)

• High-level: Assignment mechanism is the rule (possibly probabilistic) by which subjects get their actual treatments \(\{T_i\}\). The assigned treatments unmask the potential outcomes \(Y_i(T_i)\) (denoted by \(Y_i^{obs}\)), but mask the rest of potential outcomes, denoted by \(Y_i^{miss}\)
• Central to causal inference (look for it when reading literature; many not mentioning this)
• Example: doctor who can give to every patient the best treatment

• Next lecture: Who is right? (come back to Lord's paradox); Causal Diagrams
• Required reading:
  • Robins JM (2001). Data, Design, and Background Knowledge in Etiologic Inference. Epidemiology.
  • This is to prepare for causal diagram discussions