03-study-designs.Rmd

```{r 03_setup, include=FALSE}
knitr::opts_chunk$set(echo=TRUE, eval=FALSE, fig.align="center")
```

# Study Designs

## Learning goals {-}

- Identify appropriate study designs for answering causal questions based on a description of available data
- Explain how study designs "work" to estimate causal effects. Explain what assumptions they make to make statements about missing potential outcomes.

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Slides from today are available [here](https://docs.google.com/presentation/d/1SWVwW4L1QULgLapuOpJoW3yupifZQfnv9EvdUvFGxgU/edit?usp=sharing).


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## Exercises {-}

### Peer check-in {-}

Start by checking on the guiding questions:

- Why are randomized experiments often called the "gold standard" for causal inference? What is the relationship between randomized experiments and exchangeability?
- Consider the quasi-experimental designs discussed in the video. How do these designs try to mimic randomization? What assumptions do they make to allow making statements about missing potential outcomes?

What ideas were confusing, less clear, or intriguing? Make note of what your peers have noticed. This is a gold mine of information for your Metacognitive Reflections.


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### Exercise 1 {-}

When dealing with an infection, should we suppress fever (e.g., with Tylenol or Motrin) or let the fever run its course? Randomized experiments have been used to examine this question. ([Source 1](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4703655/), [Source 2](https://academic.oup.com/emph/article/9/1/26/5998648))

a. Why might we want to use stratified randomization to examine the effect of fever suppressors on health outcomes? What variables might we want to stratify on and why?

b. "Blinding" refers to the act of hiding from researchers and study participants the treatment group that the patients are actually in. Blinding is an important design consideration in randomized experiments.    
    - Suppose that hospital caregivers are not blinded and know whether a patient is receiving fever suppressors or not. How might this lead to a lack of exchangeability?
    - What if patients knowing their treatment group? How might this lead to a lack of exchangeability?

c. Compliance with assigned treatment is a practical concern in randomized experiments. What could be a reason for a patient's lack of compliance with assigned treatment, and how might this affect exchangeability?

d. Randomized trials with noncompliance can be viewed as an instrumental variables design. Explain this connection. (What is the instrument, and what is the treatment of interest?)


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### Exercise 2 {-}

Radon is an element naturally found in air that can cause lung cancer. It has a very low concentration outdoors and can have higher concentrations indoors. When buying a home, a radon check is typically ordered to assess if the home needs a radon mitigation system installed (a system to reduce radon levels). If radon levels are above a certain threshold, a radon mitigation system is recommended.

Given this context, what study design(s) might be used to study the effect of radon mitigation systems on lung cancer rates?


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### Exercise 3 {-}

Interrupted time series analyses typically use models that can handle the correlated nature of time series data. (If you are curious about these methods, take STAT 452: Correlated Data!)

For now, we can gain intuition for how these models are used in practice by examining linear regression models.

a. The general form of a linear regression model for an interrupted time series design is below:

$$ E[Y \mid T, I, A] = \beta_0 + \beta_1 T + \beta_2 I + \beta_3 TI + \beta_4 A + \beta_5 AT + \beta_6 AI + \beta_7 AIT $$

- $Y$: outcome/response variable
- $T$: time
- $I$: 1 if in the time period post-intervention, 0 for pre-intervention
- $A$: 1 for treatment sites receiving the intervention, 0 for control sites

    Draw a figure showing the relationship between $Y$ and $T$ and showing how the slopes change over time and in between treatment vs. control sites. Label slopes, intercepts, and any changes or discontinuities with model coefficients.

b. Ideally, control units should have pre-intervention trends that are as similar as possible to the pre-intervention trends for units that are treated. If this is the case, for which coefficients should we expect the confidence intervals to overlap zero?

c. Which coefficients represent the causal effect of the intervention, and how can we interpret them?


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### Extra {-}

If you have time, work on Part 4 of [Homework 1](homework-1.html), and get feedback from peers about your proposed study.