14-tvt-mediation.Rmd

```{r 14_setup, include=FALSE}
knitr::opts_chunk$set(echo=TRUE, eval=FALSE, fig.align="center")
```

# (PART) New Research Questions {-}

# Time-Varying Treatments and Mediation Analysis

## Learning Goals {-}

- Formulate research questions that can be answered in a time-varying treatment setting
- Formulate research questions that can be answered via mediation analysis
- Explain why regression does not generally work in time-varying settings with treatment-confounder feedback using d-separation ideas
- Relate d-separation ideas to exchangeability conditions for mediation


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Slides from today are available [here](https://docs.google.com/presentation/d/1bAYaNzoYV9mKyOwNxk5uLyuqzTZmpuWZRRleec61fNo/edit?usp=sharing).


<br><br><br>


## Exercises {-}

### Exercise 1 {-}

For those of you working on a data analysis (or a plan of a data analysis) for the final project, share your data context and research questions with others.

- Mediation
    - Brainstorm some research questions that could be answered in a mediation analysis framework.
    - What mediators would be of interest? (That is, what direct and indirect effects would be of interest?)
    - How realistic would it be to collect data on those mediators?

- Time-varying treatments
    - Brainstorm some research questions that could be answered in a time-varying treatments framework.
    - Is it more useful to consider time-fixed or time-varying treatments in your context?
    - How realistic would it be to collect the longitudinal data needed for a time-varying treatments analysis?


### Exercise 2 {-}

The following causal graph shows a time-varying treatment setting where treatment is measured at two time points (`A0` and `A1`). It depicts a common occurrence in longitudinal data: **treatment-confounder feedback**. This is when past treatment $A_{t-1}$ affects the value of future confounders $L_{t}$.

a. Using causal graph ideas, explain why a regression model of the form $E[Y \mid A_0, A_1, L_1]$ creates a problem for estimating the effect of a treatment strategy for $A_0$ and $A_1$.

b. How would you expect this graph to change under inverse probability weighting? Why does IPW allow us to estimate the effect of a treatment strategy for $A_0$ and $A_1$?

```{r 14_tvt, echo=FALSE, eval=TRUE, fig.width=11, fig.align="center"}
library(dagitty)
dag <- dagitty("dag {
bb=\"0,0,1,1\"
A0 [pos=\"0.135,0.400\"]
A1 [pos=\"0.472,0.400\"]
L1 [pos=\"0.300,0.400\"]
U1 [pos=\"0.300,0.565\"]
Y [pos=\"0.691,0.400\"]
A0 -> L1
L1 -> A1
U1 -> L1
U1 -> Y
}
")
plot(dag)
```


### Exercise 3 {-}

In mediation analysis, a common first instinct to estimate direct effects is to control for the mediator by including it in a regression model. Let's explore this intuition by examining the following causal graph.

```{r 14_mediation, echo=FALSE, eval=TRUE, fig.width=11, fig.align="center"}
dag <- dagitty("dag {
bb=\"0,0,1,1\"
A [exposure,pos=\"0.200,0.400\"]
C1 [pos=\"0.500,0.200\"]
C2 [pos=\"0.334,0.569\"]
C3 [pos=\"0.658,0.581\"]
M [pos=\"0.500,0.400\"]
Y [outcome,pos=\"0.800,0.400\"]
A -> M
A -> Y [pos=\"0.500,0.200\"]
C1 -> A
C1 -> Y
C2 -> A
C2 -> M
C3 -> M
C3 -> Y
M -> Y
}
")
plot(dag)
```

Based on this graph, what considerations need to be kept in mind in order for this approach to validly estimate a direct effect?