Propensity Scores

# Propensity Scores
### Lucy D’Agostino McGowan
### Wake Forest University
### 2020-07-29 (updated: 2020-07-29)

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## Observational Studies

**Goal**: To answer a research question

![](img/obs-studies.png)

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## Observational Studies

**Goal**: To answer a research question

![](img/obs-studies-2.png)

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## ~~Observational Studies~~
### **Randomized Controlled Trial**

![](img/randomized.png)

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## ~~Observational Studies~~
### **Randomized Controlled Trial**

![](img/randomized-2.png)

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## Observational Studies

![](img/obs-studies-3.png)

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![](img/trt.png)

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![](img/trt-conf.png)
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## Confounding

![](img/conf-2.png)

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## Confounding

![](img/conf-3.png)

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## Propensity scores

Rosenbaum and Rubin showed in observational studies, conditioning on **propensity scores** can lead to unbiased estimates of the exposure effect

1. There are no unmeasured confounders
2. Every subject has a nonzero probability of receiving either exposure

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## Propensity scores

* Fit a **logistic regression** predicting exposure using known covariates

`$$Pr(exposure = 1) = \frac{1}{1+\exp(-X\beta)}$$`

* Each individuals' predicted values are the **propensity scores**

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## Propensity scores

```r
library(tidyverse)
library(broom)
```

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## Propensity scores

```r
glm(exposure ~ confounder_1 + confounder_2 + confounder_3 + ..., 
    data = df,
    family = binomial())
```

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## Propensity scores

```r
glm(exposure ~ confounder_1 + confounder_2 + confounder_3 + ..., 
    data = df,
    family = binomial()) %>%
  augment(type.predict = "response", data = df) 
```

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## Propensity scores

```r
glm(exposure ~ confounder_1 + confounder_2 + confounder_3 + ..., 
    data = df,
    family = binomial()) %>%
* augment(type.predict = "response", data = df)
```

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## Propensity scores

![](img/pscores.png)

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## Your turn

1. Using the **confounders** identified in the previous DAG, fit a propensity score model for `qsmk`
2. Stretch: Create two histograms, one of the propensity scores for those that quit smoking and one for those that do not