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# 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

---

## 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())
```

---

## Propensity scores

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

---

## 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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<img src="03-pscores_files/figure-html/unnamed-chunk-6-1.png" style="display: block; margin: auto;" />

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## Your turn

<div class="countdown" id="timer_5f218f59" style="right:0;bottom:0;" data-warnwhen="0">
<code class="countdown-time"><span class="countdown-digits minutes">05</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">00</span></code>
</div>

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

Notes for current slide

Notes for next slide

Propensity ScoresLucy D’Agostino McGowanWake Forest University2020-07-29 (updated: 2020-07-29)1 / 19

Observational Studies

Goal: To answer a research question

2 / 19

Observational Studies

Goal: To answer a research question

3 / 19

Observational Studies

Randomized Controlled Trial

4 / 19

Observational Studies

Randomized Controlled Trial

5 / 19

Observational Studies

6 / 19

7 / 19

8 / 19

Confounding

9 / 19

Confounding

10 / 19

Propensity scores

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

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

11 / 19

Propensity scores

Fit a logistic regression predicting exposure using known covariates

Each individuals' predicted values are the propensity scores

12 / 19

Propensity scores

library(tidyverse)
library(broom)

13 / 19

Propensity scores

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

14 / 19

Propensity scores

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

15 / 19

Propensity scores

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

16 / 19

Propensity scores

17 / 19

18 / 19

Your turn
05:00
Using the confounders identified in the previous DAG, fit a propensity score model for qsmk
Stretch: Create two histograms, one of the propensity scores for those that quit smoking and one for those that do not
19 / 19

Observational Studies

Goal: To answer a research question

2 / 19

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