class: center, middle, inverse, title-slide

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

---

class: inverse

## Propensity scores

* Weighting
* Matching
* Stratification
* Direct Adjustment
* ...

---
class: inverse

## Propensity scores

* **Weighting**
* Matching
* Stratification
* Direct Adjustment
* ...

---
class: inverse

## Target estimands

### Average Treatment Effect (ATE)

`$$\Large w_{ATE} = \frac{Z_i}{p_i} + \frac{1-Z_i}{1 - p_i}$$`

---
class: inverse

## Target estimands

### Average Treatment Effect Among the Treated (ATT)
`$$\Large w_{ATT} = \frac{p_i Z_i}{p_i} + \frac{p_i (1-Z_i)}{1-p_i}$$`
--

### Average Treatment Effect Among the Controls (ATC)
`$$\Large w_{ATC} = \frac{(1-p_i)Z_i}{p_i} + \frac{(1-p_i)(1-Z_i)}{(1-p_i)}$$`

---
class: inverse

## Target estimands

### Average Treatment Effect Among the Evenly Matchable (ATM)
`$$\Large w_{ATM} = \frac{\min \{p_i, 1-p_i\}}{z_ip_i + (1-Z_i)(1-p_i)}$$`
--

### Average Treatment Effect Among the Overlap Population
`$$\Large w_{ATO} = (1-p_i)Z_i + p_i(1-Z_i)$$`

---

## Histogram of propensity scores

<img src="04-pscore-weighting_files/figure-html/unnamed-chunk-3-1.png" style="display: block; margin: auto;" />

---

## ATE

<img src="04-pscore-weighting_files/figure-html/unnamed-chunk-4-1.png" style="display: block; margin: auto;" />

---

## ATT

<img src="04-pscore-weighting_files/figure-html/unnamed-chunk-5-1.png" style="display: block; margin: auto;" />

---

## ATC

<img src="04-pscore-weighting_files/figure-html/unnamed-chunk-6-1.png" style="display: block; margin: auto;" />

---

## ATM

<img src="04-pscore-weighting_files/figure-html/unnamed-chunk-7-1.png" style="display: block; margin: auto;" />

---

## ATO

<img src="04-pscore-weighting_files/figure-html/unnamed-chunk-8-1.png" style="display: block; margin: auto;" />

---

## ATE in R

* Average Treatment Effect (ATE)
  * `\(w_{ATE} = \frac{Z_i}{p_i} + \frac{1-Z_i}{1 - p_i}\)`

```r
df <- propensity_model %>% 
  augment(type.predict = "response", data = nhefs_complete) %>% 
* mutate(w_ate = (qsmk / .fitted) +  ((1 - qsmk) / (1 - .fitted)))
```

---
class: inverse

## Your Turn

<div class="countdown" id="timer_5f21917c" 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 propensity scores you created in the previous exercise, add the ATE weights to your data frame `df`

2. Stretch: Using the same propensity scores, create ATT weights

Notes for current slide

Notes for next slide

Propensity Score WeightingLucy D’Agostino McGowanWake Forest University2020-07-29 (updated: 2020-07-29)1 / 14

Propensity scoresWeighting
Matching
Stratification
Direct Adjustment
...
2 / 14

Propensity scoresWeighting
Matching
Stratification
Direct Adjustment
...
3 / 14

Target estimands

Average Treatment Effect (ATE)

$w_{A T E} = \frac{Z_{i}}{p_{i}} + \frac{1 - Z_{i}}{1 - p_{i}}$

4 / 14

Target estimands

Average Treatment Effect Among the Treated (ATT)

$w_{A T T} = \frac{p_{i} Z_{i}}{p_{i}} + \frac{p_{i} (1 - Z_{i})}{1 - p_{i}}$

5 / 14

Target estimands

Average Treatment Effect Among the Treated (ATT)

$w_{A T T} = \frac{p_{i} Z_{i}}{p_{i}} + \frac{p_{i} (1 - Z_{i})}{1 - p_{i}}$

Average Treatment Effect Among the Controls (ATC)

$w_{A T C} = \frac{(1 - p_{i}) Z_{i}}{p_{i}} + \frac{(1 - p_{i}) (1 - Z_{i})}{(1 - p_{i})}$

5 / 14

Target estimands

Average Treatment Effect Among the Evenly Matchable (ATM)

$w_{A T M} = \frac{min {p_{i}, 1 - p_{i}}}{z_{i} p_{i} + (1 - Z_{i}) (1 - p_{i})}$

6 / 14

Target estimands

Average Treatment Effect Among the Evenly Matchable (ATM)

$w_{A T M} = \frac{min {p_{i}, 1 - p_{i}}}{z_{i} p_{i} + (1 - Z_{i}) (1 - p_{i})}$

Average Treatment Effect Among the Overlap Population

$w_{A T O} = (1 - p_{i}) Z_{i} + p_{i} (1 - Z_{i})$

6 / 14

Histogram of propensity scores

7 / 14

ATE

8 / 14

ATT

9 / 14

ATC

10 / 14

ATM

11 / 14

ATO

12 / 14

ATE in R

Average Treatment Effect (ATE)
- $w_{A T E} = \frac{Z_{i}}{p_{i}} + \frac{1 - Z_{i}}{1 - p_{i}}$

df <- propensity_model %>% 
  augment(type.predict = "response", data = nhefs_complete) %>% 
  mutate(w_ate = (qsmk / .fitted) +  ((1 - qsmk) / (1 - .fitted)))

13 / 14

Your Turn

05:00

Using the propensity scores you created in the previous exercise, add the ATE weights to your data frame df
Stretch: Using the same propensity scores, create ATT weights

14 / 14

Propensity scoresWeighting
Matching
Stratification
Direct Adjustment
...
2 / 14

Paused

Help

Keyboard shortcuts

↑, ←, Pg Up, k	Go to previous slide
↓, →, Pg Dn, Space, j	Go to next slide
Home	Go to first slide
End	Go to last slide
Number + Return	Go to specific slide
b / m / f	Toggle blackout / mirrored / fullscreen mode
c	Clone slideshow
p	Toggle presenter mode
t	Restart the presentation timer
?, h	Toggle this help

Esc	Back to slideshow