# When Standard Methods Succeed

Lucy D’Agostino McGowan

Wake Forest University

## Even in these cases, using the methods you will learn here can help!

1. Adjusting for baseline covariates can make an estimate more efficient
2. Propensity score weighting is more efficient that direct adjustment
3. Sometimes we are more comfortable with the functional form of the propensity score (predicting exposure) than the outcome model

## Example

• simulated data (100 observations)
• Treatment is randomly assigned
• There are two baseline covariates: age and weight

## Example

• True average treatment effect: 1

lm(y ~ treatment, data = data)
Characteristic Beta SE1 95% CI1 p-value
treatment 0.93 0.803 -0.66, 2.5 0.2
1 SE = Standard Error, CI = Confidence Interval

lm(y ~ treatment + weight + age, data = data)
Characteristic Beta SE1 95% CI1 p-value
treatment 1.0 0.204 0.59, 1.4 <0.001
weight 0.34 0.106 0.13, 0.55 0.002
age 0.20 0.005 0.19, 0.22 <0.001
1 SE = Standard Error, CI = Confidence Interval

Characteristic Beta SE 95% CI p-value
treatment 1 0.202 0.6, 1.4 <0.001

## Example

• simulated data (10,000 observations)
• Treatment is randomly assigned
• There are two baseline covariates: age and weight

lm(y ~ treatment, data = data)
Characteristic Beta SE1 95% CI1 p-value
treatment 0.96 0.083 0.80, 1.1 <0.001
1 SE = Standard Error, CI = Confidence Interval

lm(y ~ treatment + weight + age, data = data)
Characteristic Beta SE1 95% CI1 p-value
treatment 1.0 0.020 0.98, 1.1 <0.001
weight 0.20 0.010 0.18, 0.22 <0.001
age 0.20 0.000 0.20, 0.20 <0.001
1 SE = Standard Error, CI = Confidence Interval

Characteristic Beta SE 95% CI p-value
treatment 1 0.02 1, 1.1 <0.001

## Example

• simulated data (10,000 observations)
• Treatment is not randomly assigned
• There are two baseline confounders: age and weight
• The treatment effect is homogeneous

## Example

• True average treatment effect: 1

lm(y ~ treatment, data = data)
Characteristic Beta SE1 95% CI1 p-value
treatment 1.8 0.085 1.7, 2.0 <0.001
1 SE = Standard Error, CI = Confidence Interval

lm(y ~ treatment + weight + age, data = data)