When Standard Methods Succeed

Lucy D’Agostino McGowan

Wake Forest University

when correlation is causation

When you have no confounders and there is a linear relationship between the exposure and the outcome, that correlation is a causal relationship

😮

When you have no confounders and there is a linear relationship between the exposure and the outcome, that correlation is a causal relationship

😮

When you have no confounders and there is a linear relationship between the exposure and the outcome, that correlation is a causal relationship

😮

When you have no confounders and there is a linear relationship between the exposure and the outcome, that correlation is a causal relationship

😮

randomized controlled trials

A/B testing

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 than 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

Unadjusted model

lm(y ~ treatment, data = data)

Characteristic

Beta

SE

1

95% CI

1

p-value
treatment 0.93 0.803 -0.66, 2.5 0.2
1

SE = Standard Error, CI = Confidence Interval

Adjusted model

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

Characteristic

Beta

SE

1

95% CI

1

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

Propensity score adjusted model

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

Unadjusted model

lm(y ~ treatment, data = data)

Characteristic

Beta

SE

1

95% CI

1

p-value
treatment 0.96 0.083 0.80, 1.1 <0.001
1

SE = Standard Error, CI = Confidence Interval

Adjusted model

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

Characteristic

Beta

SE

1

95% CI

1

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

Propensity score adjusted model

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

Unadjusted model

lm(y ~ treatment, data = data)

Characteristic

Beta

SE

1

95% CI

1

p-value
treatment 1.8 0.085 1.7, 2.0 <0.001
1

SE = Standard Error, CI = Confidence Interval

Adjusted model

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

Characteristic

Beta

SE

1

95% CI

1

p-value
treatment 0.98 0.021 0.94, 1.0 <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

Propensity score adjusted model

Characteristic Beta SE 95% CI p-value
treatment 1 0.022 0.9, 1 <0.001

time-varying confounding