# 3 Real-World Examples of Using Instrumental Variables

The instrumental variable approach is a method to identify the causal effect of a treatment on an outcome of interest by controlling for unobserved confounding between them.

A valid instrumental variable, Z, is one that influences the outcome, Y, through the treatment, X, without being related to the confounding variable, C, as shown in the following diagram:

Therefore, the effect of the instrumental variable Z on the outcome Y can be used to estimate the effect of the treatment X on the outcome Y bypassing the confounding effect of C.

For more details, see: 7 Different Ways to Control for Confounding.

## Example 1: Measuring the effect of smoking during pregnancy on birth weight

### Problem

Smoking during pregnancy is correlated with low birth weight. But this association is confounded by all sort of unobserved (and hard to measure) maternal characteristics that complicate the relationship between smoking and low birth weight.

### Solution

Evans and Ringel used cigarette taxes as an instrumental variable to study the causal effect of smoking on birth weight, as shown in the diagram below:

Cigarette taxes is a valid instrumental variable since:

• Cigarette taxes alter the smoking behavior of pregnant women (the instrumental variable Z affects the treatment X).
• Cigarettes taxes can only affect birth weight through the change in the smoking behavior of pregnant women (Z has no direct influence on the outcome Y).
• Cigarette taxes are not affected by the characteristics of the pregnant women (Z is not caused by the confounder C).

Therefore, cigarette taxes can be considered as a source of exogenous variation in the smoking behavior of pregnant women, resembling random assignment of pregnant women to either smoking or not.

### Study results:

The authors concluded that an increase in the cigarette tax rates has a beneficial impact on birth weight.

Their estimate of the effect of smoking during pregnancy on birth weight was close to that of a randomized controlled trial, and larger in magnitude than the estimates obtained from other observational studies that used more classical methods of confounding control.

## Example 2: Measuring the effect of smoking cessation on weight gain

### Problem

In order to measure the effect of smoking cessation on weight gain, studies typically compare the average weight gain of quitters to that of continuing smokers while controlling for confounding factors such as age, gender, and initial body weight.

These studies, however, may still be biased since the relationship between smoking cessation and weight gain could be confounded by a long list of unmeasurable and unknown factors.

### Solution

Eisenberg and Quinn used the instrumental variable approach on data from a randomized controlled trial that randomized smokers to either receive a smoking cessation intervention or not.

Here’s a causal diagram that represents relationships between variables in their study:

Random assignment of smokers to the intervention is a valid instrumental variable since:

• This random assignment affects the probability of quitting smoking (Z affects X).
• This random assignment can only affect weight gain through smoking cessation (Z has no direct influence on Y).
• This random assignment is not affected by any type of confounding (Z is not caused by C).

Therefore, random assignment of smokers to a smoking cessation intervention can be considered as a source of exogenous variation in smoking cessation, allowing us to study the effect of the latter on weight gain bypassing any confounding effect.

### Study results

The authors concluded that smoking cessation caused twice the increase in weight as estimated by other studies using suboptimal methods to control confounding.

## Example 3: Measuring the effect of heart attack treatment intensity on survival

### Problem

Patients with a heart attack receive different treatments according to their health status (such as: the presence of other diseases, the severity of the case, etc.). So, if we want to study the causal effect of heart attack treatment intensity on survival we will have to face confounding by all kinds of patient characteristics.

### Solution

Controlling for all these observable and unobservable characteristics is a real pain that can be avoided by using the instrumental variable approach.

In their study, McClellan and colleagues used the patient proximity to different types of hospitals as an instrumental variable to study the effect of treatment intensity on survival, as shown in the following diagram:

Patient proximity to hospitals is a valid instrumental variable since:

• The patient proximity to a certain type of hospital determines the type and intensity of the received treatment (Z affects X).
• The patient proximity to a certain type of hospital affects the outcome only through the treatment received. In other words, it does not have a direct effect on survival (Z affects Y only through X).
• The patient proximity to a certain type of hospital is not affected by the health status of the patient (Z is not related to C).

So, differential distances approximately randomize patients to receive different intensities of treatments, and therefore can be used to estimate the causal effect of the treatment intensity on survival.

### Study results

The authors concluded that, when it comes to heart attacks, using a more aggressive treatment is not as efficacious as the timing of that treatment.