surrogates.qmd

---
title: "Surrogates"
share:
  permalink: "https://book.martinez.fyi/surrogates.html"
  description: "Business Data Science: What Does it Mean to Be Data-Driven?"
  linkedin: true
  email: true
  mastodon: true
---

## What are Surrogates?

A surrogate, in essence, is a stand-in for a long-term outcome that is difficult
or time-consuming to measure directly. For example, instead of waiting to see
how a new feature impacts annual revenue, we might look at its effect on daily
active users or click-through rates. By understanding the relationship between
these short-term surrogates and the long-term outcome, we can gain insights into
how our actions are likely to impact the metrics we truly care about.

### Importance of Surrogates

In many cases, a single surrogate may not fully capture the complexity of the
long-term outcome. This is where the concept of a surrogate index comes in. By
combining multiple surrogates into a single metric, we can create a more
comprehensive and nuanced picture of the impact of our decisions. For example,
we might combine metrics like user engagement, satisfaction ratings, and
retention rates into a single index that reflects the overall health of our
product.

### Validity of Surrogate Studies

To ensure the validity of a surrogate study, two key ingredients are essential:

  - Validity of Surrogates: The surrogates must be valid, meaning that the
    policy or decision we are interested in truly affects the ultimate outcome
    through the chosen surrogates.
  - Robust Identification: We need to robustly identify the policy's effects on
    the surrogates. This is often achieved through randomized experiments, but
    other methods can also be used.

The tech sector is awash in data, offering a wide range of potential surrogates.
These might include metrics like website traffic, click-through rates, user
engagement, social media mentions, and app downloads. The specific surrogates to
choose will depend on the nature of the decision being studied and the available
data.

### Choosing the Right Surrogates

Selecting appropriate surrogates requires a deep understanding of the domain and
the long-term outcomes of interest. It's crucial to choose surrogates that are
closely linked to these outcomes. For example:

  - **E-commerce:** For an online store, short-term surrogates might include cart
    abandonment rates, average order value, and customer reviews.
  - **Healthcare:** In a clinical trial, blood pressure and cholesterol levels can
    be surrogates for long-term cardiovascular health.

## Estimating Effects in Practice
There are several ways to estimate long-term effects using a surrogate index.
The simplest approach is to use an experimental setup, where we know the
probability of a unit being assigned to a particular group. In this case, we can
estimate the surrogate index and then use it to impute the long-term outcome.

### Methods for Estimating Surrogacy

The method used to estimate the surrogacy index is flexible, as long as it
captures the average effect of the index on the long-term outcome. In scenarios
with many potential surrogates, techniques like LASSO (Least Absolute Shrinkage
and Selection Operator) can be used to identify the most relevant ones. Other
machine learning techniques such as Random Forests or Gradient Boosting can also
be employed to handle complex, high-dimensional data.


### Practical Example

To illustrate the application of surrogate indices, consider a tech company
running an A/B test to evaluate a new feature. The company might track several
metrics during the experiment, such as user engagement, time spent on the
platform, and frequency of feature usage. By combining these metrics into a
surrogate index, the company can predict the feature's impact on long-term user
retention and revenue growth.

#### Example with Code

```{r example, message=FALSE}
# TODO WRITE EXAMPLE!

```

### Conclusion

Surrogates are powerful tools that can help bridge the gap between short-term
metrics and long-term outcomes. By carefully selecting and validating
surrogates, and employing robust estimation methods, we can make more informed
decisions and predict the long-term impact of our actions with greater
precision.

::: {.callout-tip}
## Learn more
  - @athey2019surrogate The surrogate index: Combining short-term proxies to
    estimate long-term treatment effects more rapidly and precisely.
  - @imbens2022long Long-term causal inference under persistent confounding via
    data combination.
  - @chen2023semiparametric Semiparametric estimation of long-term treatment
    effects.
  - @zhang2023evaluating Evaluating the Surrogate Index as a Decision-Making
    Tool Using 200 A/B Tests at Netflix.
:::