The

introductory postof a three-part series to help beginners understand Targeted Maximum Likelihood Estimation (TMLE). This section contains a brief overview of thetargeted learning frameworkand motivation forsemiparametric estimation methods for inference, including causal inference.

# Table of Contents

*This blog post series has three parts:*

### Part I: Motivation

### Part II: Algorithm

### Part III: Evaluation

# TMLE in three sentences 🎯

Targeted Maximum Likelihood Estimation (TMLE) is a semiparametric estimation framework to **estimate a statistical quantity of interest**. TMLE allows the use of **machine learning** (ML) models which place **minimal assumptions on the distribution of the data**. Unlike estimates normally obtained from ML, the **final TMLE estimate will still have valid standard errors for statistical inference**.

# An Analyst’s Motivation for Learning TMLE 👩🏼💻

When I graduated with my MS in Biostatistics two years ago, I had a mental framework of statistics and data science that I think is pretty common among new graduates. It went like this:

If the goal is inference (e.g., an effect size with a confidence interval), use an interpretable, usually parametric, model and explain what the coefficients and their standard errors mean.

If the goal is prediction, use data-adaptive machine learning algorithms and then look at performance metrics, with the understanding that standard errors, and sometimes even coefficients, no longer exist.

This mentality changed drastically when I started learning about semiparametric estimation methods like TMLE in the context of causal inference. I quickly realized two flaws in this mental framework.

First, I was thinking about inference backwards: I was choosing a model based on my outcome type (binary, continuous, time-to-event, repeated measures) and then interpreting specific coefficients as my estimates of interest. Yet it makes way more sense to *first* determine the statistical quantity, or **estimand**, that best answers a scientific question, and *then* use the method, or **estimator**, best suited for estimating it. This is the paradigm TMLE is based upon: **we want to build an algorithm, or estimator, targeted to an estimand of interest**.

Second, I thought flexible, data-adaptive models we commonly classify as statistical and/or **machine learning** (e.g. LASSO, random forests, gradient boosting, etc.) could only be used for prediction, since they don’t have **asymptotic properties for inference** (i.e. standard errors). However, certain **semiparametric estimation methods** like TMLE can actually use these models to **obtain a final estimate that is closer to the target quantity** than would be obtained using classic parametric models (e.g. linear and logistic regression). This is because machine learning models are generally designed to accommodate **large numbers of covariates** with **complex, non-linear relationships**.

*Semiparametric estimation methods like TMLE can rely on machine learning to avoid making unrealistic parametric assumptions about the underlying distribution of the data (e.g. multivariate normality).*

The way we use the machine learning estimates in TMLE, surprisingly enough, yields **known asymptotic properties of bias and variance** – just like we see in parametric maximum likelihood estimation – for our target estimand.

Besides allowing us to compute 95% confidence intervals and p-values for our estimates even after using flexible models, TMLE achieves other beneficial statistical properties, such as **double robustness**. These are discussed further in *Part III*.

# Is TMLE Causal Inference? 🤔

If you’ve heard about TMLE before, it was likely in the context of **causal inference**. Although TMLE was developed for causal inference due to its many attractive properties, it cannot be considered causal inference by itself. Causal inference is a two-step process that first requires **causal assumptions**^{1} before a statistical estimand can be interpreted causally.

^{1} I won’t discuss causal assumptions in these posts, but this is referring to fundamental assumptions in causal inference like consistency, exchangeability, and positivity. A primary motivation for using TMLE and other semiparametric estimation methods for causal inference is that if you’ve already taken the time to carefully evaluate *causal* assumptions, it does not make sense to then damage an otherwise well-designed analysis by making unrealistic *statistical* assumptions.

**TMLE can be used to estimate various statistical estimands** (odds ratio, risk ratio, mean outcome difference, etc.) **even when causal assumptions are not met**. TMLE is, as its name implies, simply a tool for estimation.

In *Part II*, I’ll walk step-by-step through a basic version of the TMLE algorithm: estimating the mean difference in outcomes, adjusted for confounders, for a binary outcome and binary treatment. If causal assumptions are met, this is called the **Average Treatment Effect (ATE)**, or the mean difference in outcomes in a world in which everyone had received the treatment compared to a world in which everyone had not.

➡️*Continue to Part II: The Algorithm*

*References*

My primary reference for all three posts is *Targeted Learning* by Mark van der Laan and Sherri Rose. I detail many other resources I’ve used to learn TMLE, semiparametric theory, and causal inference in *Part III*.