# statistics

## An Illustrated Introduction to Optimal Treatment Rules

This post walks through the basic statistical intuition for Optimal Treatment Rules (OTRs) for applied scientists. Each concept is accompanied by a small visual to aid in comprehension. Optimal treatment rules (OTRs) is a fast-growing topic in the medical research community. A treatment rule is a decision for treatment based upon a patient’s characteristics. The intuition behind this is that not all patients will respond to a treatment in the same way.

## An Illustrated Guide to TMLE, Part III: Properties, Theory, and Learning More

The is the third and final post in a three-part series to help beginners and/or visual learners understand Targeted Maximum Likelihood Estimation (TMLE). In this section, I discuss more statistical properties of TMLE, offer a brief explanation for the theory behind TMLE, and provide resources for learning more. Properties of TMLE 📈 To reiterate a point from Parts I and II, a main motivation for TMLE is that it allows the use of machine learning algorithms while still yielding asymptotic properties for inference.

## An Illustrated Guide to TMLE, Part II: The Algorithm

The second post of a three-part series to help beginners and/or visual learners understand Targeted Maximum Likelihood Estimation (TMLE). This section walks through the TMLE algorithm for the mean difference in outcomes for a binary treatment and binary outcome. This post is an expansion of a printable “visual guide” available on my Github. I hope it helps analysts who feel out-of-practice reading mathematical notation follow along with the TMLE algorithm.

## An Illustrated Guide to TMLE, Part I: Introduction and Motivation

The introductory post of a three-part series to help beginners and/or visual learners understand Targeted Maximum Likelihood Estimation (TMLE). This section contains a brief overview of the targeted learning framework and motivation for semiparametric estimation methods for inference, including causal inference. Table of Contents This blog post series has three parts: Part I: Motivation TMLE in three sentences 🎯 An Analyst’s Motivation for Learning TMLE 👩🏼‍💻 Is TMLE Causal Inference?

## Rethinking Conditional and Iterated Expectations with Linear Regression Models

An “aha!” moment: the day I realized I should rethink all the probability theorems using linear regressions. TL;DR You can a regress an outcome on a grouping variable plus any other variable(s) and the unadjusted and adjusted group means will be identical. We can see this in a simple example using the palmerpenguins data: #remotes::install_github("allisonhorst/palmerpenguins") library(palmerpenguins) library(tidyverse) library(gt) # use complete cases for simplicity penguins <- drop_na(penguins) penguins %>% # fit a linear regression for bill length given bill depth and species # make a new column containing the fitted values for bill length mutate(preds = predict(lm(bill_length_mm ~ bill_depth_mm + species, data = .

## A Day in the Life of a Biostatistician

It seems fitting that my first blog post is on a topic that I tried and failed to find via Google search a few years ago. I’ll back up for a second. A few years ago I was a recent college graduate, and trying hard to “figure out my life.” My major was biochemistry, which is one of those degrees where 99%* of people just keep on going to school.

## A Condensed Key for A Visual Guide to Targeted Maximum Likelihood Estimation (TMLE)

A condensed key for my corresponding TMLE tutorial blog post. Initial set up Estimand of interest: $ATE = \Psi = E_W[\mathrm{E}[Y|A=1,\mathbf{W}] - \mathrm{E}[Y|A=0,\mathbf{W}]]$ Step 1: Estimate the Outcome First, estimate the expected value of the outcome using treatment and confounders as predictors. $Q(A,\mathbf{W}) = \mathrm{E}[Y|A,\mathbf{W}]$ Then use that fit to obtain estimates of the expected outcome under varying three different treatment conditions: