4 The TMLE Framework (Brief Review)

Jeremy Coyle and Nima Hejazi

Based on the tmle3 R package.

4.1 Learning Objectives

By the end of this chapter, you will be able to

Use tmle3 to estimate an Average Treatment Effect (ATE).
Understand how to use tmle3 “Specs” objects.

4.2 Introduction

Mark and Alan introduced the core concepts associated with TMLE in their intro talk. Today, we’ll be focused on some more advanced applications of tmle3, but we’d like to review the basics of how to use the package. Before we do that, are there any conceptual clarifications on TMLE?

The following sections describe a simple way of specifying and estimating a TMLE in the tlverse. In designing tmle3, we sought to replicate as closely as possible the very general estimation framework of TMLE, and so each theoretical object relevant to TMLE is encoded in a corresponding software object/method. More information on this design can be found in the handbook.

4.3 Easy-Bake Example: `tmle3` for ATE

We’ll illustrate the most basic use of TMLE using the WASH Benefits data introduced earlier and estimating an average treatment effect. Similar specifications will be relevant during the later sections on advanced tmle3 usage.

4.3.1 Load the Data

We’ll use the same WASH Benefits data as the earlier chapters:

library(data.table)
library(dplyr)
library(tmle3)
library(sl3)
washb_data <- fread(
  paste0(
    "https://raw.githubusercontent.com/tlverse/tlverse-data/master/",
    "wash-benefits/washb_data.csv"
  ),
  stringsAsFactors = TRUE
)

4.3.2 Define the variable roles

We’ll use the common \(W\) (covariates), \(A\) (treatment/intervention), \(Y\) (outcome) data structure. tmle3 needs to know what variables in the dataset correspond to each of these roles. We use a list of character vectors to tell it. We call this a “Node List” as it corresponds to the nodes in a Directed Acyclic Graph (DAG), a way of displaying causal relationships between variables.

node_list <- list(
  W = c(
    "month", "aged", "sex", "momage", "momedu",
    "momheight", "hfiacat", "Nlt18", "Ncomp", "watmin",
    "elec", "floor", "walls", "roof", "asset_wardrobe",
    "asset_table", "asset_chair", "asset_khat",
    "asset_chouki", "asset_tv", "asset_refrig",
    "asset_bike", "asset_moto", "asset_sewmach",
    "asset_mobile"
  ),
  A = "tr",
  Y = "whz"
)

4.3.3 Handle Missingness

Currently, missingness in tmle3 is handled in a fairly simple way:

Missing covariates are median- (for continuous) or mode- (for discrete) imputed, and additional covariates indicating imputation are generated, just as described in the sl3 chapter.
Missing treatment variables are excluded – such observations are dropped.
Missing outcomes are efficiently handled by the automatic calculation (and incorporation into estimators) of inverse probability of censoring weights (IPCW); this is also known as IPCW-TMLE and may be thought of as a joint intervention to remove missingness and is analogous to the procedure used with classical inverse probability weighted estimators.

These steps are implemented in the process_missing function in tmle3:

processed <- process_missing(washb_data, node_list)
washb_data <- processed$data
node_list <- processed$node_list

4.3.4 Create a “Spec” Object

tmle3 is general, and allows most components of the TMLE procedure to be specified in a modular way. However, most end-users will not be interested in manually specifying all of these components. Therefore, tmle3 implements a tmle3_Spec object that bundles a set of components into a specification (“Spec”) that, with minimal additional detail, can be run by an end-user.

We’ll start with using one of the specs, and then work our way down into the internals of tmle3.

ate_spec <- tmle_ATE(
  treatment_level = "Nutrition + WSH",
  control_level = "Control"
)

4.3.5 Define the learners

Currently, the only other thing a user must define are the sl3 learners used to estimate the relevant factors of the likelihood: Q and g.

This takes the form of a list of sl3 learners, one for each likelihood factor to be estimated with sl3:

# choose base learners
lrnr_mean <- make_learner(Lrnr_mean)
lrnr_rf <- make_learner(Lrnr_ranger)

# define metalearners appropriate to data types
ls_metalearner <- make_learner(Lrnr_nnls)
mn_metalearner <- make_learner(
  Lrnr_solnp, metalearner_linear_multinomial,
  loss_loglik_multinomial
)
sl_Y <- Lrnr_sl$new(
  learners = list(lrnr_mean, lrnr_rf),
  metalearner = ls_metalearner
)
sl_A <- Lrnr_sl$new(
  learners = list(lrnr_mean, lrnr_rf),
  metalearner = mn_metalearner
)
learner_list <- list(A = sl_A, Y = sl_Y)

Here, we use a Super Learner as defined in the previous chapter. In the future, we plan to include reasonable defaults learners.

4.3.6 Fit the TMLE

We now have everything we need to fit the tmle using tmle3:

tmle_fit <- tmle3(ate_spec, washb_data, node_list, learner_list)
print(tmle_fit)
A tmle3_Fit that took 1 step(s)
   type                                    param   init_est  tmle_est       se
1:  ATE ATE[Y_{A=Nutrition + WSH}-Y_{A=Control}] -0.0031624 0.0077013 0.050351
       lower   upper psi_transformed lower_transformed upper_transformed
1: -0.090985 0.10639       0.0077013         -0.090985           0.10639

4.3.7 Evaluate the Estimates

We can see the summary results by printing the fit object. Alternatively, we can extra results from the summary by indexing into it:

estimates <- tmle_fit$summary$psi_transformed
print(estimates)
[1] 0.0077013

4.4 Summary

tmle3 is a general purpose framework for generating TML estimates. The easiest way to use it is to use a predefined spec, allowing you to just fill in the blanks for the data, variable roles, and sl3 learners. In the next sections, we’ll see how this framework can be used to estimate advanced parameters such as optimal treatments and stochastic shift interventions.

There are no exercises for this brief chapter, but you may find the exercises in the corresponding handbook chapter helpful.

3 Super Learning with sl3

5 Optimal Individualized Treatment Regimes