In clinical research and real-world evidence generation, one of the most common scientific questions we face is deceptively simple: what would happen to outcomes if all patients received treatment A instead of treatment B?
While the question sounds straightforward, the statistical reality behind it is far more complex. At its core, this is a population-level causal question, and the way we choose to answer it should not depend on arbitrary modelling decisions or analyst preferences. In practice, however, different analysts working with the same dataset can often arrive at different answers depending on how the problem is framed and which modelling choices are made.
This highlights an important challenge in causal inference: moving from a scientific question, to a statistical estimand, and finally to an estimator is not always straightforward. Each step requires careful definition, because even small differences in how we translate a question into a model can lead to meaningfully different results.
A common starting point is covariate-adjusted regression. These models are widely used in both clinical trials and observational studies, and typically estimate treatment effects conditional on baseline covariates. However, what is often reported, such as an odds ratio from a logistic regression model, is a conditional effect. This represents the treatment effect at a fixed set of covariate values, often an average or reference level.
In contrast, many research questions are actually concerned with marginal effects. That is, we want to understand the average difference in outcomes if everyone were treated versus if no one were treated, across the entire population. These two estimands can be meaningfully different, particularly when relationships are non-linear or when effect modification is present.
This distinction becomes even more important when we consider that most real-world models are, by necessity, misspecified to some degree. The assumption of perfectly linear or correctly specified relationships between treatment, covariates, and outcomes rarely holds in practice. As a result, relying on a single model can introduce bias that is difficult to detect.
Another complication arises from non-collapsibility. For effect measures such as odds ratios and hazard ratios, adjusting for variables that are not true confounders can still change the estimated effect, even in a randomised setting. This means that simply adding covariates to a model can alter results in ways that are purely mathematical rather than causal in nature. Similarly, conditioning on post-treatment variables, such as biomarkers influenced by treatment, can introduce bias by blocking parts of the causal pathway or inducing selection effects.
These challenges motivate the need for more robust approaches to estimation. One such approach is Targeted Maximum Likelihood Estimation, or TMLE. [1]
TMLE is designed to directly target the causal quantity of interest, typically a marginal treatment effect, while maintaining flexibility in how nuisance components such as the outcome model and treatment mechanism are estimated. These nuisance models are often built using flexible machine learning approaches, such as ensemble learning or super learning, rather than relying on a single parametric form.
Once initial models are estimated, TMLE then updates these estimates in a targeted way using what is known as a clever covariate. This step is designed to reduce bias in the direction that is most relevant for the causal estimand. The result is a final estimator that is a substitution estimator but also has strong theoretical properties, including double robustness and, under certain conditions, efficiency at the semi-parametric bound.
The concept of double robustness is central to understanding why TMLE is so powerful. The key idea is that the bias of the estimator is driven by the product of the biases in the outcome model and the treatment model. As a result, if either model is correctly specified, the overall bias can be eliminated. Even when neither model is perfect, the structure of TMLE often leads to substantial bias reduction compared to traditional approaches.
From a practical standpoint, the TMLE workflow typically begins with estimating the outcome regression and the treatment mechanism. These are often fit using flexible machine learning methods to reduce reliance on strict parametric assumptions. Next, a clever covariate is constructed based on the efficient influence curve, which guides how the initial estimates should be updated. Finally, the model is iteratively targeted until it converges on the desired estimand.
One of the key advantages of TMLE is that it directly targets marginal, policy-relevant effects, rather than conditional associations. This makes it particularly well suited to decision-making contexts where the question of interest is population-level impact rather than subgroup-specific associations.
Simulation studies consistently show the advantages of TMLE compared to more traditional approaches. While standard regression methods can exhibit bias and poor coverage, and inverse probability weighting approaches may suffer from high variance, TMLE tends to achieve low bias and improved efficiency by balancing both components of the estimation problem.
Importantly, TMLE does not remove the need for careful causal thinking. Standard assumptions such as no unmeasured confounding and correct specification of the causal structure still apply. However, it does provide a more robust framework for estimation when working with complex and realistic data structures.
Ultimately, TMLE represents a shift in how we approach causal inference. Rather than relying on a single model to answer a complex question, it embraces flexibility, targets the estimand directly, and improves robustness through its double robust structure. In doing so, it helps bridge the gap between statistical modelling and meaningful clinical decision-making.
References
- Rosenblum, M., & van der Laan, M. J. (2010). Targeted maximum likelihood estimation of the parameter of a marginal structural model. International Journal of Biostatistics, 6(2), Article 19. https://doi.org/10.2202/1557-4679.1238
