Causal inference in case of near-violation of positivity: comparison of methods.

In causal studies, the near-violation of the positivity may occur by chance, because of sample-to-sample fluctuation despite the theoretical veracity of the positivity assumption in the population. It may mostly happen when the exposure prevalence is low or when the sample size is small. We aimed to compare the robustness of g-computation (GC), inverse probability weighting (IPW), truncated IPW, targeted maximum likelihood estimation (TMLE), and truncated TMLE in this situation, using simulations and one real application. We also tested different extrapolation situations for the sub-group with a positivity violation. The results illustrated that the near-violation of the positivity impacted all methods. We demonstrated the robustness of GC and TMLE-based methods. Truncation helped in limiting the bias in near-violation situations, but at the cost of bias in normal conditions. The application illustrated the variability of the results between the methods and the importance of choosing the most appropriate one. In conclusion, compared to propensity score-based methods, methods based on outcome regression should be preferred when suspecting near-violation of the positivity assumption.

Léger M ，Chatton A ，Le Borgne F ，Pirracchio R ，Lasocki S ，Foucher Y ... -  《-》

Effect Estimation in Point-Exposure Studies with Binary Outcomes and High-Dimensional Covariate Data - A Comparison of Targeted Maximum Likelihood Estimation and Inverse Probability of Treatment Weighting.

Pang M ，Schuster T ，Filion KB ，Schnitzer ME ，Eberg M ，Platt RW ... -  《-》

On adaptive propensity score truncation in causal inference.

Ju C ，Schwab J ，van der Laan MJ 《-》

Data-Adaptive Selection of the Propensity Score Truncation Level for Inverse-Probability-Weighted and Targeted Maximum Likelihood Estimators of Marginal Point Treatment Effects.

Inverse probability weighting (IPW) and targeted maximum likelihood estimation (TMLE) are methodologies that can adjust for confounding and selection bias and are often used for causal inference. Both estimators rely on the positivity assumption that within strata of confounders there is a positive probability of receiving treatment at all levels under consideration. Practical applications of IPW require finite inverse probability (IP) weights. TMLE requires that propensity scores (PS) be bounded away from 0 and 1. Although truncation can improve variance and finite sample bias, this artificial distortion of the IP weights and PS distribution introduces asymptotic bias. As sample size grows, truncation-induced bias eventually swamps variance, rendering nominal confidence interval coverage and hypothesis tests invalid. We present a simple truncation strategy based on the sample size, n, that sets the upper bound on IP weights at $\sqrt{\textit{n}}$ ln n/5. For TMLE, the lower bound on the PS should be set to 5/($\sqrt{\textit{n}}$ ln n/5). Our strategy was designed to optimize the mean squared error of the parameter estimate. It naturally extends to data structures with missing outcomes. Simulation studies and a data analysis demonstrate our strategy's ability to minimize both bias and mean squared error in comparison with other common strategies, including the popular but flawed quantile-based heuristic.

Gruber S ，Phillips RV ，Lee H ，van der Laan MJ ... -  《-》

Targeted Maximum Likelihood Estimation for Causal Inference in Observational Studies.

Estimation of causal effects using observational data continues to grow in popularity in the epidemiologic literature. While many applications of causal effect estimation use propensity score methods or G-computation, targeted maximum likelihood estimation (TMLE) is a well-established alternative method with desirable statistical properties. TMLE is a doubly robust maximum-likelihood-based approach that includes a secondary "targeting" step that optimizes the bias-variance tradeoff for the target parameter. Under standard causal assumptions, estimates can be interpreted as causal effects. Because TMLE has not been as widely implemented in epidemiologic research, we aim to provide an accessible presentation of TMLE for applied researchers. We give step-by-step instructions for using TMLE to estimate the average treatment effect in the context of an observational study. We discuss conceptual similarities and differences between TMLE and 2 common estimation approaches (G-computation and inverse probability weighting) and present findings on their relative performance using simulated data. Our simulation study compares methods under parametric regression misspecification; our results highlight TMLE's property of double robustness. Additionally, we discuss best practices for TMLE implementation, particularly the use of ensembled machine learning algorithms. Our simulation study demonstrates all methods using super learning, highlighting that incorporation of machine learning may outperform parametric regression in observational data settings.

Schuler MS ，Rose S 《-》