TABLE 1.
Overview of literature on comparison of TMLE and other estimators
| Authors | Title | Year | Description of results | Pro/Con |
|---|---|---|---|---|
| Chatton, et al20 | G-computation, propensity score-based methods, and targeted maximum likelihood estimator for causal inference with different covariates sets: a comparative simulation study | 2020 | Article compares different semiparametic approaches, including TMLE and matching, but finds G-computation performs relatively best. Given their simulation, this was predictable because they simulated from a parametric model and used the same model for estimating the regression, thus showing the superiority of maximum likelihood estimation in parametric models. This is not a realistic setting. | Con |
| Talbot and Beaudoin21 | A generalized double robust Bayesian model averaging approach to causal effect estimation with application to the study of osteoporotic fractures | 2020 | Proposed a generalized Bayesian causal effect estimation (GBCEE), which outperformed double robust alternatives(including C-TMLE). Also showed “target” A-IPTW is superior than C-TMLE in a nonrealistic setting(only using true confounders). | Con |
| Zivich and Breskin16 | Machine learning for causal inference: on the use of cross-fit estimators | 2020 | A simulation study assessing the performance of G-computation, IPW, AIPW, TMLE, doubly robust cross-fit (DC) AIPW and DC-TMLE. With correctly specified parametric models, all of the estimators performed well. When used with machine learning, the DC estimators outperformed other estimators. | Neutral |
| Ju, et al22 | Scalable collaborative targeted learning for high-dimensional data | 2019 | Results from simulations suggested superior performance of C-TMLE relative to both A-IPTW and noncollaborative (“standard”) TMLE estimators. | Pro |
| Ju, et al23 | On adaptive propensity score truncation in causal inference | 2019 | By adaptively truncating the estimated propensity score with a more targeted objective function, the Positivity-C-TMLE estimator achieves the best performance for both point estimation and confidence interval coverage among all estimators considered. | Pro |
| Bahamyirou, et al24 | Understanding and diagnosing the potential for bias when using machine learning methods with doubly robust causal estimators | 2019 | Simulation results showed superior performance of C-TMLE and TMLE relative to IPTW. | Pro |
| Wei, et al25 | A data-adaptive targeted learning approach of evaluating viscoelastic assay driven trauma treatment protocols | 2019 | C-TMLE outperformed the other doubly robust estimators (IPTW, A-IPTW, stabilized IPTW, TMLE) in the simulation study. | Pro |
| Rudolph, et al.26 | Complier stochastic direct effects: identification and Robust Estimation | 2019 | Showed that the EE and TMLE estimators have advantages over the IPTW estimator in terms of efficiency and reduced reliance on correct parametric model specification. | Pro |
| Pirracchio, et al.18 | Collaborative targeted maximum likelihood estimation for variable importance measure: illustration for functional outcome prediction in mild traumatic brain injuries | 2018 | Showed much more robust performance of C-TMLE relative to TMLE using the same type of realistic parametric bootstrap as used in this paper. This was under severe near-positivity violations. | Pro |
| Luque-Fernandez, et al.27 | Targeted maximum likelihood estimation for a binary treatment: A tutorial | 2018 | Showed relatively superior performance of TMLE when compared with A-IPTW estimator in terms of bias. | Pro |
| Levy, et al28 | A fundamental measure of treatment effect heterogeneity | 2018 | Showed the advantage of CV-TMLE over TMLE in that TMLE was affected by overfitting while CV-TMLE appeared unaffected. | Pro |
| Schuler and Rose29 | Targeted maximum likelihood estimation for causal inference in observational studies | 2017 | Showed superior performance of TMLE relative to misspecified parametric models. | Pro |
| Pang, et al30 | 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 | 2016 | Showed relatively superior performance for the TMLE to IPTW, which showed greater instability when positivity violations occurred. | Pro |
| Schnitzer, et al31 | Variable selection for confounder control, flexible modeling and collaborative targeted minimum loss-based estimation in causal inference | 2016 | Using IPTW with flexible prediction for the propensity score can result in inferior estimation, while TMLE and C-TMLE may benefit from flexible prediction and remain robust to the presence of variables that are highly correlated with treatment. | Pro |
| Zheng, et al32 | Doubly robust and efficient estimation of marginal structural models for the hazard function | 2016 | Showed that the TMLE for marginal structual model (MSM) for a hazard function has relatively superior performance. The bias reduction over a misspecified IPTW or Gcomp estimator is clear in the simulation studies even for a moderate sample size. | Pro |
| Schnitzer, et al33 | Double robust and efficient estimation of a prognostic model for events in the presence of dependent censoring | 2016 | This study demonstrated that even when the analyst is ignorant of the true data generating form, TMLE with super learner can perform about as well as IPTW or TMLE with correct parametric model specification. | Pro |
| Kreif, et al34 | Evaluating treatment effectiveness under model misspecification: A comparison of targeted maximum likelihood estimation with bias-corrected matching | 2014 | Examined the relative performance of TMLE, EE, and matching estimators showing superior performance of TMLE when the outcome regression is misspecified. | Pro |
| Schnitzer, et al35 | Effect of breastfeeding on gastrointestinal infection in infants: A targeted maximum likelihood approach for clustered longitudinal data | 2014 | Compared TMLE with IPTW and G-computation, under the plausible scenario of being given transformed versions of the confounders. Only TMLE with super learner was able to unbiasedly estimate the parameter of interest. | Pro |
| Gruber and van der Laan36 | An application of targeted maximum likelihood estimation to the meta-analysis of safety data | 2013 | Reported superiority of both TMLE and A-IPTW to misspecified parametric models, but the data-generating distributions used resulted in little difference between the semiparametric approaches. | Neutral |
| Lendle, et al37 | Targeted maximum likelihood estimation in safety analysis | 2013 | Showed superior performance of TMLE and C-TMLE relative to A-IPTW estimators in the context of positivity violations. | Pro |
| Díaz and van der Laan38 | Targeted data adaptive estimation of the causal dose response curve | 2013 | Showed relatively superior performance of CV-TMLE relative to CV-A-IPTW estimators, especially in the presence of empirical violations of the positivity assumption. | Pro |
| Schnitzer, et al39 | Targeted maximum likelihood estimation for marginal time-dependent treatment effects under density misspecification | 2013 | In the simulation study, TMLE did not produce a reduction in finite-sample bias or variance for correctly specified densities compared with the G-computation estimator, but it had much better performance than G-computation when the outcome model was misspecified. | Neutral |
| Petersen, et al17 | Diagnosing and responding to violations in the positivity assumption | 2012 | Showed superior performance of TMLE relative to misspecified parametric models, in comparison with A-IPTW, IPTW and G-computation. | Pro |
| van der Laan and Gruber40 | Targeted minimum loss based estimation of causal effects of multiple time point interventions | 2012 | In the setting of multiple time point interventions, showed TMLE outperformed IPTW and MLE estimators. | Pro |
| Porter, et al.41 | The relative performance of targeted maximum likelihood estimators | 2011 | Showed relatively superior performance of C-TMLE relative to A-IPTW estimators particularly when there are covariates that are strongly associated with the missingness, while being weakly or not at all associated with the outcome. | Pro |
| Wang, et al42 | Finding quantitative trait loci genes with collaborative targeted maximum likelihood learning | 2011 | Based on actual genetic data, results suggested greater robustness of findings using C-TMLE relative to parametric approaches for high throughput genetic data. | Pro |
| Díaz and van der Laan43 | Population intervention causal effects based on stochastic interventions | 2011 | Paper focused on new estimators for stochastic (eg, shift) interventions relevant to estimating causal effects of continuous interventions. In their simulation, they did not observe significant differences between the TMLE and the A-IPTW. | Neutral |
| Gruber and van der Laan44 | An application of collaborative targeted maximum likelihood estimation in causal inference and genomics | 2010 | Showed more robust performance in high-dimensional simulations comparing TMLE to estimating equation approaches (A-IPTW). | Pro |
| Stitelman and van der Laan45 | Collaborative Targeted Maximum Likelihood for Time to Event Data | 2010 | The results show that, compared with TMLE, IPTW, and A-IPTW, the C-TMLE method does at least as well as the best estimator under every scenario and, in many of the more realistic scenarios, behaves much better than the next best estimator in terms of both bias and variance. | Pro |
| Moore and van der Laan46 | Covariate adjustment in randomized trials with binary outcomes: targeted maximum likelihood estimation | 2009 | Demonstrated how the use of covariate information in randomized clinical trials could use the TMLE framework, which results in improved performance, without bias, relative to standard methods. | Pro |
| Rose and van der Laan47 | Simple optimal weighting of cases and controls in case-control studies | 2008 | IPTW method for causal parameter estimation was outperformed in conditions similar to a practical setting by the new case-control weighted TMLE methodology. | Pro |
Note: The Pro/Con column refers to a simple binary classification of the relative performance of the TMLE estimators reported in the paper, “Pro” indicating that the TMLE performed superior to other competing estimators.