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Journal articles on the topic 'Targeted Maximum Likelihood Estimation'

Author: Grafiati

Published: 25 January 2025

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1

Pang, Menglan, Tibor Schuster, Kristian B. Filion, Maria Eberg, and Robert W. Platt. "Targeted Maximum Likelihood Estimation for Pharmacoepidemiologic Research." Epidemiology 27, no. 4 (July 2016): 570–77. http://dx.doi.org/10.1097/ede.0000000000000487.

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2

Lendle, Samuel D., Bruce Fireman, and Mark J. van der Laan. "Targeted maximum likelihood estimation in safety analysis." Journal of Clinical Epidemiology 66, no. 8 (August 2013): S91—S98. http://dx.doi.org/10.1016/j.jclinepi.2013.02.017.

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3

Zheng, Wenjing, and Mark J. van der Laan. "Targeted Maximum Likelihood Estimation of Natural Direct Effects." International Journal of Biostatistics 8, no. 1 (January 6, 2012): 1–40. http://dx.doi.org/10.2202/1557-4679.1361.

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4

Dijkhuis, Talko B., and Frank J. Blaauw. "Transfering Targeted Maximum Likelihood Estimation for Causal Inference into Sports Science." Entropy 24, no. 8 (July 31, 2022): 1060. http://dx.doi.org/10.3390/e24081060.

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Although causal inference has shown great value in estimating effect sizes in, for instance, physics, medical studies, and economics, it is rarely used in sports science. Targeted Maximum Likelihood Estimation (TMLE) is a modern method for performing causal inference. TMLE is forgiving in the misspecification of the causal model and improves the estimation of effect sizes using machine-learning methods. We demonstrate the advantage of TMLE in sports science by comparing the calculated effect size with a Generalized Linear Model (GLM). In this study, we introduce TMLE and provide a roadmap for making causal inference and apply the roadmap along with the methods mentioned above in a simulation study and case study investigating the influence of substitutions on the physical performance of the entire soccer team (i.e., the effect size of substitutions on the total physical performance). We construct a causal model, a misspecified causal model, a simulation dataset, and an observed tracking dataset of individual players from 302 elite soccer matches. The simulation dataset results show that TMLE outperforms GLM in estimating the effect size of the substitutions on the total physical performance. Furthermore, TMLE is most robust against model misspecification in both the simulation and the tracking dataset. However, independent of the method used in the tracking dataset, it was found that substitutes increase the physical performance of the entire soccer team.

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Schuler, Megan S., and Sherri Rose. "Targeted Maximum Likelihood Estimation for Causal Inference in Observational Studies." American Journal of Epidemiology 185, no. 1 (December 9, 2016): 65–73. http://dx.doi.org/10.1093/aje/kww165.

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6

Luque-Fernandez, Miguel Angel, Michael Schomaker, Bernard Rachet, and Mireille E. Schnitzer. "Targeted maximum likelihood estimation for a binary treatment: A tutorial." Statistics in Medicine 37, no. 16 (April 23, 2018): 2530–46. http://dx.doi.org/10.1002/sim.7628.

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Cho, Sunyoung, Heejo Koo, Beom Kyung Kim, and Euna Han. "Causal Analyses of Statin to Prevent Liver Disease Progression: A Nationwide Study Using Superlearning Targeted Maximum Likelihood Estimation." Yakhak Hoeji 68, no. 1 (February 28, 2024): 44–55. http://dx.doi.org/10.17480/psk.2024.68.1.44.

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Many studies have shown that statins reduce the risk of progression to liver cirrhosis (LC) and hepatocellular carcinoma (HCC) among at-risk populations. However, causality has not been proved. This study examined whether statins could prevent LC and HCC in patients with progressive and worsening chronic liver disease, using a robust methodology for causality. Between 2002 and 2013, 52,145 patients with chronic liver diseases were identified from the National Health Insurance Service database in South Korea. The inverse probability weighting (IPW) and superlearning targeted maximum likelihood estimation (TMLE) were used to assess the causality of statin use on the risk of LC and HCC, adjusting for sex, age, comorbidities, and co-medications. Multivariable superlearning TMLE revealed that statin use was associated with reduction in the incidence risk of LC (Marginal odds ratio (MOR) 0.59, 95% confidence interval [CI] 0.50-0.65) and HCC (MOR 0.59, 95% CI 0.50-0.67). Such a protective effect was more evident with atorvastatin and lipophilic statin. This population-based observational study indicated the benefit of statin use, particularly atorvastatin and lipophilic statin, for causally reducing the risk of LC and HCC.

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Cai, Weixin, and Mark J. Laan. "One‐step targeted maximum likelihood estimation for time‐to‐event outcomes." Biometrics 76, no. 3 (November 28, 2019): 722–33. http://dx.doi.org/10.1111/biom.13172.

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9

Stitelman, Ori M., C. William Wester, Victor De Gruttola, and Mark J. van der Laan. "Targeted Maximum Likelihood Estimation of Effect Modification Parameters in Survival Analysis." International Journal of Biostatistics 7, no. 1 (January 30, 2011): 1–34. http://dx.doi.org/10.2202/1557-4679.1307.

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10

Grossman, J., M. Ghadessi, A. Contijoch, H. Ostojic, A. Cervantes, J. M. O'Connor, and M. Ducreux. "MSR75 Correlate: Assessing Dose Effect Using Targeted Maximum Likelihood Estimation (TMLE)." Value in Health 26, no. 12 (December 2023): S407. http://dx.doi.org/10.1016/j.jval.2023.09.2134.

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11

Petersen, Maya, Joshua Schwab, Susan Gruber, Nello Blaser, Michael Schomaker, and Mark van der Laan. "Targeted Maximum Likelihood Estimation for Dynamic and Static Longitudinal Marginal Structural Working Models." Journal of Causal Inference 2, no. 2 (September 1, 2014): 147–85. http://dx.doi.org/10.1515/jci-2013-0007.

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AbstractThis paper describes a targeted maximum likelihood estimator (TMLE) for the parameters of longitudinal static and dynamic marginal structural models. We consider a longitudinal data structure consisting of baseline covariates, time-dependent intervention nodes, intermediate time-dependent covariates, and a possibly time-dependent outcome. The intervention nodes at each time point can include a binary treatment as well as a right-censoring indicator. Given a class of dynamic or static interventions, a marginal structural model is used to model the mean of the intervention-specific counterfactual outcome as a function of the intervention, time point, and possibly a subset of baseline covariates. Because the true shape of this function is rarely known, the marginal structural model is used as a working model. The causal quantity of interest is defined as the projection of the true function onto this working model. Iterated conditional expectation double robust estimators for marginal structural model parameters were previously proposed by Robins (2000, 2002) and Bang and Robins (2005). Here we build on this work and present a pooled TMLE for the parameters of marginal structural working models. We compare this pooled estimator to a stratified TMLE (Schnitzer et al. 2014) that is based on estimating the intervention-specific mean separately for each intervention of interest. The performance of the pooled TMLE is compared to the performance of the stratified TMLE and the performance of inverse probability weighted (IPW) estimators using simulations. Concepts are illustrated using an example in which the aim is to estimate the causal effect of delayed switch following immunological failure of first line antiretroviral therapy among HIV-infected patients. Data from the International Epidemiological Databases to Evaluate AIDS, Southern Africa are analyzed to investigate this question using both TML and IPW estimators. Our results demonstrate practical advantages of the pooled TMLE over an IPW estimator for working marginal structural models for survival, as well as cases in which the pooled TMLE is superior to its stratified counterpart.

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12

Moore, K. L., and M. J. van der Laan. "Covariate adjustment in randomized trials with binary outcomes: Targeted maximum likelihood estimation." Statistics in Medicine 28, no. 1 (January 15, 2009): 39–64. http://dx.doi.org/10.1002/sim.3445.

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13

Schomaker, M., M. A. Luque‐Fernandez, V. Leroy, and M. A. Davies. "Using longitudinal targeted maximum likelihood estimation in complex settings with dynamic interventions." Statistics in Medicine 38, no. 24 (August 22, 2019): 4888–911. http://dx.doi.org/10.1002/sim.8340.

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van der Laan, Mark, and Susan Gruber. "One-Step Targeted Minimum Loss-based Estimation Based on Universal Least Favorable One-Dimensional Submodels." International Journal of Biostatistics 12, no. 1 (May 1, 2016): 351–78. http://dx.doi.org/10.1515/ijb-2015-0054.

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AbstractConsider a study in which one observesnindependent and identically distributed random variables whose probability distribution is known to be an element of a particular statistical model, and one is concerned with estimation of a particular real valued pathwise differentiable target parameter of this data probability distribution. The targeted maximum likelihood estimator (TMLE) is an asymptotically efficient substitution estimator obtained by constructing a so called least favorable parametric submodel through an initial estimator with score, at zero fluctuation of the initial estimator, that spans the efficient influence curve, and iteratively maximizing the corresponding parametric likelihood till no more updates occur, at which point the updated initial estimator solves the so called efficient influence curve equation. In this article we construct a one-dimensional universal least favorable submodel for which the TMLE only takes one step, and thereby requires minimal extra data fitting to achieve its goal of solving the efficient influence curve equation. We generalize these to universal least favorable submodels through the relevant part of the data distribution as required for targeted minimum loss-based estimation. Finally, remarkably, given a multidimensional target parameter, we develop a universal canonical one-dimensional submodel such that the one-step TMLE, only maximizing the log-likelihood over a univariate parameter, solves the multivariate efficient influence curve equation. This allows us to construct a one-step TMLE based on a one-dimensional parametric submodel through the initial estimator, that solves any multivariate desired set of estimating equations.

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Baumann, Philipp F. M., Michael Schomaker, and Enzo Rossi. "Estimating the effect of central bank independence on inflation using longitudinal targeted maximum likelihood estimation." Journal of Causal Inference 9, no. 1 (January 1, 2021): 109–46. http://dx.doi.org/10.1515/jci-2020-0016.

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Abstract The notion that an independent central bank reduces a country’s inflation is a controversial hypothesis. To date, it has not been possible to satisfactorily answer this question because the complex macroeconomic structure that gives rise to the data has not been adequately incorporated into statistical analyses. We develop a causal model that summarizes the economic process of inflation. Based on this causal model and recent data, we discuss and identify the assumptions under which the effect of central bank independence on inflation can be identified and estimated. Given these and alternative assumptions, we estimate this effect using modern doubly robust effect estimators, i.e., longitudinal targeted maximum likelihood estimators. The estimation procedure incorporates machine learning algorithms and is tailored to address the challenges associated with complex longitudinal macroeconomic data. We do not find strong support for the hypothesis that having an independent central bank for a long period of time necessarily lowers inflation. Simulation studies evaluate the sensitivity of the proposed methods in complex settings when certain assumptions are violated and highlight the importance of working with appropriate learning algorithms for estimation.

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16

Schnitzer, Mireille E., Erica E. M. Moodie, and Robert W. Platt. "Targeted maximum likelihood estimation for marginal time-dependent treatment effects under density misspecification." Biostatistics 14, no. 1 (July 12, 2012): 1–14. http://dx.doi.org/10.1093/biostatistics/kxs024.

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17

Hu, Liangyuan, Chenyang Gu, Michael Lopez, Jiayi Ji, and Juan Wisnivesky. "Estimation of causal effects of multiple treatments in observational studies with a binary outcome." Statistical Methods in Medical Research 29, no. 11 (May 25, 2020): 3218–34. http://dx.doi.org/10.1177/0962280220921909.

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There is a dearth of robust methods to estimate the causal effects of multiple treatments when the outcome is binary. This paper uses two unique sets of simulations to propose and evaluate the use of Bayesian additive regression trees in such settings. First, we compare Bayesian additive regression trees to several approaches that have been proposed for continuous outcomes, including inverse probability of treatment weighting, targeted maximum likelihood estimator, vector matching, and regression adjustment. Results suggest that under conditions of non-linearity and non-additivity of both the treatment assignment and outcome generating mechanisms, Bayesian additive regression trees, targeted maximum likelihood estimator, and inverse probability of treatment weighting using generalized boosted models provide better bias reduction and smaller root mean squared error. Bayesian additive regression trees and targeted maximum likelihood estimator provide more consistent 95% confidence interval coverage and better large-sample convergence property. Second, we supply Bayesian additive regression trees with a strategy to identify a common support region for retaining inferential units and for avoiding extrapolating over areas of the covariate space where common support does not exist. Bayesian additive regression trees retain more inferential units than the generalized propensity score-based strategy, and shows lower bias, compared to targeted maximum likelihood estimator or generalized boosted model, in a variety of scenarios differing by the degree of covariate overlap. A case study examining the effects of three surgical approaches for non-small cell lung cancer demonstrates the methods.

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18

Decker, Anna L., Alan Hubbard, Catherine M. Crespi, Edmund Y. W. Seto, and May C. Wang. "Semiparametric Estimation of the Impacts of Longitudinal Interventions on Adolescent Obesity using Targeted Maximum-Likelihood: Accessible Estimation with the ltmle Package." Journal of Causal Inference 2, no. 1 (March 1, 2014): 95–108. http://dx.doi.org/10.1515/jci-2013-0025.

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AbstractWhile child and adolescent obesity is a serious public health concern, few studies have utilized parameters based on the causal inference literature to examine the potential impacts of early intervention. The purpose of this analysis was to estimate the causal effects of early interventions to improve physical activity and diet during adolescence on body mass index (BMI), a measure of adiposity, using improved techniques. The most widespread statistical method in studies of child and adolescent obesity is multivariable regression, with the parameter of interest being the coefficient on the variable of interest. This approach does not appropriately adjust for time-dependent confounding, and the modeling assumptions may not always be met. An alternative parameter to estimate is one motivated by the causal inference literature, which can be interpreted as the mean change in the outcome under interventions to set the exposure of interest. The underlying data-generating distribution, upon which the estimator is based, can be estimated via a parametric or semi-parametric approach. Using data from the National Heart, Lung, and Blood Institute Growth and Health Study, a 10-year prospective cohort study of adolescent girls, we estimated the longitudinal impact of physical activity and diet interventions on 10-year BMI z-scores via a parameter motivated by the causal inference literature, using both parametric and semi-parametric estimation approaches. The parameters of interest were estimated with a recently released R package, ltmle, for estimating means based upon general longitudinal treatment regimes. We found that early, sustained intervention on total calories had a greater impact than a physical activity intervention or non-sustained interventions. Multivariable linear regression yielded inflated effect estimates compared to estimates based on targeted maximum-likelihood estimation and data-adaptive super learning. Our analysis demonstrates that sophisticated, optimal semiparametric estimation of longitudinal treatment-specific means via ltmle provides an incredibly powerful, yet easy-to-use tool, removing impediments for putting theory into practice.

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19

Gruber, Susan, and Mark J. van der Laan. "An Application of Targeted Maximum Likelihood Estimation to the Meta-Analysis of Safety Data." Biometrics 69, no. 1 (February 4, 2013): 254–62. http://dx.doi.org/10.1111/j.1541-0420.2012.01829.x.

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20

Lim, Sungwoo, Marisol Tellez, and Amid I. Ismail. "Estimating a Dynamic Effect of Soda Intake on Pediatric Dental Caries Using Targeted Maximum Likelihood Estimation Method." Caries Research 53, no. 5 (2019): 532–40. http://dx.doi.org/10.1159/000497359.

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An effect of soda intake on dental caries in young children (birth to 5 years) may vary over time. Estimating a dynamic effect may be challenging due to time-varying confounding and loss to follow-up. The purpose of this paper is to demonstrate utility of targeted maximum likelihood estimation (TMLE) method in addressing longitudinal data analysis challenges and estimating a dynamic effect of soda intake on pediatric caries. Data came from the Detroit Dental Health Project, a 4-year cohort study of low-income African-American children and caregivers. The sample included 995 child–caregiver pairs who participated in 2002–03 (W1) and were followed up in 2004–05 (W2) and 2007 (W3). The outcome was counts of caries surfaces at W3, and the exposure was child’s soda intake at W1 and W2. Time-varying covariates included caregiver’s smoking status, oral health fatalism, and social support. Forty-three percent of children consistently consumed soda at W1 and W2, whereas 21% were nonconsumers throughout 2 surveys. The remaining 35% switched intake status between W1 and W2. Association between soda intake patterns and caries was tested using TMLE. Children with a consistent soda intake had 1.03 more caries lesions at W3 than those with consistently no soda intake (95% CI 0.09–1.97) on average. If soda was consumed only at W1 or W2, an estimated effect of soda on caries development at W3 was no longer statistically significant. In conclusion, consistent soda intake during the early childhood led to one additional caries tooth surface. The study highlights utility of TMLE in pediatric caries research as it can handle modeling challenges associated with longitudinal data.

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van der Laan, Mark J. "Causal Inference for a Population of Causally Connected Units." Journal of Causal Inference 2, no. 1 (March 1, 2014): 13–74. http://dx.doi.org/10.1515/jci-2013-0002.

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AbstractSuppose that we observe a population of causally connected units. On each unit at each time-point on a grid we observe a set of other units the unit is potentially connected with, and a unit-specific longitudinal data structure consisting of baseline and time-dependent covariates, a time-dependent treatment, and a final outcome of interest. The target quantity of interest is defined as the mean outcome for this group of units if the exposures of the units would be probabilistically assigned according to a known specified mechanism, where the latter is called a stochastic intervention. Causal effects of interest are defined as contrasts of the mean of the unit-specific outcomes under different stochastic interventions one wishes to evaluate. This covers a large range of estimation problems from independent units, independent clusters of units, and a single cluster of units in which each unit has a limited number of connections to other units. The allowed dependence includes treatment allocation in response to data on multiple units and so called causal interference as special cases. We present a few motivating classes of examples, propose a structural causal model, define the desired causal quantities, address the identification of these quantities from the observed data, and define maximum likelihood based estimators based on cross-validation. In particular, we present maximum likelihood based super-learning for this network data. Nonetheless, such smoothed/regularized maximum likelihood estimators are not targeted and will thereby be overly bias w.r.t. the target parameter, and, as a consequence, generally not result in asymptotically normally distributed estimators of the statistical target parameter.To formally develop estimation theory, we focus on the simpler case in which the longitudinal data structure is a point-treatment data structure. We formulate a novel targeted maximum likelihood estimator of this estimand and show that the double robustness of the efficient influence curve implies that the bias of the targeted minimum loss-based estimation (TMLE) will be a second-order term involving squared differences of two nuisance parameters. In particular, the TMLE will be consistent if either one of these nuisance parameters is consistently estimated. Due to the causal dependencies between units, the data set may correspond with the realization of a single experiment, so that establishing a (e.g. normal) limit distribution for the targeted maximum likelihood estimators, and corresponding statistical inference, is a challenging topic. We prove two formal theorems establishing the asymptotic normality using advances in weak-convergence theory. We conclude with a discussion and refer to an accompanying technical report for extensions to general longitudinal data structures.

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22

Gianfrancesco, M. A., L. Balzer, K. E. Taylor, L. Trupin, J. Nititham, M. F. Seldin, A. W. Singer, L. A. Criswell, and L. F. Barcellos. "Genetic risk and longitudinal disease activity in systemic lupus erythematosus using targeted maximum likelihood estimation." Genes & Immunity 17, no. 6 (July 28, 2016): 358–62. http://dx.doi.org/10.1038/gene.2016.33.

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23

Pirracchio, Romain, John K. Yue, Geoffrey T. Manley, Mark J. van der Laan, and Alan E. Hubbard. "Collaborative targeted maximum likelihood estimation for variable importance measure: Illustration for functional outcome prediction in mild traumatic brain injuries." Statistical Methods in Medical Research 27, no. 1 (June 29, 2016): 286–97. http://dx.doi.org/10.1177/0962280215627335.

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Standard statistical practice used for determining the relative importance of competing causes of disease typically relies on ad hoc methods, often byproducts of machine learning procedures (stepwise regression, random forest, etc.). Causal inference framework and data-adaptive methods may help to tailor parameters to match the clinical question and free one from arbitrary modeling assumptions. Our focus is on implementations of such semiparametric methods for a variable importance measure (VIM). We propose a fully automated procedure for VIM based on collaborative targeted maximum likelihood estimation (cTMLE), a method that optimizes the estimate of an association in the presence of potentially numerous competing causes. We applied the approach to data collected from traumatic brain injury patients, specifically a prospective, observational study including three US Level-1 trauma centers. The primary outcome was a disability score (Glasgow Outcome Scale - Extended (GOSE)) collected three months post-injury. We identified clinically important predictors among a set of risk factors using a variable importance analysis based on targeted maximum likelihood estimators (TMLE) and on cTMLE. Via a parametric bootstrap, we demonstrate that the latter procedure has the potential for robust automated estimation of variable importance measures based upon machine-learning algorithms. The cTMLE estimator was associated with substantially less positivity bias as compared to TMLE and larger coverage of the 95% CI. This study confirms the power of an automated cTMLE procedure that can target model selection via machine learning to estimate VIMs in complicated, high-dimensional data.

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Bembom, Oliver, Maya L. Petersen, Soo-Yon Rhee, W. Jeffrey Fessel, Sandra E. Sinisi, Robert W. Shafer, and Mark J. van der Laan. "Biomarker discovery using targeted maximum-likelihood estimation: Application to the treatment of antiretroviral-resistant HIV infection." Statistics in Medicine 28, no. 1 (September 29, 2008): 152–72. http://dx.doi.org/10.1002/sim.3414.

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Ju, Cheng, Joshua Schwab, and Mark J. van der Laan. "On adaptive propensity score truncation in causal inference." Statistical Methods in Medical Research 28, no. 6 (July 11, 2018): 1741–60. http://dx.doi.org/10.1177/0962280218774817.

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The positivity assumption, or the experimental treatment assignment (ETA) assumption, is important for identifiability in causal inference. Even if the positivity assumption holds, practical violations of this assumption may jeopardize the finite sample performance of the causal estimator. One of the consequences of practical violations of the positivity assumption is extreme values in the estimated propensity score (PS). A common practice to address this issue is truncating the PS estimate when constructing PS-based estimators. In this study, we propose a novel adaptive truncation method, Positivity-C-TMLE, based on the collaborative targeted maximum likelihood estimation (C-TMLE) methodology. We demonstrate the outstanding performance of our novel approach in a variety of simulations by comparing it with other commonly studied estimators. Results show that by adaptively truncating the estimated PS 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.

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McCoy, David, Alan Hubbard, and Mark Van der Laan. "CVtreeMLE: Efficient Estimation of Mixed Exposures using Data Adaptive Decision Trees and Cross-Validated Targeted Maximum Likelihood Estimation in R." Journal of Open Source Software 8, no. 82 (February 21, 2023): 4181. http://dx.doi.org/10.21105/joss.04181.

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Kreif, Noémi, Susan Gruber, Rosalba Radice, Richard Grieve, and Jasjeet S. Sekhon. "Evaluating treatment effectiveness under model misspecification: A comparison of targeted maximum likelihood estimation with bias-corrected matching." Statistical Methods in Medical Research 25, no. 5 (September 30, 2016): 2315–36. http://dx.doi.org/10.1177/0962280214521341.

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Zheng, Wenjing, Maya Petersen, and Mark J. van der Laan. "Doubly Robust and Efficient Estimation of Marginal Structural Models for the Hazard Function." International Journal of Biostatistics 12, no. 1 (May 1, 2016): 233–52. http://dx.doi.org/10.1515/ijb-2015-0036.

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Abstract In social and health sciences, many research questions involve understanding the causal effect of a longitudinal treatment on mortality (or time-to-event outcomes in general). Often, treatment status may change in response to past covariates that are risk factors for mortality, and in turn, treatment status may also affect such subsequent covariates. In these situations, Marginal Structural Models (MSMs), introduced by Robins (1997. Marginal structural models Proceedings of the American Statistical Association. Section on Bayesian Statistical Science, 1–10), are well-established and widely used tools to account for time-varying confounding. In particular, a MSM can be used to specify the intervention-specific counterfactual hazard function, i. e. the hazard for the outcome of a subject in an ideal experiment where he/she was assigned to follow a given intervention on their treatment variables. The parameters of this hazard MSM are traditionally estimated using the Inverse Probability Weighted estimation Robins (1999. Marginal structural models versus structural nested models as tools for causal inference. In: Statistical models in epidemiology: the environment and clinical trials. Springer-Verlag, 1999:95–134), Robins et al. (2000), (IPTW, van der Laan and Petersen (2007. Causal effect models for realistic individualized treatment and intention to treat rules. Int J Biostat 2007;3:Article 3), Robins et al. (2008. Estimaton and extrapolation of optimal treatment and testing strategies. Statistics in Medicine 2008;27(23):4678–721)). This estimator is easy to implement and admits Wald-type confidence intervals. However, its consistency hinges on the correct specification of the treatment allocation probabilities, and the estimates are generally sensitive to large treatment weights (especially in the presence of strong confounding), which are difficult to stabilize for dynamic treatment regimes. In this paper, we present a pooled targeted maximum likelihood estimator (TMLE, van der Laan and Rubin (2006. Targeted maximum likelihood learning. The International Journal of Biostatistics 2006;2:1–40)) for MSM for the hazard function under longitudinal dynamic treatment regimes. The proposed estimator is semiparametric efficient and doubly robust, offering bias reduction over the incumbent IPTW estimator when treatment probabilities may be misspecified. Moreover, the substitution principle rooted in the TMLE potentially mitigates the sensitivity to large treatment weights in IPTW. We compare the performance of the proposed estimator with the IPTW and a on-targeted substitution estimator in a simulation study.

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Balzer, Laura B., Wenjing Zheng, Mark J. van der Laan, and Maya L. Petersen. "A new approach to hierarchical data analysis: Targeted maximum likelihood estimation for the causal effect of a cluster-level exposure." Statistical Methods in Medical Research 28, no. 6 (June 19, 2018): 1761–80. http://dx.doi.org/10.1177/0962280218774936.

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We often seek to estimate the impact of an exposure naturally occurring or randomly assigned at the cluster-level. For example, the literature on neighborhood determinants of health continues to grow. Likewise, community randomized trials are applied to learn about real-world implementation, sustainability, and population effects of interventions with proven individual-level efficacy. In these settings, individual-level outcomes are correlated due to shared cluster-level factors, including the exposure, as well as social or biological interactions between individuals. To flexibly and efficiently estimate the effect of a cluster-level exposure, we present two targeted maximum likelihood estimators (TMLEs). The first TMLE is developed under a non-parametric causal model, which allows for arbitrary interactions between individuals within a cluster. These interactions include direct transmission of the outcome (i.e. contagion) and influence of one individual’s covariates on another’s outcome (i.e. covariate interference). The second TMLE is developed under a causal sub-model assuming the cluster-level and individual-specific covariates are sufficient to control for confounding. Simulations compare the alternative estimators and illustrate the potential gains from pairing individual-level risk factors and outcomes during estimation, while avoiding unwarranted assumptions. Our results suggest that estimation under the sub-model can result in bias and misleading inference in an observational setting. Incorporating working assumptions during estimation is more robust than assuming they hold in the underlying causal model. We illustrate our approach with an application to HIV prevention and treatment.

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Kreif, Noémi, Linh Tran, Richard Grieve, Bianca De Stavola, Robert C. Tasker, and Maya Petersen. "Estimating the Comparative Effectiveness of Feeding Interventions in the Pediatric Intensive Care Unit: A Demonstration of Longitudinal Targeted Maximum Likelihood Estimation." American Journal of Epidemiology 186, no. 12 (June 24, 2017): 1370–79. http://dx.doi.org/10.1093/aje/kwx213.

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31

Rodríguez-Molina, Daloha, Swaantje Barth, Ronald Herrera, Constanze Rossmann, Katja Radon, and Veronika Karnowski. "An educational intervention to improve knowledge about prevention against occupational asthma and allergies using targeted maximum likelihood estimation." International Archives of Occupational and Environmental Health 92, no. 5 (January 14, 2019): 629–38. http://dx.doi.org/10.1007/s00420-018-1397-1.

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32

Brooks, Jordan C., Mark J. van der Laan, Daniel E. Singer, and Alan S. Go. "Targeted Minimum Loss-Based Estimation of Causal Effects in Right-Censored Survival Data with Time-Dependent Covariates: Warfarin, Stroke, and Death in Atrial Fibrillation." Journal of Causal Inference 1, no. 2 (November 29, 2013): 235–54. http://dx.doi.org/10.1515/jci-2013-0001.

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AbstractCausal effects in right-censored survival data can be formally defined as the difference in the marginal cumulative event probabilities under particular interventions. Conventional estimators, such as the Kaplan-Meier (KM), fail to consistently estimate these marginal parameters under dependent treatment assignment or dependent censoring. Several modern estimators have been developed that reduce bias under both dependent treatment assignment and dependent censoring by incorporating information from baseline and time-dependent covariates. In the present article we describe a recently developed targeted minimum loss-based estimation (TMLE) algorithm for general longitudinal data structures and present in detail its application in right-censored survival data with time-dependent covariates. The treatment-specific marginal cumulative event probability is defined via a series of iterated conditional expectations in a time-dependent counting process framework. The TMLE involves an initial estimator of each conditional expectation and sequentially updates these such that the resulting estimator solves the efficient influence curve estimating equation in the nonparametric statistical model. We describe the assumptions required for consistent estimation of statistical parameters and additional assumptions required for consistent estimation of the causal effect parameter. Using simulated right-censored survival data, the mean squared error, bias, and 95% confidence interval coverage probability of the TMLE is compared with those of the conventional KM and the inverse probability of censoring weight estimating equation, conventional maximum likelihood substitution estimator, and the double robustaugmented inverse probability of censoring weighted estimating equation. We conclude the article with estimation of the causal effect of warfarin medical therapy on the probability of “stroke or death” within a 1-year time frame using data from the ATRIA-1 observational cohort of persons with atrial fibrillation. Our results suggest that a fixed policy of warfarin treatment for all patients would result in 2% fewer deaths or strokes within 1-year as compared with a policy of withholding warfarin from all patients.

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Ehrlich, Samantha F., Romain S. Neugebauer, Juanran Feng, Monique M. Hedderson, and Assiamira Ferrara. "Exercise During the First Trimester and Infant Size at Birth: Targeted Maximum Likelihood Estimation of the Causal Risk Difference." American Journal of Epidemiology 189, no. 2 (October 2, 2019): 133–45. http://dx.doi.org/10.1093/aje/kwz213.

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Abstract This cohort study sought to estimate the differences in risk of delivering infants who were small or large for gestational age (SGA or LGA, respectively) according to exercise during the first trimester of pregnancy (vs. no exercise) among 2,286 women receiving care at Kaiser Permanente Northern California in 2013–2017. Exercise was assessed by questionnaire. SGA and LGA were determined by the sex- and gestational-age-specific birthweight distributions of the 2017 US Natality file. Risk differences were estimated by targeted maximum likelihood estimation, with and without data-adaptive prediction (machine learning). Analyses were also stratified by prepregnancy weight status. Overall, exercise at the cohort-specific 75th percentile was associated with an increased risk of SGA of 4.5 (95% CI: 2.1, 6.8) per 100 births, and decreased risk of LGA of 2.8 (95% CI: 0.5, 5.1) per 100 births; similar findings were observed among the underweight and normal-weight women, but no associations were found among those with overweight or obesity. Meeting Physical Activity Guidelines was associated with increased risk of SGA and decreased risk of LGA but only among underweight and normal-weight women. Any vigorous exercise reduced the risk of LGA in underweight and normal-weight women only and was not associated with SGA risk.

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Ekwaru, J. P., S. McMullen, T. Cowling, M. Bhutani, and M. van der Laan. "PT41 Benefits of Inhaled Corticosteroids (ICS) in COPD Maintenance Combinations: Real-World Evidence Using Longitudinal Targeted Maximum Likelihood Estimation." Value in Health 27, no. 12 (December 2024): S486. https://doi.org/10.1016/j.jval.2024.10.3840.

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Zakhidov, Dilshodbek, Zulfiya Sagdillayeva, and Ali R. A. Moursy. "Dividing Social Networks into Two Communities Using the Maximum Likelihood Method: Application to ESG." E3S Web of Conferences 574 (2024): 03007. http://dx.doi.org/10.1051/e3sconf/202457403007.

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This article explores the application of the Maximum Likelihood Estimation method (MLE) for community detection in environmental, social, and governance (ESG) networks. ESG factors are important in assessing the sustainability and ethical impact of investments. By understanding the structure of social networks that discuss and promote ESG practices, we can gain important insights. It proposes a probabilistic framework for identifying community structures by dividing the network into two distinct groups based on connectivity patterns using the MLE method. The network structure is analyzed, and the method identifies groups of united organizations such as companies, investors, and NGOs with similar ESG orientations and interaction patterns. The results reveal important insights into how ESG information flows within and between these communities, highlighting key influencers and central nodes whose connections play a key role in the diffusion of ESG practices. These conclusions can be important in developing targeted communication strategies, identifying potential opportunities for cooperation, and forming informed investment decisions. By providing a solid framework for analyzing ESG networks, this paper is relevant to a broader understanding of ESG dynamics and supports the development of a more sustainable and interconnected global ecosystem.

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Fayomi, Aisha, and Hamdah Al-Shammari. "Estimating the Parameters of the Exponential-Geometric distribution based on progressively type-II censored data." International Journal of Advanced Statistics and Probability 6, no. 1 (April 5, 2018): 37. http://dx.doi.org/10.14419/ijasp.v6i1.10450.

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This paper deals with the problem of parameters estimation of the Exponential-Geometric (EG) distribution based on progressive type-II censored data. It turns out that the maximum likelihood estimators for the distribution parameters have no closed forms, therefore the EM algorithm are alternatively used. The asymptotic variance of the MLEs of the targeted parameters under progressive type-II censoring is computed along with the asymptotic confidence intervals. Finally, a simple numerical example is given to illustrate the obtained results.

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Siddique, Arman Alam, Mireille E. Schnitzer, Asma Bahamyirou, Guanbo Wang, Timothy H. Holtz, Giovanni B. Migliori, Giovanni Sotgiu, et al. "Causal inference with multiple concurrent medications: A comparison of methods and an application in multidrug-resistant tuberculosis." Statistical Methods in Medical Research 28, no. 12 (October 31, 2018): 3534–49. http://dx.doi.org/10.1177/0962280218808817.

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This paper investigates different approaches for causal estimation under multiple concurrent medications. Our parameter of interest is the marginal mean counterfactual outcome under different combinations of medications. We explore parametric and non-parametric methods to estimate the generalized propensity score. We then apply three causal estimation approaches (inverse probability of treatment weighting, propensity score adjustment, and targeted maximum likelihood estimation) to estimate the causal parameter of interest. Focusing on the estimation of the expected outcome under the most prevalent regimens, we compare the results obtained using these methods in a simulation study with four potentially concurrent medications. We perform a second simulation study in which some combinations of medications may occur rarely or not occur at all in the dataset. Finally, we apply the methods explored to contrast the probability of patient treatment success for the most prevalent regimens of antimicrobial agents for patients with multidrug-resistant pulmonary tuberculosis.

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Herrera, Ronald, Ursula Berger, Ondine von Ehrenstein, Iván Díaz, Stella Huber, Daniel Moraga Muñoz, and Katja Radon. "Estimating the Causal Impact of Proximity to Gold and Copper Mines on Respiratory Diseases in Chilean Children: An Application of Targeted Maximum Likelihood Estimation." International Journal of Environmental Research and Public Health 15, no. 1 (December 27, 2017): 39. http://dx.doi.org/10.3390/ijerph15010039.

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Brown, Daniel, Maya Petersen, Mark van der Laan, Sadie Costello, Elizabeth Noth, Katherine Hammond, Mark Cullen, and Ellen Eisen. "0124 PM2.5 and Heart Disease in a Cohort of Aluminium Workers: An Application of Longitudinal Targeted Maximum Likelihood-based Estimation (TMLE)." Occupational and Environmental Medicine 71, Suppl 1 (June 2014): A14.2—A14. http://dx.doi.org/10.1136/oemed-2014-102362.44.

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Elduma, Adel Hussein, Kourosh Holakouie-Naieni, Amir Almasi-Hashiani, Abbas Rahimi Foroushani, Hamdan Mustafa Hamdan Ali, Muatsim Ahmed Mohammed Adam, Asma Elsony, and Mohammad Ali Mansournia. "The Targeted Maximum Likelihood estimation to estimate the causal effects of the previous tuberculosis treatment in Multidrug-resistant tuberculosis in Sudan." PLOS ONE 18, no. 1 (January 17, 2023): e0279976. http://dx.doi.org/10.1371/journal.pone.0279976.

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Introduction This study used Targeted Maximum Likelihood Estimation (TMLE) as a double robust method to estimate the causal effect of previous tuberculosis treatment history on the occurrence of multidrug-resistant tuberculosis (MDR-TB). TMLE is a method to estimate the marginal statistical parameters in case-control study design. The aim of this study was to estimate the causal effect of the previous tuberculosis treatment on the occurrence of MDR-TB using TMLE in Sudan. Method A case-control study design combined with TMLE was used to estimate parameters. Cases were MDR-TB patients and controls were and patients who cured from tuberculosis. The history of previous TB treatment was considered the main exposure, and MDR-TB as an outcome. A designed questionnaire was used to collect a set of covariates including age, time to reach a health facility, number of times stopping treatment, gender, education level, and contact with MDR-TB cases. TMLE method was used to estimate the causal association of parameters. Statistical analysis was carried out with ltmle package in R-software. Result presented in graph and tables. Results A total number of 430 cases and 860 controls were included in this study. The estimated risk difference of the previous tuberculosis treatment was (0.189, 95% CI; 0.161, 0.218) with SE 0.014, and p-value (<0.001). In addition, the estimated risk ratio was (16.1, 95% CI; 12.932, 20.001) with SE = 0.014 and p-value (<0.001). Conclusion Our findings indicated that previous tuberculosis treatment history was determine as a risk factor for MDR-TB in Sudan. Also, TMLE method can be used to estimate the risk difference and the risk ratio in a case-control study design.

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Rudolph, Kara E., Dana E. Goin, and Elizabeth A. Stuart. "The Peril of Power: A Tutorial on Using Simulation to Better Understand When and How We Can Estimate Mediating Effects." American Journal of Epidemiology 189, no. 12 (May 16, 2020): 1559–67. http://dx.doi.org/10.1093/aje/kwaa083.

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Abstract Mediation analyses are valuable for examining mechanisms underlying an association, investigating possible explanations for nonintuitive results, or identifying interventions that can improve health in the context of nonmanipulable exposures. However, designing a study for the purpose of answering a mediation-related research question remains challenging because sample size and power calculations for mediation analyses are typically not conducted or are crude approximations. Consequently, many studies are probably conducted without first establishing that they have the statistical power required to detect a meaningful effect, potentially resulting in wasted resources. In an effort to advance more accurate power calculations for estimating direct and indirect effects, we present a tutorial demonstrating how to conduct a flexible, simulation-based power analysis. In this tutorial, we compare power to estimate direct and indirect effects across various estimators (the Baron and Kenny estimator (J Pers Soc Psychol. 1986;51(6):1173–1182), inverse odds ratio weighting, and targeted maximum likelihood estimation) using various data structures designed to mimic important features of real data. We include step-by-step commented R code (R Foundation for Statistical Computing, Vienna, Austria) in an effort to lower implementation barriers to ultimately improving power assessment in mediation studies.

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Ahmed, Syed Ejaz, Reza Arabi Belaghi, Abdulkadir Hussein, and Alireza Safariyan. "New and Efficient Estimators of Reliability Characteristics for a Family of Lifetime Distributions under Progressive Censoring." Mathematics 12, no. 10 (May 20, 2024): 1599. http://dx.doi.org/10.3390/math12101599.

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Estimation of reliability and stress–strength parameters is important in the manufacturing industry. In this paper, we develop shrinkage-type estimators for the reliability and stress–strength parameters based on progressively censored data from a rich class of distributions. These new estimators improve the performance of the commonly used Maximum Likelihood Estimators (MLEs) by reducing their mean squared errors. We provide analytical asymptotic and bootstrap confidence intervals for the targeted parameters. Through a detailed simulation study, we demonstrate that the new estimators have better performance than the MLEs. Finally, we illustrate the application of the new methods to two industrial data sets, showcasing their practical relevance and effectiveness.

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Elduma, Adel Hussein, Kourosh Holakouie-Naieni, Amir Almasi-Hashiani, Abbas Rahimi Foroushani, Hamdan Mustafa Hamdan Ali, Muatsim Ahmed Mohammed Adam, Asma Elsony, and Mohammad Ali Mansournia. "Correction: The Targeted Maximum Likelihood estimation to estimate the causal effects of the previous tuberculosis treatment in Multidrug-resistant tuberculosis in Sudan." PLOS ONE 19, no. 12 (December 2, 2024): e0314954. https://doi.org/10.1371/journal.pone.0314954.

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Uchoa, Frederico. "An assessment about the relationship between educational inequality and economic growth in Brazilian Northeast region." Reflexões Econômicas 5, no. 1 (July 6, 2020): 1–12. http://dx.doi.org/10.36113/rec.v5i1.2760.

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In this paper we analyze the impact of education inequality on the income of formal workers in Northeast Brazil. For this study, we analyzed the data collected from censuses data and estimate a dynamic panel data model. Statistical analyses were performed by using the quasi-maximum likelihood linear dynamic panel data estimation, an approach that produce consistent estimates with large n and small T. We found a negative and statistically significant impact of education inequality on economic growth, which is convergent with the literature that advocates that an unequal distribution of education reduces growth. Our results suggest that economic policies should be targeted not only more at education but also more equal access to education.

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Zhang, D., Y. Zhang, SW Ahn, S. Gruber, van der Laan M, R. Iyer, S. Reshef, and MY Tian. "MSR48 Utilization of High-Dimensional Propensity Score and Targeted Maximum Likelihood Estimation with Machine Learning to Improve Causal Effect Estimation in Patients with Nonvalvular Atrial Fibrillation and Hypertension." Value in Health 27, no. 6 (June 2024): S268. http://dx.doi.org/10.1016/j.jval.2024.03.1481.

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Balzer, Laura, Patrick Staples, Jukka-Pekka Onnela, and Victor DeGruttola. "Using a network-based approach and targeted maximum likelihood estimation to evaluate the effect of adding pre-exposure prophylaxis to an ongoing test-and-treat trial." Clinical Trials 14, no. 2 (January 26, 2017): 201–10. http://dx.doi.org/10.1177/1740774516679666.

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Background: Several cluster-randomized trials are underway to investigate the implementation and effectiveness of a universal test-and-treat strategy on the HIV epidemic in sub-Saharan Africa. We consider nesting studies of pre-exposure prophylaxis within these trials. Pre-exposure prophylaxis is a general strategy where high-risk HIV– persons take antiretrovirals daily to reduce their risk of infection from exposure to HIV. We address how to target pre-exposure prophylaxis to high-risk groups and how to maximize power to detect the individual and combined effects of universal test-and-treat and pre-exposure prophylaxis strategies. Methods: We simulated 1000 trials, each consisting of 32 villages with 200 individuals per village. At baseline, we randomized the universal test-and-treat strategy. Then, after 3 years of follow-up, we considered four strategies for targeting pre-exposure prophylaxis: (1) all HIV– individuals who self-identify as high risk, (2) all HIV– individuals who are identified by their HIV+ partner (serodiscordant couples), (3) highly connected HIV– individuals, and (4) the HIV– contacts of a newly diagnosed HIV+ individual (a ring-based strategy). We explored two possible trial designs, and all villages were followed for a total of 7 years. For each village in a trial, we used a stochastic block model to generate bipartite (male–female) networks and simulated an agent-based epidemic process on these networks. We estimated the individual and combined intervention effects with a novel targeted maximum likelihood estimator, which used cross-validation to data-adaptively select from a pre-specified library the candidate estimator that maximized the efficiency of the analysis. Results: The universal test-and-treat strategy reduced the 3-year cumulative HIV incidence by 4.0% on average. The impact of each pre-exposure prophylaxis strategy on the 4-year cumulative HIV incidence varied by the coverage of the universal test-and-treat strategy with lower coverage resulting in a larger impact of pre-exposure prophylaxis. Offering pre-exposure prophylaxis to serodiscordant couples resulted in the largest reductions in HIV incidence (2% reduction), and the ring-based strategy had little impact (0% reduction). The joint effect was larger than either individual effect with reductions in the 7-year incidence ranging from 4.5% to 8.8%. Targeted maximum likelihood estimation, data-adaptively adjusting for baseline covariates, substantially improved power over the unadjusted analysis, while maintaining nominal confidence interval coverage. Conclusion: Our simulation study suggests that nesting a pre-exposure prophylaxis study within an ongoing trial can lead to combined intervention effects greater than those of universal test-and-treat alone and can provide information about the efficacy of pre-exposure prophylaxis in the presence of high coverage of treatment for HIV+ persons.

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Mozafar Saadati, Hossein, Yadollah Mehrabi, Siamak Sabour, Mohammad Ali Mansournia, and Seyed Saeed Hashemi Nazari. "Estimating the effects of body mass index and central obesity on stroke in diabetics and non‐diabetics using targeted maximum likelihood estimation: Atherosclerosis Risk in Communities study." Obesity Science & Practice 6, no. 6 (August 18, 2020): 628–37. http://dx.doi.org/10.1002/osp4.447.

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Schnitzer, Mireille E., Erica E. M. Moodie, Mark J. van der Laan, Robert W. Platt, and Marina B. Klein. "Modeling the impact of hepatitis C viral clearance on end-stage liver disease in an HIV co-infected cohort with targeted maximum likelihood estimation." Biometrics 70, no. 1 (November 13, 2013): 144–52. http://dx.doi.org/10.1111/biom.12105.

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Benhidour, Hafida, and Takehisa Onisawa. "Interactive Learning of Verbal Descriptors Meanings for Face Drawing System." Journal of Advanced Computational Intelligence and Intelligent Informatics 14, no. 6 (September 20, 2010): 606–15. http://dx.doi.org/10.20965/jaciii.2010.p0606.

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This paper presents an approach for online learning of descriptors meanings in the Face Drawing System with verbal descriptors. The targeted descriptors are those describing the size of the facial features. The users of the system have the possibility to draw faces using linguistic terms and retouch the features of the drawn face using a combination of an adverb and a linguistic descriptor until the desired face is obtained. The system learns interactively the meanings of the terms from the retouches made by the user on the drawn face. For the current user, the system interactively learns the meanings of the descriptors using the proposed algorithm for online learning of Gaussian fuzzy sets approach based on the Maximum Likelihood Estimation (MLE) of Gaussian mixture. The system then adjusts the drawn face according to the new meaning of the descriptors.

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Pabebang, Sriyanti Rahayu, and Jessy Yunus Dannari. "The Influence of Content Marketing on Instagram on Online Purchase Decisions for MsGlow Products with Purchase Intention as an Intervening Variable." Jurnal Indonesia Sosial Sains 5, no. 12 (December 10, 2024): 3102–16. https://doi.org/10.59141/jiss.v5i12.1526.

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This research aims to examine the effect of Content Marketing on Instagram on purchasing decisions for Ms Glow products online, with Purchase Intention as an intermediary variable. The approach used in this research is quantitative with an explanatory research design. The population targeted by this study are Instagram users who have purchased Ms Glow products online or often shop at the MS Glow Makassar distributor store. The sample used consisted of 120 respondents, who were selected using the Maximum Likelihood Estimation (MLE) method. Several tests were conducted to ensure data validity and classical assumptions required in the analysis, which finally used path analysis to see the relationship between variables. The results of this study show that content marketing on Instagram has a strong and significant influence on purchasing decisions, both directly and through increasing purchase intention.

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