Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Biostatistics (118)
- Statistical Theory (116)
- Statistical Methodology (114)
- Statistical Models (60)
- Survival Analysis (48)
-
- Medicine and Health Sciences (31)
- Epidemiology (26)
- Public Health (26)
- Life Sciences (20)
- Multivariate Analysis (20)
- Longitudinal Data Analysis and Time Series (19)
- Genetics and Genomics (18)
- Applied Mathematics (17)
- Numerical Analysis and Computation (17)
- Genetics (15)
- Clinical Trials (13)
- Microarrays (12)
- Design of Experiments and Sample Surveys (7)
- Categorical Data Analysis (5)
- Bioinformatics (4)
- Computational Biology (4)
- Disease Modeling (4)
- Diseases (4)
- Laboratory and Basic Science Research (4)
- Applied Statistics (3)
- Medical Specialties (3)
- Other Statistics and Probability (1)
- Vital and Health Statistics (1)
- Keyword
-
- Cross-validation (23)
- Causal inference (20)
- Influence curve (14)
- Prediction (12)
- Efficient influence curve (11)
-
- Model selection (11)
- Targeted maximum likelihood estimation (11)
- Loss function (10)
- Bootstrap (9)
- Causal effect (9)
- Counterfactual (9)
- Adjusted p-value (8)
- Asymptotic linearity (8)
- Multiple testing (8)
- Super-learning (8)
- Type I error rate (8)
- Confounding (7)
- Empirical process (7)
- One-step estimator (7)
- Survival analysis (7)
- Counting process (6)
- Estimating equation (6)
- False discovery rate (6)
- Gene expression (6)
- Null distribution (6)
- Pathwise differentiable parameter (6)
- Semiparametric statistical model (6)
- Asymptotic control (5)
- Censored data (5)
- Censoring (5)
Articles 61 - 90 of 242
Full-Text Articles in Statistics and Probability
Avoiding Boundary Estimates In Linear Mixed Models Through Weakly Informative Priors, Yeojin Chung, Sophia Rabe-Hesketh, Andrew Gelman, Jingchen Liu, Vincent Dorie
Avoiding Boundary Estimates In Linear Mixed Models Through Weakly Informative Priors, Yeojin Chung, Sophia Rabe-Hesketh, Andrew Gelman, Jingchen Liu, Vincent Dorie
U.C. Berkeley Division of Biostatistics Working Paper Series
Variance parameters in mixed or multilevel models can be difficult to estimate, especially when the number of groups is small. We propose a maximum penalized likelihood approach which is equivalent to estimating variance parameters by their marginal posterior mode, given a weakly informative prior distribution. By choosing the prior from the gamma family with at least 1 degree of freedom, we ensure that the prior density is zero at the boundary and thus the marginal posterior mode of the group-level variance will be positive. The use of a weakly informative prior allows us to stabilize our estimates while remaining faithful …
Identification And Efficient Estimation Of The Natural Direct Effect Among The Untreated, Samuel D. Lendle, Mark J. Van Der Laan
Identification And Efficient Estimation Of The Natural Direct Effect Among The Untreated, Samuel D. Lendle, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
The natural direct effect (NDE), or the effect of an exposure on an outcome if an intermediate variable was set to the level it would have been in the absence of the exposure, is often of interest to investigators. In general, the statistical parameter associated with the NDE is difficult to estimate in the non-parametric model, particularly when the intermediate variable is continuous or high dimensional. In this paper we introduce a new causal parameter called the natural direct effect among the untreated, discus identifiability assumptions, and show that this new parameter is equivalent to the NDE in a randomized …
Estimation Of A Non-Parametric Variable Importance Measure Of A Continuous Exposure, Chambaz Antoine, Pierre Neuvial, Mark J. Van Der Laan
Estimation Of A Non-Parametric Variable Importance Measure Of A Continuous Exposure, Chambaz Antoine, Pierre Neuvial, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
We define a new measure of variable importance of an exposure on a continuous outcome, accounting for potential confounders. The exposure features a reference level x0 with positive mass and a continuum of other levels. For the purpose of estimating it, we fully develop the semi-parametric estimation methodology called targeted minimum loss estimation methodology (TMLE) [van der Laan & Rubin, 2006; van der Laan & Rose, 2011]. We cover the whole spectrum of its theoretical study (convergence of the iterative procedure which is at the core of the TMLE methodology; consistency and asymptotic normality of the estimator), practical implementation, simulation …
Targeted Minimum Loss Based Estimation Of An Intervention Specific Mean Outcome, Mark J. Van Der Laan, Susan Gruber
Targeted Minimum Loss Based Estimation Of An Intervention Specific Mean Outcome, Mark J. Van Der Laan, Susan Gruber
U.C. Berkeley Division of Biostatistics Working Paper Series
Targeted minimum loss based estimation (TMLE) provides a template for the construction of semiparametric locally efficient double robust substitution estimators of the target parameter of the data generating distribution in a semiparametric censored data or causal inference model based on a sample of independent and identically distributed copies from this data generating distribution (van der Laan and Rubin (2006), van der Laan (2008), van der Laan and Rose (2011)). TMLE requires 1) writing the target parameter as a particular mapping from a typically infinite dimensional parameter of the probability distribution of the unit data structure into the parameter space, 2) …
Population Intervention Causal Effects Based On Stochastic Interventions, Ivan Diaz Munoz, Mark J. Van Der Laan
Population Intervention Causal Effects Based On Stochastic Interventions, Ivan Diaz Munoz, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Estimating the causal effect of an intervention on a population typically involves defining parameters in a nonparametric structural equation model (Pearl, 2000, NPSEM) in which the treatment or exposure is deter- ministically assigned in a static or dynamic way. We define a new causal parameter that takes into account the fact that intervention policies can result in stochastically assigned exposures. The statistical parameter that identifies the causal parameter of interest is established. Inverse probability of treatment weighting (IPTW), augmented IPTW (A-IPTW), and targeted maximum likelihood estimators (TMLE) are developed. A simulation study is performed to demonstrate the properties of these …
Targeted Maximum Likelihood Estimation Of Natural Direct Effect, Wenjing Zheng, Mark J. Van Der Laan
Targeted Maximum Likelihood Estimation Of Natural Direct Effect, Wenjing Zheng, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
In many causal inference problems, one is interested in the direct causal effect of an exposure on an outcome of interest that is not mediated by certain intermediate variables. Robins and Greenland (1992) and Pearl (2000) formalized the definition of two types of direct effects (natural and controlled) under the counterfactual framework. Since then, identifiability conditions for these effects have been studied extensively. By contrast, considerably fewer efforts have been invested in the estimation problem of the natural direct effect. In this article, we propose a semiparametric efficient, multiply robust estimator for the natural direct effect of a binary treatment …
Targeted Minimum Loss Based Estimation Based On Directly Solving The Efficient Influence Curve Equation, Paul Chaffee, Mark J. Van Der Laan
Targeted Minimum Loss Based Estimation Based On Directly Solving The Efficient Influence Curve Equation, Paul Chaffee, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Applying targeted maximum likelihood estimation to longitudinal data can be computationally intensive. As the number of time points and/or number of intermediate factors grows, the computation resources consumed by these algorithms likewise increases. Different TMLE algorithms have different computational speeds and implementation challenges; there may also be efficiency differences of the corresponding estimators. The algorithm we describe here proceeds by solving the empirical efficient influence curve equation directly using numerical computation methods, rather than indirectly (by solving a score equation), which is the usual route. We believe that this estimator is the simplest of the TMLE procedures to implement in …
Variable Importance Analysis With The Multipim R Package, Stephan J. Ritter, Nicholas P. Jewell, Alan E. Hubbard
Variable Importance Analysis With The Multipim R Package, Stephan J. Ritter, Nicholas P. Jewell, Alan E. Hubbard
U.C. Berkeley Division of Biostatistics Working Paper Series
We describe the R package multiPIM, including statistical background, functionality and user options. The package is for variable importance analysis, and is meant primarily for analyzing data from exploratory epidemiological studies, though it could certainly be applied in other areas as well. The approach taken to variable importance comes from the causal inference field, and is different from approaches taken in other R packages. By default, multiPIM uses a double robust targeted maximum likelihood estimator (TMLE) of a parameter akin to the attributable risk. Several regression methods/machine learning algorithms are available for estimating the nuisance parameters of the models, including …
Targeted Methods For Finding Quantitative Trait Loci, Hui Wang, Sherri Rose, Mark J. Van Der Laan
Targeted Methods For Finding Quantitative Trait Loci, Hui Wang, Sherri Rose, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Conventional genetic mapping methods typically assume parametric models with Gaussian errors, and obtain parameter estimates through maximum likelihood estimation. We propose a general semiparametric model to map quantitative trait loci (QTL) in experimental crosses. In contrast with widely-used interval mapping (IM) derived methods, our model requires fewer assumptions and also accommodates various machine learning algorithms. Estimation using both targeted maximum likelihood and collaborative targeted maximum likelihood methods is compared to a composite interval mapping (CIM) approach. We demonstrate with simulations and real data analyses that, on average, our semiparametric targeted learning approach produces less biased QTL effect estimates than those …
Targeted Maximum Likelihood Estimation Of Conditional Relative Risk In A Semi-Parametric Regression Model, Cathy Tuglus, Kristin E. Porter, Mark J. Van Der Laan
Targeted Maximum Likelihood Estimation Of Conditional Relative Risk In A Semi-Parametric Regression Model, Cathy Tuglus, Kristin E. Porter, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
The conditional relative risk is an important measure in medical and epidemiological studies when the outcome of interest is binary (i.e. disease vs. no disease). When the outcome is common, estimation of conditional relative risk and related parameters can be problematic, especially when the exposure or covariates are continuous. We propose a new estimation procedure based on targeted maximum likelihood methodology that targets the parameters relating to the conditional relative risk for common outcomes under a log-linear, or multiplicative, semi-parametric model. In this paper, we present three possible targeted maximum likelihood estimators for relative risk parameters implied by such a …
Super Learner Based Conditional Density Estimation With Application To Marginal Structural Models, Ivan Diaz Munoz, Mark J. Van Der Laan
Super Learner Based Conditional Density Estimation With Application To Marginal Structural Models, Ivan Diaz Munoz, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
In this paper we present a histogram-like estimator of a conditional density that uses super learner crossvalidation to estimate the histogram probabilities, as well as the optimal number and position of the bins. This estimator is an alternative to kernel density estimators when the dimension of the problem is large. We demonstrate its applicability to estimation of Marginal Structural Model (MSM) parameters in which an initial estimator of the treatment %mechanism is needed. MSM estimation based on the proposed density estimator results in less biased estimates, when compared to estimates based on a misspecified parametric model.
A General Implementation Of Tmle For Longitudinal Data Applied To Causal Inference In Survival Analysis, Ori M. Stitelman, Victor De Gruttola, Mark J. Van Der Laan
A General Implementation Of Tmle For Longitudinal Data Applied To Causal Inference In Survival Analysis, Ori M. Stitelman, Victor De Gruttola, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
In many randomized controlled trials the outcome of interest is a time to event, and one measures on each subject baseline covariates and time-dependent covariates until the subject either drops-out, the time to event is observed, or the end of study is reached. The goal of such a study is to assess the causal effect of the treatment on the survival curve. Standard methods (e.g., Kaplan-Meier estimator, Cox-proportional hazards) ignore the available baseline and time-dependent covariates, and are therefore biased if the drop-out is affected by these covariates, and are always inefficient. We present a targeted maximum likelihood estimator of …
Targeted Minimum Loss Based Estimator That Outperforms A Given Estimator, Susan Gruber, Mark J. Van Der Laan
Targeted Minimum Loss Based Estimator That Outperforms A Given Estimator, Susan Gruber, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Targeted minimum loss based estimation (TMLE) provides a template for the construction of semiparametric locally efficient double robust substitution estimators of the target parameter of the data generating distribution in a semiparametric censored data or causal inference model (van der Laan and Rubin (2006),van der Laan (2008), van der Laan and Rose (2011)). In this article we demonstrate how to construct a TMLE that also satisfies the property that it is at least as efficient as a user supplied asymptotically linear estimator. For the sake of illustration we focus on estimation of the additive average causal effect of a point …
The Relative Performance Of Targeted Maximum Likelihood Estimators, Kristin E. Porter, Susan Gruber, Mark J. Van Der Laan, Jasjeet S. Sekhon
The Relative Performance Of Targeted Maximum Likelihood Estimators, Kristin E. Porter, Susan Gruber, Mark J. Van Der Laan, Jasjeet S. Sekhon
U.C. Berkeley Division of Biostatistics Working Paper Series
There is an active debate in the literature on censored data about the relative performance of model based maximum likelihood estimators, IPCW-estimators, and a variety of double robust semiparametric efficient estimators. Kang and Schafer (2007) demonstrate the fragility of double robust and IPCW-estimators in a simulation study with positivity violations. They focus on a simple missing data problem with covariates where one desires to estimate the mean of an outcome that is subject to missingness. Responses by Robins et al. (2007), Tsiatis and Davidian (2007), Tan (2007a) and Ridgeway and McCaffrey (2007) further explore the challenges faced by double robust …
Estimation And Testing In Targeted Group Sequential Covariate-Adjusted Randomized Clinical Trials, Antoine Chambaz, Mark J. Van Der Laan
Estimation And Testing In Targeted Group Sequential Covariate-Adjusted Randomized Clinical Trials, Antoine Chambaz, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
This article is devoted to the construction and asymptotic study of adaptive group sequential covariate-adjusted randomized clinical trials analyzed through the prism of the semiparametric methodology of targeted maximum likelihood estimation (TMLE). We show how to build, as the data accrue group-sequentially, a sampling design which targets a user-supplied optimal design. We also show how to carry out a sound TMLE statistical inference based on such an adaptive sampling scheme (therefore extending some results known in the i.i.d setting only so far), and how group-sequential testing applies on top of it. The procedure is robust (i.e., consistent even if the …
Targeted Maximum Likelihood Estimation For Dynamic Treatment Regimes In Sequential Randomized Controlled Trials, Paul Chaffee, Mark J. Van Der Laan
Targeted Maximum Likelihood Estimation For Dynamic Treatment Regimes In Sequential Randomized Controlled Trials, Paul Chaffee, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Sequential Randomized Controlled Trials (SRCTs) are rapidly becoming essential tools in the search for optimized treatment regimes in ongoing treatment settings. Analyzing data for multiple time-point treatments with a view toward optimal treatment regimes is of interest in many types of afflictions: HIV infection, Attention Deficit Hyperactivity Disorder in children, leukemia, prostate cancer, renal failure, and many others. Methods for analyzing data from SRCTs exist but they are either inefficient or suffer from the drawbacks of estimating equation methodology. We describe an estimation procedure, targeted maximum likelihood estimation (TMLE), which has been fully developed and implemented in point treatment settings, …
Threshold Regression Models Adapted To Case-Control Studies, And The Risk Of Lung Cancer Due To Occupational Exposure To Asbestos In France, Antoine Chambaz, Dominique Choudat, Catherine Huber, Jean-Claude Pairon, Mark J. Van Der Laan
Threshold Regression Models Adapted To Case-Control Studies, And The Risk Of Lung Cancer Due To Occupational Exposure To Asbestos In France, Antoine Chambaz, Dominique Choudat, Catherine Huber, Jean-Claude Pairon, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Asbestos has been known for many years as a powerful carcinogen. Our purpose is quantify the relationship between an occupational exposure to asbestos and an increase of the risk of lung cancer. Furthermore, we wish to tackle the very delicate question of the evaluation, in subjects suffering from a lung cancer, of how much the amount of exposure to asbestos explains the occurrence of the cancer. For this purpose, we rely on a recent French case-control study. We build a large collection of threshold regression models, data-adaptively select a better model in it by multi-fold likelihood-based cross-validation, then fit the …
Tmle: An R Package For Targeted Maximum Likelihood Estimation, Susan Gruber, Mark J. Van Der Laan
Tmle: An R Package For Targeted Maximum Likelihood Estimation, Susan Gruber, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Targeted maximum likelihood estimation (TMLE) presents an approach for construction of an efficient double-robust semi-parametric substitution estimator of a target feature of the data generating distribution, such as a statistical association measure or a causal effect parameter. tmle is a recently developed R package that implements TMLE for estimation of the effect of a binary treatment at a single point in time on an outcome of interest, controlling for user supplied covariates: the additive treatment effect, the relative risk, the odds ratio. The package allows outcome data with missingness, and experimental units that contribute repeated records of the point-treatment data …
A Generalized Approach For Testing The Association Of A Set Of Predictors With An Outcome: A Gene Based Test, Benjamin A. Goldstein, Alan E. Hubbard, Lisa F. Barcellos
A Generalized Approach For Testing The Association Of A Set Of Predictors With An Outcome: A Gene Based Test, Benjamin A. Goldstein, Alan E. Hubbard, Lisa F. Barcellos
U.C. Berkeley Division of Biostatistics Working Paper Series
In many analyses, one has data on one level but desires to draw inference on another level. For example, in genetic association studies, one observes units of DNA referred to as SNPs, but wants to determine whether genes that are comprised of SNPs are associated with disease. While there are some available approaches for addressing this issue, they usually involve making parametric assumptions and are not easily generalizable. A statistical test is proposed for testing the association of a set of variables with an outcome of interest. No assumptions are made about the functional form relating the variables to the …
Asymptotic Theory For Cross-Validated Targeted Maximum Likelihood Estimation, Wenjing Zheng, Mark J. Van Der Laan
Asymptotic Theory For Cross-Validated Targeted Maximum Likelihood Estimation, Wenjing Zheng, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
We consider a targeted maximum likelihood estimator of a path-wise differentiable parameter of the data generating distribution in a semi-parametric model based on observing n independent and identically distributed observations. The targeted maximum likelihood estimator (TMLE) uses V-fold sample splitting for the initial estimator in order to make the TMLE maximally robust in its bias reduction step. We prove a general theorem that states asymptotic efficiency (and thereby regularity) of the targeted maximum likelihood estimator when the initial estimator is consistent and a second order term converges to zero in probability at a rate faster than the square root of …
Observational Study And Individualized Antiretroviral Therapy Initiation Rules For Reducing Cancer Incidence In Hiv-Infected Patients, Romain Neugebauer, Michael J. Silverberg, Mark J. Van Der Laan
Observational Study And Individualized Antiretroviral Therapy Initiation Rules For Reducing Cancer Incidence In Hiv-Infected Patients, Romain Neugebauer, Michael J. Silverberg, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Targeted Maximum Likelihood Learning (TMLL) has been proposed as a general estimation methodology that can, in particular, be applied to draw causal inferences based on marginal structural modeling with observational data using either a point treatment approach (all confounders are assumed not to be affected by the exposure(s) of interest) or a longitudinal data approach (some confounders may be affected by one of the exposures of interest). While formal development of TMLL has included road maps for applications in longitudinal data approaches, real-life implementations have been restricted to studies based on a point treatment approach. In this article, we illustrate …
Gains In Power From Structured Two-Sample Tests Of Means On Graphs, Laurent Jacob, Pierre Neuvial, Sandrine Dudoit
Gains In Power From Structured Two-Sample Tests Of Means On Graphs, Laurent Jacob, Pierre Neuvial, Sandrine Dudoit
U.C. Berkeley Division of Biostatistics Working Paper Series
We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially expressed genes between two patient populations, as shifts in expression levels are expected to be coherent with the structure of graphs reflecting gene properties such as biological process, molecular function, regulation, or metabolism. For a fixed graph of interest, we demonstrate that accounting for graph structure can yield more powerful tests under the assumption of smooth distribution shift on the graph. We also investigate …
Targeted Bayesian Learning, Ivan Diaz Munoz, Alan E. Hubbard, Mark J. Van Der Laan
Targeted Bayesian Learning, Ivan Diaz Munoz, Alan E. Hubbard, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Targeted maximum likelihood estimation (van der Laan & Rubin 2006) is a loss-based semi-parametric estimation method that yields a substitution estimator of a target parameter of the probability distribution of the data that solves the efficient influence curve estimating equation, and thereby yields a double robust locally efficient estimator of the parameter of interest, under regularity conditions. The Bayesian paradigm is concerned with including the researcher’s prior uncertainty about the parameter through a prior distribution, which combined with the likelihood yields a posterior distribution for the parameter that reflects the researcher’s posterior uncertainty. In this paper, we present a way …
Diagnosing And Responding To Violations In The Positivity Assumption, Maya L. Petersen, Kristin Porter, Susan Gruber, Yue Wang, Mark J. Van Der Laan
Diagnosing And Responding To Violations In The Positivity Assumption, Maya L. Petersen, Kristin Porter, Susan Gruber, Yue Wang, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
The assumption of positivity or experimental treatment assignment requires that observed treatment levels vary within confounder strata. This article discusses the positivity assumption in the context of assessing model and parameter-specific identifiability of causal effects. Positivity violations occur when certain subgroups in a sample rarely or never receive some treatments of interest. The resulting sparsity in the data may increase bias with or without an increase in variance and can threaten valid inference. The parametric bootstrap is presented as a tool to assess the severity of such threats and its utility as a diagnostic is explored using simulated data. Several …
Estimation Of Causal Effects Of Community Based Interventions, Mark J. Van Der Laan
Estimation Of Causal Effects Of Community Based Interventions, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Suppose one assigns two interventions to a small number K of different populations or communities, and one measures covariates and outcomes on a random sample of independent individuals from each of the K populations. We investigate the problem of identification and estimation of the causal effect of the choice of intervention assigned at the community level, and, if the intervention is time-dependent, the causal effect of the changes in the intervention at time t, on the outcome. The challenge one is confronted with is that different populations have different environmental factors and that the intervention and environment are assigned to …
Optimizing Randomized Trial Designs To Distinguish Which Subpopulations Benefit From Treatment, Michael Rosenblum, Mark J. Van Der Laan
Optimizing Randomized Trial Designs To Distinguish Which Subpopulations Benefit From Treatment, Michael Rosenblum, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
It is a challenge to evaluate experimental treatments where it is suspected that the treatment effect may only be strong for certain subpopulations, such as those having a high initial severity of disease, or those having a particular gene variant. Standard randomized controlled trials can have low power in such situations. They also are not optimized to distinguish which subpopulations benefit from a treatment. With the goal of overcoming these limitations, we consider randomized trial designs in which the criteria for patient enrollment may be changed, in a preplanned manner, based on interim analyses. Since such designs allow data-dependent changes …
A Targeted Maximum Likelihood Estimator Of A Causal Effect On A Bounded Continuous Outcome, Susan Gruber, Mark J. Van Der Laan
A Targeted Maximum Likelihood Estimator Of A Causal Effect On A Bounded Continuous Outcome, Susan Gruber, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Targeted maximum likelihood estimation of a parameter of a data generating distribution, known to be an element of a semiparametric model, involves constructing a parametric model through an initial density estimator with parameter epsilon representing an amount of fluctuation of the initial density estimator, where the score of this fluctuation model at epsilon=0 equals the efficient influence curve/canonical gradient. The latter constraint can be satisfied by many parametric fluctuation models, since it represents only a local constraint of its behavior at zero fluctuation. However, it is very important that the fluctuations stay within the semiparametric model for the observed data …
Super Learner In Prediction, Eric C. Polley, Mark J. Van Der Laan
Super Learner In Prediction, Eric C. Polley, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Super learning is a general loss based learning method that has been proposed and analyzed theoretically in van der Laan et al. (2007). In this article we consider super learning for prediction. The super learner is a prediction method designed to find the optimal combination of a collection of prediction algorithms. The super learner algorithm finds the combination of algorithms minimizing the cross-validated risk. The super learner framework is built on the theory of cross-validation and allows for a general class of prediction algorithms to be considered for the ensemble. Due to the previously established oracle results for the cross-validation …
Simple Examples Of Estimating Causal Effects Using Targeted Maximum Likelihood Estimation, Michael Rosenblum, Mark J. Van Der Laan
Simple Examples Of Estimating Causal Effects Using Targeted Maximum Likelihood Estimation, Michael Rosenblum, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
We present a brief overview of targeted maximum likelihood for estimating the causal effect of a single time point treatment and of a two time point treatment. We focus on simple examples demonstrating how to apply the methodology developed in (van der Laan and Rubin, 2006; Moore and van der Laan, 2007; van der Laan, 2010a,b). We include R code for the single time point case.
Targeted Maximum Likelihood Method For Repeated Measures Semiparametric Regression: Discovery For Transcription Factor Activity, Catherine Tuglus, Mark J. Van Der Laan
Targeted Maximum Likelihood Method For Repeated Measures Semiparametric Regression: Discovery For Transcription Factor Activity, Catherine Tuglus, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
In longitudinal and repeated measures data analysis, often the goal is to determine the effect of a treatment or aspect on a particular outcome (e.g. disease progression). We consider semiparametric repeated measures regression model, where the parametric component models effect of the variable of interest and any modification by other covariates. The expectation of this parametric component over the other covariates is a measure of variable importance. Here we present a targeted maximum likelihood estimator of the finite dimensional regression parameter, which is easily estimated using standard software for generalized estimating equations. The targeted maximum likelihood method provides double robust …