Targeted learning in data science: causal inference for complex longitudinal studies
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Datensatz im Suchindex
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Contents Part I Targeted Learning in Data Science: Introduction 1 2 3 Research Questions in Data Science. 3 Sherri Rose and Mark J. van der Laan 1.1 Learning from (Big) Data . 1.2 Traditional Approaches to Estimation Fail. 1.3 Targeted Learning in Practice. 1.4 The Statistical Estimation Problem. 1.4.1 Data. 1.4.2 Model and Parameter. 1.4.3 Targeted Minimum Loss-Based Estimators. 1.4.4 Other Common Estimation Problems. 1.5 Roadmap for Targeted Learning. 1.6 Notes and Further Reading . 4 5 6 7 8 8 9 10 11 13 Defining the Model and Parameter. 15 Sherri Rose and Mark J. van der Laan 2.1 Defining the Structural Causal Model . 2.2 Causal Graphs. 2.3 Defining the Causal Target Parameter . 2.3.1 Interventions. 2.3.2 Counterfactuals. 2.3.3 Establishing
Identifiability. 2.3.4 Commit to a Statistical Modeland Target Parameter . 2.3.5 Interpretation of Target Parameter. 2.4 Notes and Further Reading . 16 19 21 21 22 22 24 25 25 Sequential Super Learning. 27 Sherri Rose and Mark J. van der Laan 3.1 Background: Ensemble Learning. 3.2 Defining the Estimation Problem. 3.3 Sequential Super (Machine) Learning. . 28 31 32 xxi
Contents xxii Computation. Notes and Further Reading . 34 34 LTMLE. Sherri Rose and Mark J. van der Laan 4.1 LTMLE in Action: When to Start HIV Treatment. 4.2 Defining the Estimation Problem. 4.3 What Does It Mean to Follow a Rule?. 4.4 LTMLE for When to Start Treatment. 4.4.1 Determining the Efficient Influence Curve. 4.4.2 Determining the Loss Function and Fluctuation Submodel. 4.4.3 LTMLE Algorithm. 4.5 Analysis of TMLE and Inference. 4.5.1 TMLE Solves Efficient Influence Curve Equation. 4.5.2 Second-Order Remainder for TMLE. 4.5.3 Asymptotic Efficiency. 4.5.4 Inference. 4.6 Notes and Further Reading . 35 3.4 3.5 4 36 36 37 40 40 41 42 44 44 44 45 46 47 Part II Additional Core Topics 5 One-Step TMLE. Mark J. van der
Laan, Wilson Cai, and Susan Gruber 5.1 Local and Universal Least Favorable Submodels. 5.2 A Universal Least Favorable Submodel for Targeted Maximum Likelihood Estimation. 53 5.2.1 Analytic Formula. 5.2.2 Universal Least Favorable Submodel in Terms of a Local Least Favorable Submodel. 5.3 Example: One-Step TMLE for the ATT. 5.4 Universal Least Favorable Model for Targeted Minimum Loss-Based Estimation. 60 5.5 Universal Canonical One-dimensional Submodel for a Multidimensional Target Parameter. 64 5.5.1 Practical Construction. 5.5.2 Existence of MLE or Approximate MLE en. 5.5.3 Universal Score-Specific One-Dimensional Submodel. 5.6 Example: One-Step TMLE, Based on Universal Canonical One-Dimensional Submodel, of an Infinite-Dimensional Target Parameter. . 68 5.7 Universal Canonical One-Dimensional Submodel for Targeted Minimum Loss-Based Estimation of a Multidimensional Target Parameter. 73 51 51 54 55 57 65 66 67
Contents 6 7 8 xxiii Highly Adaptive Lasso (HAL). Mark J. van der Laan and David Benkeser 6.1 Statistical Formulation of the Estimation Problem. 6.2 Representation of a Cadlag Function as a Linear Combination of Basis Functions . 80 6.3 A Minimum Loss-Based Estimator (MLE) Minimizing over all Functions with Variation Norm Smaller than A. 82 6.4 The HAL Estimator. 6.5 Further Dimension Reduction Considerations. 6.6 Applications . 6.6.1 Constructing the Highly Adaptive Lasso. 6.6.2 Prediction Simulation. 6.6.3 Prediction Data Analysis . . 6.6.4 Simulation for Missing Data. 6.6.5 Conclusion. 77 A Generally Efficient HAL-TMLE. Mark J. van der Laan 7.1 Treatment Specific Mean. 7.1.1 HAL-TMLE. 7.1.2 Asymptotic Efficiency. 7.2 General HAL-TMLE and Asymptotic Efficiency. 7.3 Discussion.
95 HAL Estimator of the Efficient Influence Curve . Mark J. van der Laan 8.1 Formulation of HAL Least Squares Linear Regression Estimator of the Efficient Influence Curve. 8.2 Rate of Convergence of the HAL Estimator of the Efficient Influence Curve. . . 107 8.2.1 Application to Estimate Projection of Initial Gradient onto Subtangent Spaces. 8.2.2 Using the Actual Data Set from the True Data Distribution. 109 8.3 Truncated Mean Based on Current Status Data. 8.4 Truncated Mean Based on Interval Censored Data. 8.5 Causal Effect of Binary Treatment on Interval Censored Time to Event. 113 8.6 Bivariate Survival Function Basedon Bivariate Right-Censored Data. 8.7 Causal Effect of Binary Treatment on Bivariate Survival Probability Based on Bivariate Right-Censored Data. 121 8.8 Discussion. 79 83 84 85 86 88 91 91 94 96 96 97 98 101 103 104 108 109 Ill 118 123
Contents xxiv 9 10 Data-Adaptive Target Parameters. Alan E. Hubbard, Chris J. Kennedy, and Mark J. van der Laan 9.1 Example: Defining Treatment or Exposure Levels. 9.2 Methodology for Data-Adaptive Parameters. . 9.3 TMLE of v-Specific Data-Adaptive Parameter. 9.4 Combining v-Specific TMLEs Across Estimation Samples. 9.5 CV-TMLE. 9.6 CV-TMLE for Data-Adaptive Parameters. 9.7 CV-TMLE for Variable Importance Measure . 9.8 Software for Data-Adaptive VIMs: varImpact. 9.9 Data Analysis: Framingham Heart Study. 9.9.1 Super Learner Library. 9.9.2 Results. 9.10 Discussion. C-TMLE for Continuous Tuning. Mark J. van der Laan, Antoine Chambaz, and Cheng Ju 10.1 Formal Motivation for Targeted Tuning of Nuisance Parameter Estimator in TMLE. 145 10.1.1 Contrasting Discrete and Continuous Tuning Parameters. 10.1.2 Key Theoretical Property and Rational for Proposed C-TMLE That Drives Its Asymptotic Superiority Relative
to Standard TMLE. 150 10.1.3 Implicitly Defined Tuning Parameter. 10.2 A General C-TMLE Algorithm. 10.3 Verifying That C-TMLE Solves Critical Equation (10.4). 10.3.1 Condition for C-TMLE Solving Critical Equation (10.4) . 154 10.3.2 A TMLE and C-TMLE that Solve Equation (10.3) Exactly. 157 10.4 General Theorem for C-TMLE Asymptotic Linearity. 10.5 Discussion. 125 127 128 129 131 132 132 135 136 138 139 140 142 143 149 152 152 154 158 160 PartlH Randomized Trials 11 Targeted Estimation of Cumulative Vaccine Sieve Effects. David Benkeser, Marco Carone, and Peter Gilbert 11.1 Observed Data. 11.2 Causal Model and Parameters of Interest. 11.3 Identification. . 11.4 Efficient Influence Function. 11.5 Initial Estimates . 11.6 Submodels and Loss Functions. 11.7 TMLE Algorithm. 11.8 Statistical Properties of
TMLE. 11.9 HVTN 505 HIV Vaccine Sieve Analysis. 11.10 Discussion. 165 167 168 169 169 170 170 171 172 172 174
Contents 12 13 xxv The Sample Average Treatment Effect. 175 Laura B. Balzer, Maya L. Petersen, and Mark J. van der Laan 12.1 The Causal Model and Causal Parameters. 12.2 Identifiability. 12.3 Estimation and Inference. 12.3.1 TMLE for the Population Effect. 12.3.2 TMLE for the Sample Effect. 12.4 Extensions to Pair-Matched Trials . 12.5 Simulation . . . . 12.6 Discussion. 177 180 182 183 185 187 190 193 195 Laura B. Balzer, Mark J. van der Laan, and Maya L. Petersen 13.1 Motivating Example and Causal Parameters. 198 13.2 Targeted Estimation in a Randomized Trial Without Matching. 199 13.3 Targeted Estimation in a Randomized Trial with Matching . 203 13.4 Collaborative Estimation of the Exposure Mechanism. 206 13.5 Obtaining Inference. 208 13.6 Small Sample Simulations. 209 13.6.1 Study 1. 209 13.6.2 Study 2. 212 13.7
Discussion. 214 Data-Adaptive Estimation in Cluster Randomized Trials. Part IV Observational Data 14 15 Stochastic Treatment Regimes. . 219 Ivan Dfaz and Mark J. van der Laan 14.1 Data, Notation, and Parameter of Interest. 14.1.1 Identification. 14.1.2 Positivity Assumption. 14.2 Optimality Theory for Stochastic Regimes . . 14.3 Targeted Minimum Loss-Based Estimation. 14.3.1 Asymptotic Distribution of TMLE. 14.4 Initial Estimators. 14.4.1 Super Learning for a Conditional Density. 14.4.2 Construction of the Library. 14.5 Notes and Further Reading. 221 223 224 224 226 228 229 229 230 232 LTMLE with Clustering. 233 Mireille E. Schnitzer, Mark J. van der Laan, Erica E. M. Moodie, and Robert W. Platt 15.1 The PROBIT Study . 15.1.1 Observed Data. 15.1.2 Causal Assumptions. 15.1.3 Model and Parameter .
. 15.2 Two Parametrizations of the g-Formula. 15.2.1 g-Computation for the PROBIT. 234 234 236 238 239 240
Contents XXvi 15.2.2 Sequential g-Computation . 15.2.3 Sequential g-Computation for the PROBIT. 15.2.4 g-Computation Assumptions. LTMLE for a Saturated Marginal Structural Model. 15.3.1 Construction of Weights. 15.3.2 Efficient Influence Function. 15.3.3 LTMLE. . 15.3.4 LTMLE for the PROBIT. Variance Estimation and Clustering. 15.4.1 Distinction Between Clustering and Interference . 15.4.2 Estimation with the EIF. 15.4.3 Simulation Study. PROBIT Results. Discussion. 240 241 242 243 243 243 244 245 246 246 246 248 249 250 Comparative Effectiveness of Adaptive Treatment Strategies. 253 Romain S. Neugebauer, Julie A. Schmittdiel, Patrick J. O’Connor, and Mark J. van der Laan 16.1 The Treatment Intensification Study. 16.2 Data. 16.3 Causal Model and Statistical
Estimands. 16.4 Estimation. 16.4.1 TMLE. 254 256 258 260 261 Action Mechanism, 88 . 265 16.4.3 Outcome Regressions, 2^. 16.5 Practical Performance . 16.6 Discussion. 268 269 275 15.3 15.4 15.5 15.6 16 16.4.2 17 Mediation Analysis with Time-Varying Mediators and Exposures. 277 Wenjing Zheng and Mark J. van der Laan 17.1 The Mediation Formula, Natural Direct,and Natural Indirect Effects . 17.1.1 Counterfactual Outcome Under Conditional Mediator Distribution. 17.1.2 Causal Parameters and Identifiability. 17.1.3 Longitudinal Mediation Analysis with Marginal vs Conditional RandomInterventions. 17.2 Efficient Influence Curve. 17.3 Estimators. 17.3.1 Nontargeted Substitution Estimator. 17.3.2 IPW
Estimator. 17.3.3 TMLE. 17.4 Simulation . 17.5 Discussion. 279 280 281 284 286 290 290 292 294 296 298
Contents xxvii PartV Online Learning 18 19 Online Super Learning. 303 Mark J. van der Laan and David Benkeser 18.1 Statistical Formulation of Estimation Problem. 18.1.1 Statistical Model. 18.1.2 Statistical Target Parameterand Loss Function. 18.1.3 Regression Example. 18.2 Cross-Validation for Ordered Sequence of Dependent Experiments. 306 18.2.1 Online Cross-Validation Selector. 18.2.2 Online Oracle Selector. 18.2.3 The Online Super Learner for a Continuous Finite Dimensional Family of Candidate Estimators. 18.3 An Oracle Inequality for Online Cross-Validation Selector. 18.3.1 Quadratic Loss Functions. . 18.3.2 Nonquadratic Loss Functions. 18.4 Special Online-Cross-Validation Selector for Independent Identically Distributed Observations. 312 18.4.1 Online Cross-Validation Selector. 18.4.2 Imitating V-Fold Cross-Validation . 18.4.3 Online Oracle Selector. 18.5 Discussion. 312 313 313 315 Online
Targeted Learning for Time Series . 317 Mark J. van der Laan, Antoine Chambaz, and Sam Lendle 19.1 Statistical Formulation of the Estimation Problem. 19.1.1 Statistical Model: Stationarity and Markov Assumptions . 319 19.1.2 Underlying Causal Model and Target Quantity. 19.1.3 g-Computation Formula for Post-intervention Distribution. 321 19.1.4 Statistical Estimand: Intervention-Specific Counterfactual Mean. 19.1.5 Sequential Regression Representation of Counterfactual Mean. 19.1.6 General Class of Target Parameters. 19.1.7 Statistical Estimation Problem. . 19.2 Efficient Influence Curve of the Target Parameter. 19.2.1 Monte-Carlo Approximation of the Efficient Influence Curve using the Nesting Assumption. 326 19.2.2 A Special Representation of the Efficient Influence Curve for Binary Variables. 328 305 305 305 306 306 307 309 310 310 311 318 320 321 322 322 323 324
Contents xxviii 19.3 19.4 19.5 19.6 19.7 19.8 First Order Expansions for the Target Parameter in Terms of Efficient Influence Curve. 330 19.3.1 Expansion for Standard TMLE. 19.3.2 Expansion for Online One-Step Estimator and Online TMLE. TMLE . 19.4.1 Local Least Favorable Fluctuation Model . 19.4.2 One-Step TMLE. 19.4.3 Iterative TMLE. 19.4.4 Analysis of the TMLE . Online One-Step Estimator. Online TMLE. Online Targeted Learning withIndependent Identically Distributed Data. 19.7.1 Online Targeted Learning of the Average Causal Effect 19.7.2 Online One-Step Estimator . 19.7.3 Online TMLE . Discussion. . 330 332 332 332 333 334 334 335 336 341 341 341 342 346 Part VI Networks 20 Causai Inference in Longitudinal Network-Dependent Data. Sofrygin and Mark J. van der Laan Modeling
Approach. Data Structure. Example. Estimation Problem. 20.4.1 Counterfactuals and Stochastic Interventions. 20.4.2 Post-Intervention Distribution and Sequential Randomization Assumption . 20.4.3 Target Parameter as the Average Causal Effect (ACE) . 356 20.4.4 Dimension Reduction and Exchangeability Assumptions . 357 20.4.5 Independence Assumptions on Exogenous Errors . 20.4.6 Identifiability: g-Computation Formula for Stochastic Intervention. 20.4.7 Likelihood and Statistical Model. 20.4.8 Statistical Target Parameter. 20.4.9 Statistical Estimation Problem. 20.4.10 Summary. 20.5 Efficient Influence Curve. 20.6 Maximum Likelihood Estimation, Cross-Validation, and Super Learning. 20.7 TMLE
. 20.7.1 Local Least Favorable Fluctuation Model . 20.7.2 Estimation of the Efficient Influence Curve. Oleg 20.1 20.2 20.3 20.4 349 350 352 352 353 354 355 357 358 359 359 360 360 361 363 365 365 366
xxix Contents Summary. Notes and Further Reading. 368 369 Single Time Point Interventions in Network-Dependent Data. 373 20.8 20.9 21 Oleg Sofrygin, Elizabeth L. Ogburn, and Mark J. van der Laan 21.1 Modeling Network Data . 21.1.1 Statistical Model. 21.1.2 Types of Interventions. 21.1.3 Target Parameter: Sample-Average of Expected Outcomes . 376 21.1.4 Sample Average Mean Direct Effect Under Interference. 378 21.2 Estimation. 21.2.1 The Estimator Qw,n for Qw.o. 21.2.2 The Initial (Nontargeted) Estimator ßv of ßo. 21.2.3 Estimating Mixture Densities gj and go. 21.2.4 The TMLE Algorithm . 21.3 Inference. 21.3.1 Inference in a Restricted Model for Baseline Covariates. 384 21.3.2 Ad-Hoc Upper Bound on Variance. 21.3.3 Inference for Conditional Target Parameter. 21.4 Simulating Network-Dependent Data in R
. 21.4.1 Defining the Data-Generating Distribution for Observed Network Data. 387 21.4.2 Defining Intervention, Simulating Counterfactual Data and Evaluating the Target Causal Quantity. 390 21.5 Causal Effects with Network-Dependent Data in R. 21.6 Simulation Results. 21.7 Notes and Further Reading. 374 374 376 378 381 381 382 382 383 386 386 387 392 393 395 Part VII Optimal Dynamic Rules 22 Optimal Dynamic Treatment Rules. Alexander R. Luedtke and Mark J. van der Laan 22.1 Optimal Dynamic Treatment Estimation Problem . 22.2 Efficient Influence Curve of the Mean Outcome Under V-Optimal Rule. 403 22.3 Statistical Inference for the Average of Sample-Split Specific Mean Counterfactual Outcomes Under Data Adaptively Determined Dynamic Treatments . . 405 22.3.1 General Description of CV-TMLE. 22.3.2 Statistical Inference for the Data-Adaptive Parameter Âo». 22.3.3 Statistical Inference for the True Optimal Rule ^0 ■ • • • 22.4 Discussion. 22.5
Proofs. 399 400 406 407 408 410 411
Contents XXX 22.6 22.7 23 24 CV-TMLE for the Mean Outcome Under Data-Adaptive V-Optimal Rule. 414 Notes and Further Reading. 416 Optimal Individualized Treatments Under Limited Resources. Alexander R. Luedtke and Mark J. van der Laan 23.1 Optimal Resource-Constrained Rule and Value . 23.2 Estimating the Optimal Resource-ConstrainedValue. 23.3 Canonical Gradient of the Optimal Resource-Constrained Value. . 423 23.4 Inference for Y(Po) . 23.5 Discussion of Theorem 23.4 Conditions . 23.6 Discussion. 23.7 Proofs. 419 Targeting a Simple Statistical Bandit Problem. Antoine Chambaz, Wenjing Zheng, and Mark J. van der Laan 24.1 Sampling Strategy and TMLE. 24.1.1 Sampling Strategy. 24.1.2 TMLE. 24.2 Convergence of Sampling Strategy and Asymptotic Normality of TMLE. 24.3 Confidence
Intervals. 24.4 Simulation. 24.5 Conclusion (on a Twist). 437 419 422 425 426 428 430 440 441 442 443 445 446 450 Part VIII Special Topics 25 CV-TMLE for Nonpathwise Differentiable Target Parameters. Mark J. van der Laan, Aurélien Bibaut, and Alexander R. Luedtke 25.1 Definition of the Statistical Estimation Problem. 25.2 Approximating Our Target Parameter by a Family of Pathwise Differentiable Target Parameters. 458 25.3 CV-TMLE of h-Specific Target Parameter Approximation. 25.3.1 CV-TMLE of Wo). 25.3.2 Asymptotic Normality of CV-TMLE. 25.3.3 Asymptotic Normality of CV-TMLE as an Estimator of o. 465 25.4 A Data-Adaptive Selector of the Smoothing Bandwidth. 25.5 Generalization of Result for Data-Adaptive Bandwidth Selector. 25.5.1 Selecting among Different Classes of Pathwise Differentiable Approximations of Target Parameter . 25.6 Example: Estimation of a Univariate Density at a Point. 25.7 Example: Causal Dose Response Curve Estimation at a Point . 25.8 Notes and Further Reading
. 455 456 461 461 462 466 470 473 474 477 480
Contents xxxi 26 Higher-Order Targeted Loss-Based Estimation. 483 Marco Carone, Ivan Diaz, and Mark J. van der Laan 26.1 Overview of Higher-Order TMLE. . 485 26.1.1 TMLE. 485 26.1.2 Extensions of TMLE. 487 26.1.3 Second-Order Asymptotic Expansions. 488 26.1.4 Construction of a 2-TMLE. 489 26.1.5 Insufficiently Differentiable Target Parameters. 491 26.2 Inference Using Higher-Order TMLE . . 492 26.2.1 Asymptotic Linearity and Efficiency. 492 26.2.2 Constructing Confidence Intervals . 493 26.2.3 Implementing a Higher-Order TMLE. . . 494 26.3 Inference Using Approximate Second-Order Gradients. 495 26.3.1 Asymptotic Linearity and Efficiency. 496 26.3.2 Implementation and Selection of Tuning Parameter . 496 26.4 Illustration: Estimation of a g-Computation Parameter. 498 26.4.1 Case I: Finite Support. 499 26.4.2 Case II: Infinite Support. 501 26.4.3 Numerical Results. 504 26.5 Concluding
Remarks. 507 26.6 Notes and Further Reading. 509 27 Sensitivity Analysis. 511 Ivan Dfaz, Alexander R. Luedtke, and Mark J. van der Laan 27.1 The Problem. 27.2 Sensitivity Analysis. 27.3 Bounds on the Causal Bias Are Unknown. 27.4 Notes and Further Reading. . 512 514 519 521 Targeted Bootstrap. 523 28 Jeremy Coyle and Mark J. van der Laan 28.1 Problem Statement. 28.2 TMLE . 28.2.1 TMLE for Treatment Specific Mean. 28.2.2 TMLE of the Variance of the Influence Curve. 28.2.3 Joint TMLE of Both the Target Parameter andIts Asymptotic Variance . 28.3 Super Learner. 28.4 Bootstrap. 28.4.1 Nonparametric Bootstrap. 28.4.2 Model-Based
Bootstrap. 28.4.3 Targeted Bootstrap . 28.4.4 Bootstrap Confidence Intervals. 28.5 Simulation. 28.6 Conclusion. 524 525 525 526 528 528 530 530 531 531 532 534 539
Contents xxxii 29 Targeted Learning Using Adaptive Survey Sampling. 541 Antoine Chambaz, Emilien Joly, and Xavier Mary 29.1 Template for Targeted Inference by Survey Sampling. 542 29.1.1 Retrieving the Observations by Survey Sampling. 542 29.1.2 CLT on the TMLE and Resulting Confidence Intervals. 543 29.2 Survey Sampling Designs and Assumption Al. 545 29.2.1 Sampford’s Survey Sampling Design. 545 29.2.2 Determinantal Survey Sampling Design. 546 29.3 Optimizing the Survey Sampling Designs. 549 29.4 Example: Variable Importance of a Continuous Exposure. 549 29.4.1 Preliminaries.:. 550 29.4.2 Construction of the TMLE. 551 29.5 Simulation . 553 29.6 Elements öf Proof. 555 29.6.1 Proof of Proposition 29.1 . 555 29.6.2 Proof of Eqs. (29.8) and (29.9). 556 29.6.3 Proof of Proposition 29.3 . 557 29.6.4 Proof of Proposition 29.4 . 558 30 The Predicament of Truth: On Statistics, Causality, Physics, and the Philosophy of
Science . 561 Richard J. С. M. Starmans 30.1 Statistics and the Fragility of Truth. 30.2 Truth in Epistemology and Methodology. 30.3 Eroded Models, Von Neumann and the End of Theory . 30.4 Physics, Statistics and the Philosophy of Science. 30.5 The Triptych of True Knowledge. 30.6 Some Roots and Aspects of Causality. 30.7 Elimination, Dualism, the Probabilistic Revolution, and Unification. 578 30.8 Conclusion. A Appendix: Foundations. A.l A.2 A.3 Data-Adaptive Target Parameters. A. 1.1 Statistical Inference Based on the CV-TMLE . Mediation Analysis. A.2.1 Proof of Lemma 17.1: Identifiability Result. . A.2.2 Proof of Theorem 17.1. Online Super Learning. A.3.1 Online Cross-Validated Risk Minus Online Cross-Validated True Risk Is a Discrete Martingale . A.3.2 Martingale Exponential Inequality for Tail
Probability. 593 A.3.3 Proof of Theorem 18.1. A.3.4 Brief Review of Literature on Online Estimation . 561 563 566 569 571 574 582 585 585 585 588 589 590 593 593 595 601
Contents A.4 xXXiii Online Targeted Learning . A.4.1 First Order Expansion of Target Parameter Based on Marginal Expectation of Efficient Influence Curve . A.4.2 First Order Expansion of Target Parameter Based on Conditional Expectations of Efficient Influence Curve Components. 606 A.4.3 Discussion of Ri2,g-j^ Remainder: Finite Memory Assumption. 608 A.4.4 First Order Expansion for Online Estimation Based on Marginal Expectation of Efficient Influence Curve . A.4.5 First Order Expansion for Online Estimation Based on Conditional Expectation of Efficient Influence Curve . References. 602 603 610 612 613
Springer Series in Statistics Mark J. van det Laan • Sherri Rose Targeted Learning in Data Science Causal Inference for Complex Longitudinal Studies This textbook for graduate students in statistics, data science, and public health deals with the practical challenges that come with big, complex, and dynamic data. It presents a scientific roadmap to translate real-world data science applications into formal statisti cal estimation problems by using the general template of targeted maximum likelihood estimators. These targeted machine learning algorithms estimate quantities of interest while still providing valid inference. Targeted learning methods within data science are a critical component for solving scientific problems in the modern age. The techniques can answer complex questions including optimal rules for assigning treatment based on longitudinal data with time-dependent confounding, as well as other estimands in dependent data structures, such as networks. Included in Targeted Learning in Data Science are demonstrations with software packages and real data sets that present a case that targeted learning is crucial for the next generation of statisticians and data scientists. This book is a sequel to the first textbook on machine learning for causal inference, Targeted Learning, published in 2011. Mark van der Laan, PhD, is Jiann-Ping Hsu/Karl E. Peace Professor of Biostatistics and Statistics at UC Berkeley. His research interests include statistical methods in genom ics, survival analysis, censored data, machine learning, semiparametric models, causal inference,
and targeted learning. Dr. van der Laan received the 2004 Mortimer Spiegelman Award, the 2005 Van Dantzig Award, the 2005 COPSS Snedecor Award, the 2005 COPSS Presidential Award, and has graduated over 40 PhD students in biostatistics and statistics. Care Policy (Biostatistics) at Harvard Medical School. Her work is centered on developing and integrating innovative statisti cal approaches to advance human health. Dr. Rose’s methodological research focuses on nonparametric machine learning for causal inference and prediction. She co-leads the Health Policy Data Science Lab and currently serves as an associate editor for the Journal of the American Statistical Association and Biostatistics. Sherri Rose, PhD, is Associate Professor of Health |
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| author | Laan, Mark J. van der 1967- Rose, Sherri |
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| author_facet | Laan, Mark J. van der 1967- Rose, Sherri |
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| ctrlnum | (OCoLC)1032695055 (DE-599)DNB113630228X |
| discipline | Biologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| spelling | Laan, Mark J. van der 1967- Verfasser (DE-588)128946326 aut Targeted learning in data science causal inference for complex longitudinal studies Mark J. van der Laan, Sherri Rose Cham, Switzerland Springer [2018] © 2018 xlii, 640 Seiten Illustrationen 23.5 cm x 15.5 cm txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Big Data (DE-588)4802620-7 gnd rswk-swf Kausalität (DE-588)4030102-3 gnd rswk-swf Data Science (DE-588)1140936166 gnd rswk-swf Biostatistik (DE-588)4729990-3 gnd rswk-swf Inferenzstatistik (DE-588)4247120-5 gnd rswk-swf Maschinelles Lernen (DE-588)4193754-5 gnd rswk-swf PBT KJQ targeted minimum loss estimation targeted learning longitudinal data big data precision medicine targeted maximum likelihood estimation applied statistics causal inference super learning data science dependent data Biostatistik (DE-588)4729990-3 s Inferenzstatistik (DE-588)4247120-5 s Kausalität (DE-588)4030102-3 s Data Science (DE-588)1140936166 s DE-604 Maschinelles Lernen (DE-588)4193754-5 s Big Data (DE-588)4802620-7 s Rose, Sherri Verfasser (DE-588)1068777524 aut Springer International Publishing (DE-588)1064344704 pbl Elektronische Reproduktion 9783319653044 Erscheint auch als Online-Ausgabe 978-3-319-65304-4 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=aad0fa9173c0475ca15ba39160c6b214&prov=M&dok_var=1&dok_ext=htm Inhaltstext X:MVB http://www.springer.com/ Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030305128&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030305128&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Laan, Mark J. van der 1967- Rose, Sherri Targeted learning in data science causal inference for complex longitudinal studies Big Data (DE-588)4802620-7 gnd Kausalität (DE-588)4030102-3 gnd Data Science (DE-588)1140936166 gnd Biostatistik (DE-588)4729990-3 gnd Inferenzstatistik (DE-588)4247120-5 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
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| title | Targeted learning in data science causal inference for complex longitudinal studies |
| title_auth | Targeted learning in data science causal inference for complex longitudinal studies |
| title_exact_search | Targeted learning in data science causal inference for complex longitudinal studies |
| title_full | Targeted learning in data science causal inference for complex longitudinal studies Mark J. van der Laan, Sherri Rose |
| title_fullStr | Targeted learning in data science causal inference for complex longitudinal studies Mark J. van der Laan, Sherri Rose |
| title_full_unstemmed | Targeted learning in data science causal inference for complex longitudinal studies Mark J. van der Laan, Sherri Rose |
| title_short | Targeted learning in data science |
| title_sort | targeted learning in data science causal inference for complex longitudinal studies |
| title_sub | causal inference for complex longitudinal studies |
| topic | Big Data (DE-588)4802620-7 gnd Kausalität (DE-588)4030102-3 gnd Data Science (DE-588)1140936166 gnd Biostatistik (DE-588)4729990-3 gnd Inferenzstatistik (DE-588)4247120-5 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
| topic_facet | Big Data Kausalität Data Science Biostatistik Inferenzstatistik Maschinelles Lernen |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=aad0fa9173c0475ca15ba39160c6b214&prov=M&dok_var=1&dok_ext=htm http://www.springer.com/ http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030305128&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030305128&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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