Longitudinal data analysis

June 6, 2008 16:16 C6587 C6587˙C000 Longitudinal Data Analysis June 6, 2008 16:16 C6587 C6587˙C000 Chapman & Hall/CRC Handbooks of Modern Statistical Methods Series Editor Garrett Fitzmaurice Department of Biostatistics Harvard School of Public Health Boston, MA, U.S.A Aims and Scope The objective of the series is to provide high-quality volumes covering the state-of-the-art in the theory and applications of statistical methodology The books in the series are thoroughly edited and present comprehensive, coherent, and unified summaries of specific methodological topics from statistics The chapters are written by the leading researchers in the field, and present a good balance of theory and application through a synthesis of the key methodological developments and examples and case studies using real data The scope of the series is wide, covering topics of statistical methodology that are well developed and find application in a range of scientific disciplines The volumes are primarily of interest to researchers and graduate students from statistics and biostatistics, but also appeal to scientists from fields where the methodology is applied to real problems, including medical research, epidemiology and public health, engineering, biological science, environmental science, and the social sciences Published Titles Longitudinal Data Analysis Edited by Garrett Fitzmaurice, Marie Davidian, Geert Verbeke, and Geert Molenberghs June 6, 2008 16:16 C6587 C6587˙C000 Chapman & Hall/CRC Handbooks of Modern Statistical Methods Longitudinal Data Analysis Edited by Garrett Fitzmaurice Marie Davidian Geert Verbeke Geert Molenberghs June 6, 2008 16:16 C6587 C6587˙C000 Chapman & Hall/CRC Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2009 by Taylor & Francis Group, LLC Chapman & Hall/CRC is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Printed in the United States of America on acid-free paper 10 International Standard Book Number-13: 978-1-58488-658-7 (Hardcover) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Library of Congress Cataloging-in-Publication Data Longitudinal data analysis / editors, Garrett Fitzmaurice [et al.] p cm (Chapman and Hall/CRC series of handbooks of modern statistical methods) Includes bibliographical references and index ISBN 978-1-58488-658-7 (hardback : alk paper) Longitudinal method Multivariate analysis Regression analysis I Fitzmaurice, Garrett M., 1962- II Title III Series QA278.L66 2008 519.5 dc22 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com 2008020681 June 6, 2008 16:16 C6587 C6587˙C000 Dedication To Laura, Kieran, and Aidan — G.F To Butch, Mom, and John — M.D To Godewina, Lien, Noor, and Aart — G.V To Conny, An, and Jasper — G.M June 6, 2008 16:16 C6587 C6587˙C000 Contents Preface ix Editors xi Contributors xiii PART I: Introduction and Historical Overview Chapter Advances in longitudinal data analysis: An historical perspective Garrett Fitzmaurice and Geert Molenberghs PART II: Parametric Modeling of Longitudinal Data Chapter Parametric modeling of longitudinal data: Introduction and overview 31 Garrett Fitzmaurice and Geert Verbeke Chapter Generalized estimating equations for longitudinal data analysis 43 Stuart Lipsitz and Garrett Fitzmaurice Chapter Generalized linear mixed-effects models 79 Sophia Rabe-Hesketh and Anders Skrondal Chapter Non-linear mixed-effects models 107 Marie Davidian Chapter Growth mixture modeling: Analysis with non-Gaussian random effects 143 Bengt Muth´en and Tihomir Asparouhov Chapter Targets of inference in hierarchical models for longitudinal data 167 Stephen W Raudenbush PART III: Non-Parametric and Semi-Parametric Methods for Longitudinal Data Chapter Non-parametric and semi-parametric regression methods: Introduction and overview 191 Xihong Lin and Raymond J Carroll Chapter Non-parametric and semi-parametric regression methods for longitudinal data 199 Xihong Lin and Raymond J Carroll June 6, 2008 16:16 C6587 C6587˙C000 viii CONTENTS Chapter 10 Functional modeling of longitudinal data 223 Hans-Georg Mă uller Chapter 11 Smoothing spline models for longitudinal data 253 S J Welham Chapter 12 Penalized spline models for longitudinal data 291 Babette A Brumback, Lyndia C Brumback, and Mary J Lindstrom PART IV: Joint Models for Longitudinal Data Chapter 13 Joint models for longitudinal data: Introduction and overview 319 Geert Verbeke and Marie Davidian Chapter 14 Joint models for continuous and discrete longitudinal data 327 Christel Faes, Helena Geys, and Paul Catalano Chapter 15 Random-effects models for joint analysis of repeated-measurement and time-to-event outcomes 349 Peter Diggle, Robin Henderson, and Peter Philipson Chapter 16 Joint models for high-dimensional longitudinal data 367 Steffen Fieuws and Geert Verbeke PART V: Incomplete Data Chapter 17 Incomplete data: Introduction and overview 395 Geert Molenberghs and Garrett Fitzmaurice Chapter 18 Selection and pattern-mixture models 409 Roderick Little Chapter 19 Shared-parameter models 433 Paul S Albert and Dean A Follmann Chapter 20 Inverse probability weighted methods 453 Andrea Rotnitzky Chapter 21 Multiple imputation 477 Michael G Kenward and James R Carpenter Chapter 22 Sensitivity analysis for incomplete data 501 Geert Molenberghs, Geert Verbeke, and Michael G Kenward Chapter 23 Estimation of the causal effects of time-varying exposures 553 James M Robins and Miguel A Hern´ an Author Index .601 Subject Index 613 June 6, 2008 16:16 C6587 C6587˙C000 Preface Longitudinal studies play a prominent role in the health, social, and behavioral sciences, as well as in public health, biological and agricultural sciences, education, economics, and marketing They are indispensable to the study of change in an outcome over time By measuring study participants repeatedly through time, longitudinal studies allow the direct study of temporal changes within individuals and the factors that influence change Because the study of change is so fundamental to almost every discipline, there has been a steady growth in the number of studies using longitudinal designs Moreover, the designs of many recent longitudinal studies have become increasingly complex There is a wide variety of challenges that arise in analyzing longitudinal data By their very nature, the repeated measures arising from longitudinal studies are multivariate and have a complex random-error structure that must be appropriately accounted for in the analysis Longitudinal studies also vary in the types of outcomes of interest Although linear models have been the dominant approach for the analysis of longitudinal data when the outcome is continuous, in many applications the pattern of change is more faithfully characterized by a function that is non-linear in the parameters In other settings, parametric models for longitudinal data are not sufficiently flexible to adequately capture the complex patterns of change in the outcome and their relationships to covariates; instead, more flexible functional forms are required When the outcome of interest is discrete, there are broad classes of longitudinal models that may be suitable for analysis However, there are distinctions among these models not only in approach, but in their relative targets of inference as well As a result, greater care is required in the modeling of discrete longitudinal data Another issue that complicates the analysis is the inclusion of time-varying covariates in models for longitudinal data Longitudinal studies permit repeated measures not only of the outcome, but also of the covariates The incorporation of covariates that change stochastically over time poses many intricate and complex analytic issues Finally, longitudinal studies are also more prone to problems of missing data and attrition The appropriate handling of missing data continues to pose one of the greatest challenges for the analysis of longitudinal data These, and many other issues, increase the complexity of longitudinal data analysis The last 20 years have seen many remarkable advances in statistical methodology for analyzing longitudinal data Although there are a number of books describing statistical models and methods for the analysis of longitudinal data, to date there is no volume that provides a comprehensive, coherent, unified, and up-to-date summary of the major advances This has provided the main impetus for Longitudinal Data Analysis This book constitutes a carefully edited collection of chapters that synthesize the state of the art in the theory and application of longitudinal data analysis The book is comprised of 23 expository chapters, dealing with five broad themes These chapters have been written by many of the world’s leading experts in the field Each chapter integrates and illustrates important research threads in the statistical literature, rather than focusing on a narrowly defined topic Each part of the book begins with an introductory chapter that provides useful background material and a broad overview to set the stage for subsequent chapters The book combines a good blend of theory and applications; many of the chapters include examples and case studies using data sets drawn from various disciplines Many of the data sets used to illustrate methods can be downloaded from the Web site for the book June 6, 2008 16:16 x C6587 C6587˙C000 PREFACE (http://www.biostat.harvard.edu/∼fitzmaur/lda), as can sample source code for fitting certain models Although our coverage of topics in the book is quite broad, it is certainly not complete Our selection of topics required judicious choices to be made; we have decided to place greater emphasis on statistical models and methods that we think likely to endure The book is intended to have a broad appeal It should be of interest to all statisticians involved either in the development of methodology or the application of new and advanced methods to longitudinal research We anticipate that the book will also be of interest to quantitatively oriented researchers from various disciplines Finally, the compilation of this book would not have been possible without the willingness, persistence, and dedication of each of the contributing authors; we thank them wholeheartedly for their tremendous efforts and the excellent quality of the chapters they have written We would also like to thank the many friends and colleagues who have helped us produce this book A special word of thanks to Butch Tsiatis and Nan Laird who reviewed several chapters and provided insightful feedback Last, but not least, we thank Rob Calver, Aquiring Editor at Chapman & Hall/CRC Press of Taylor & Francis, for encouragement to undertake this project The original seeds of this book arose from conversations Rob Calver had with a number of distinguished colleagues We are grateful to all, most particularly to Rob, for his strong belief in the project and his enthusiasm and perseverance to see the project through from beginning to end Garrett Fitzmaurice Boston, Massachusetts Marie Davidian Raleigh, North Carolina Geert Verbeke Leuven, Belgium Geert Molenberghs Diepenbeek, Belgium July 2, 2008 18:0 C6587 C6587˙C024 604 Follmann, D A., 224, 402, 424, 433, 437, 439, 443, 444, 445, 446, 448, 449, 450, 509 Ford, C., 144 Foster, J J., 525 Foster, P J., 228 Fozard, J L., 368 Francis, D., 152 Freedman, L S., 94 Freeman, D H., 13, 44 Freeman, J L., 13, 44 Freeman, S N., 526 Friedman, J., 255, 297, 302 Fudala, P J., 445 Fuller, W A., 455 G Gail, M H., 39 Galecki, A T., 127, 321, 372 Gallant, A R., 39, 100, 128, 130 Gallop, R J., 450 Gange, S J., 51 Gao, J., 192 Gao, S., 439 Gardner, M F., 234 Garrett, E., 359 Gasser, T., 191, 224, 228, 229, 230, 231 Geisser, S., 4, Gelber, R D., 402 Gelfand, A E., 129, 415 Gelman, A., 95, 114, 129, 517, 547 Gervini, D., 230, 231 Geyer, C J., 279 Geys, H., 17, 94, 328, 329, 330, 333, 334, 337, 347, 374 Ghidey, W., 39 Gibaldi, M., 110, 112 Gibbons, R D., 18, 402, 546 Giesbrecht, F G., 302 Gijbels, I., 192, 193, 226 Gilks, W R., 95, 129, 486 Gill, R D., 351, 353, 454, 458, 459, 472, 483 Gillespie, B W., 363 Gillings, D B., 13 Gilmour, A R., 80, 260, 265, 273, 276 Giltinan, D M., 22, 108, 110, 111, 112, 113, 114, 116, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 132, 133, 135, 136, 375 Glonek, G F V., 13, 45, 74, 402 Glymour, C., 557, 593 Glynn, R J., 402, 416, 531 Godambe, V P., 15 Goetghebeur, E J T., 224, 400, 503, 505, 507, 522, 525, 527, 531 AUTHOR INDEX Gogel, B J., 276 Goldman, N., 93 Goldstein, A M., 39 Goldstein, H., 7, 82, 89, 92, 93, 97, 168, 171, 257, 375, 486 Golmard, J L., 125 Goodhardt, G J., 17 Goodman, L A., 20 Gordon-Salant, S., 368 Grambsch, P M., 351 Gray, S M., 374, 387 Green, P J., 192, 193, 194, 205, 255, 260, 261, 304 Greenberg, E., 95 Greene, T., 363, 433, 437 Greenhouse, S W., 4, Greenland, S., 10, 560 Greenwood, M., 17, 80 Greullich, R C., 367 Griffiths, D A., 17 Grizzle, J E., 5, 7, 13, 44, 275 Gu, C., 207, 258, 280, 314 Gueorguieva, R., 377 Gumbel, E J., 11, 12, 14 Guo, W., 208, 273, 363, 379 Guo, X., 363 Gupta, S., 135 H Ha, I D., 363 Hajivassiliou, V A., 92 Hall, D B., 56, 135 Hall, P., 195, 203, 207, 208, 229, 239, 240 Hamagami, F., 546 Hancock, G R., 382, 383 Haneuse, S J P A., 555 Hansen, L P., 469 Hansen, M H., 192, 194, 455 Hă ardle, W., 192 Harezlak, J., 285 Harrington, D P., 13, 45, 51, 56, 62, 71, 72, 74, 503 Harris, S C., 113 Hartley, H O., 415 Harville, D A., 7, 8, 79 Haseman, J K., 12, 17 Hashemi, R., 363 Hastie, T G., 235 Hastie, T J., 194, 209, 210, 255, 257, 258, 266, 285, 297, 301, 302 Hauck, W W., 39, 55 Hausman, J A., 85 He, G., 225, 242 July 2, 2008 18:0 C6587 C6587˙C024 AUTHOR INDEX Heagerty, P J., 22, 34, 39, 74, 85, 88, 119, 121, 132, 168, 169, 170, 172, 182, 186, 191, 223, 351, 374, 449 Heckman, J J., 80, 86, 355, 401, 417, 439, 531 Heckman, N E., 192, 226, 233, 280, 282 Hedeker, D., 18, 381, 402, 546 Heeringa, S G., 487 Heitjan, D F., 371, 377, 454, 484, 517, 547 Helms, R W., 376, 415 Henderson, C R., Henderson, R., 351, 355, 356, 359, 360, 362 Hendry, D F., 10 Henein, M., 351, 355 Hens, N., 503, 531, 533 Herman, B., 191, 427 Hern´ an, M A., 554, 555, 557, 559, 560, 561, 565, 573, 584, 585, 593 Hern´ andez-D´ıaz, S., 554, 573 Herzog, T., 484 Heyting, A., 423 Hildesheim, A., 39 Hills, S E., 415 Hinde, J., 80, 152 Ho, D D., 115 Hobert, J P., 19, 95 Hogan, J W., 191, 352, 402, 403, 409, 419, 427, 433, 439, 546 Holland, P W., 50 Hollis, M., 546 Hoover, D R., 201, 210 Horowitz, J L., 428 Horton, N J., 62, 63, 477 Horvitz, D G., 60, 405, 454, 455 Hosmer, D W., 63 Hosseini-Nasab, M., 239 Hotelling, H., 225 Hougaard, P., 351 Hsieh, F., 363 Hu, F.-C., 10 Hu, P H., 471 Huang, C., 210 Huang, J., 191, 207, 210 Huang, W Z., 359 Huang, Y., 115 Hubbard, A., 471, 593 Huber, P J., 49 Huet, S., , 415 Huggins, R., 206 Hughes, H M., Hunter, A., 144 Hurwitz, W N., 455 Huynh, H., 605 I Ialongo, L N., 144, 155 Ibrahim, J G., 61, 62, 114, 363, 472 Ilk, O., 381 Imbens, G W., 148 Intermittent Positive Pressure Breathing Trial Group, 441 International Conference on Harmonisation E9 Expert Working Group, 548 Irrizarry, R., 471 Irwin, S., 338 Isaki, C T., 455 J Jacobsen, M., 454 Jacqmin-Gadda, H., 363, 377 Jaffe, J H., 445 Jaffr´ezic, F., 279 James, G., 224, 235, 239, 242 James, M K., 401, 441 Jansen, I., 502, 503, 531, 533 Janssen, P., 89 Jarvelin, M R., 148 Jennrich, R I., 8, 415, 503, 504 Jewell, N P., 55, 593 Jiang, L M., 114, 129 Jin, Z., 202 Jo, B., 143, 145, 148 Johnson, R A., 327 Johnson, R E., 445 Johnston, G., 56 Jolivet, E., 415 Jones, B L., 153 Jones, C L., 62, 63 Jones, K., 89 Jones, M C., 192, 193, 226, 228, 239 Jones, P B., 148 Jones, P W., 492 Jørgensen, B., 371 K Kalbfleisch, J D., 39, 85 Kam, C.-M., 483, 487, 492 Kaplan, D., 546 Kaplan, S., 56, 64, 65 Karim, M R., 19, 94, 95 Karlin, S., 449 Karlsson, M O., 132, 135 Kass, R E., 95, 152 Ke, C., 135, 210, 224, 285, 231 Keiding, N., 351, 353, 454 Keiley, M G., 379 Keles, S., 471 Kellam, S G., 143, 144, 145, 155 Kendall, D., 255 July 2, 2008 18:0 C6587 C6587˙C024 606 Kenward, M G., 51, 195, 205, 255, 259, 264, 265, 267, 271, 273, 274, 279, 281, 282, 283, 285, 291, 307, 352, 400, 401, 402, 416, 422, 423, 424, 477, 479, 480, 490, 491, 495, 502, 503, 505, 507, 513, 514, 520, 521, 522, 525, 531, 532, 533, 534, 535, 536, 541, 542, 545, 546 Ketter, T., 442 Khoo, S T., 143, 145, 152 Kiecolt-Glaser, J., 376 Kiers, H A L., 381 Kim, C., 376 Kim, K., 51 Kimeldorf, G S., 255, 279, 298 Kirkpatrick, M., 233 Klaassen, C A J., 454 Klein, B., 314 Klein, L L., 368 Klein, R., 51, 314 Kleinman, K P., 477 Kluin-Nelemans, H C., 363 Kneib, T., 195 Kneip, A., 230, 231 Knook, D., 487 Ko, D., 442 Koch, G G., 13, 44, 97 Kă ohler, W., 191, 224, 228, 230, 231 Kohn, R., 258 Kooper, K L., 487 Kooperberg, C., 192, 194 Korkontzelou, C., 352, 409 Korn, E L., 18, 21 Kreuter, F., 153 Krzanowski, W J., 327 Kuh, E., 62 Kuk, A Y C., 19, 57 Kunselman, A R., 401, 424, 437 Kuo, W., 382, 383 Kupper, L L., 12, 17 Kurland, B F., 449 Kwon, H D., 115 L Lackland, D., 67 Lai, T L., 135 Lai, W W., 56, 64, 65 Laird, N M., 7, 8, 10, 13, 18, 44, 45, 51, 53, 56, 59, 62, 65, 71, 72, 79, 85, 119, 144, 168, 171, 176, 191, 328, 351, 352, 373, 375, 376, 400, 401, 402, 403, 404, 415, 416, 423, 424, 427, 433, 437, 439, 503, 525, 531, 546 Lakatta, E G., 367 Lambert, P., 246 Land, K C., 100, 147, 153, 154, 155, 378 Landis, J R., 13, 44, 51, 401, 424, 437 AUTHOR INDEX Landis, P K., 148, 244 Lang, J B., 13, 45, 74 Lang, S., 195, 207, 209 Lange, K L., 415 Lange, M., 427, 439 Lanoy, E., 585 Largo, R., 224 Larizza, C., 357 Larsen, K., 89 Laub, J H., 147 Laudolff, J., 144 Lavange, L M., 415 Law, N J., 363 Lawley, D N., 80 Lawrence, F R., 382, 383 Lawton, W H., 210, 235 le Cessie, S., 363 Lee, H., 56 Lee, J J., 235 Lee, J W., 263, 267, 268 Lee, K H., 135 Lee, S L., 402 Lee, T C M., 224, 314 Lee, Y J., 19, 94, 363 Leek, J T., 191 Lehnen, R G., 13, 44 Lehtinen, V., 148 Lei-Gomez, Q., 592 Lemeshow, S., 63 Leng, X., 230, 231 Leonard, J M., 115 Leport, C., 377 Leroux, B., 93 Lesaffre, E., 13, 39, 45, 51, 74, 90, 148, 158, 347, 400, 401, 423, 424, 503, 531, 534, 541, 546 Leuchter, A F., 144 Leurgans, S E., 225 Li, B., 56 Li, F., 378 Li, H., 191 Li, H G., 503, 531 Li, K H., 479 Li, L., 135, 472, 473 Li, R., 214 Li, X., 230, 231 Liang, H., 192, 210 Liang, K.-Y., 13, 15, 21, 34, 44, 45, 46, 48, 50, 52, 55, 56, 58, 71, 73, 74, 85, 119, 121, 132, 168, 183, 191, 201, 223, 351, 373, 374, 375, 399, 457, 495 Liao, J., 143, 145 Lim, E., 351, 355 Lin, D Y., 64, 191, 210, 363 Lin, H., 148, 363, 471 Lin, J Y., 148 July 2, 2008 18:0 C6587 C6587˙C024 AUTHOR INDEX Lin, S K., 247 Lin, X H., 18, 93, 127, 135, 191, 193, 195, 201, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 224, 255, 267, 268, 285, 291, 307, 314, 383, 387, 427 Lin, Y., 144, 155, 237 Lindley, D V., 168, 171 Lindsay, B G., 56, 100 Lindstrom, M J., 127, 135, 191, 210, 231 Linton, K L., 51 Linton, O B., 206 Lipshultz, S E., 56, 64, 65 Lipsitz, S R., 13, 21, 45, 51, 53, 56, 58, 61, 62, 63, 67, 71, 72, 74, 401, 402, 416, 472, 477, 503, 546 Liti`ere, S., 39 Littell, R C., 125, 415 Little, R J A., 148, 152, 224, 292, 327, 352, 353, 397, 400, 401, 402, 410, 411, 413, 414, 415, 416, 417, 419, 420, 422, 433, 439, 479, 484, 490, 491, 502, 503, 504, 505, 509, 512, 521, 525, 546 Liu, A., 135, 268 Liu, C., 100 Liu, D., 115 Liu, L C., 381 Liu, M., 486 Liu, X., 230, 231, 232, 233 Longford, N T., 93, 268, 375 Lord, F M., 80 Loughran, T., 147, 153, 154, 155 Louis, T A., 39, 74, 88, 130, 158, 224, 424, 478 Luan, Y., 191 Ludden, T M., 113 Lumley, T., 51 Lunceford, J K., 61, 472 Lundbye-Christensen, S., 371 Luo, Z., 257 Lynch, K G., 147, 152, 153 M Ma, P., 207, 258, 314 MacCallum, R., 376 Mackenzie, M L., 257 Maes, B., 369, 378 Magder, L S., 39, 100 Maggio, M S., 210 Maitre, P O., 130 Majumdar, D., 131, 135, 437, 439 Makov, U E., 158 Malarkey, W., 376 Maldonado, Y M., 210 Malfait, N., 242 Mallet, A., 125, 128 Mallinckrodt, C., 502, 546 607 Malow, B., 442 Mammen, E., 206 Mammitzsch, V., 228 Mancl, L A., 54 Mandema, J W., 131 Manski, C F., 428 Maracy, M., 148 Marathe, V V., 125 Markowitz, M., 115 Marron, J S., 224 Marshall, B C., 293, 312 Marshall, G., 377, 378, 379 Marshall, S., 293, 312 Marx, B D., 192, 194, 207, 257, 284, 297 Mas, A., 226, 240 Maslen, T K., 492 Mason, W M., 80, 171 Masyn, K., 143, 145, 148, 151 Matsuyama, Y., 376 Mayer, L S., 144 McArdle, B H., 257 McArdle, J J., 379, 382, 546 McCall, P L., 147, 153, 154, 155 McCullagh, P., 13, 45, 63, 74, 167, 204, 495 McCulloch, C E., 19, 88, 92, 93, 148, 363, 415, 439 McDonald, J W., 13 McFadden, D., 466 McIntosh, K., 64, 65 McLachlan, G J., 144, 152, 153, 160 McNee, R C., Medendorp, S V., 51 Melino, A., 355 Melmon, K L., 125 Meng, X L., 92, 421, 495 Mentr´e, F., 128 Meredith, W., 102, 378, 380 Merlo, J., 89 Mesbah, M., 363 Metter, E J., 368 Meulders, M., 517, 547 Mezzetti, M., 114 Michiels, B., 402, 416, 479, 490, 521, 546 Miglioretti, D L., 153 Miller, M E., 51, 401, 424, 441 Milliken, G A., 125, 415 Moffitt, T E., 147 Molenaar, P C M., 371, 378 Molenberghs, G., 8, 13, 17, 20, 39, 45, 51, 56, 58, 62, 74, 81, 92, 94, 119, 132, 171, 264, 274, 321, 325, 328, 329, 330, 331, 334, 337, 347, 373, 374, 375, 384, 400, 401, 402, 416, 423, 424, 477, 479, 490, 491, 495, 496, 502, 503, 504, 505, 507, 512, 513, 514, 521, 522, 525, 531, 532, 533, 534, 541, 545, 546 Molinari, L., 191, 224, 228, 230, 231 July 2, 2008 18:0 C6587 C6587˙C024 608 Montgomery, A B., 293, 312 Moodie, D S., 56, 64, 65 Morabia, A., 374, 377 Morgan, B J T., 525, 526 Morgan, M., 144 Mori, M., 402, 424, 437 Morrell, C H., 148, 244, 368 Morris, J S., 209, 234 Mountford, W K., 67 Moyeed, R A., 225 Mă uller, H G., 191, 224, 226, 228, 229, 230, 231, 232, 233, 236, 237, 239, 240, 242, 314 Mă uller, P., 100, 128, 129 Murphy, J M., 373 Murphy, S A., 585 Murray, G D., 415, 423 Muth´en, B O., 39, 94, 143, 144, 145, 148, 149, 151, 152, 153, 378, 382, 546 Muth´en, L., 144, 148 N Nadaraya, E A., 229 Nagin, D S., 100, 147, 152, 153, 154, 155, 378, 382 Nan, B., 471 Natarajan, R., 95 Nelder, J A., 9, 13, 19, 45, 63, 74, 79, 94, 167, 204, 314, 495 Neugebauer, R., 472 Neuhaus, J M., 39, 85 Neumann, A U., 115 Newey, W K., , 466 Neyman, J., 86 Ng, E S W., 92 Ngo, L., 114 Nie, L., 131, 135, 437, 439 Nordheim, E V., 400, 503, 525 N´ un ˜ez-Ant´ on, V., 279 Nychka, D W., 100, 194 Nylund, K L., 152 O O’Brien, L M., 368, 372, 373 Ochi, Y., 12, 328 O’Connell, M., 337, 339 Ohashi, Y., 376 Olkin, I., 327 Olsen, M K., 151 Oort, F J., 380, 381, 382 Opsomer, J., 195 Orav, E J., 53, 56, 64, 65 Orellana, L., 585, 586, 587 AUTHOR INDEX Otake, M., 17 Otto, K L., 293, 312 P Page, H., 148 Page, J., 593 Paik, M C., 54, 59 Pan, H Q., 257 Pan, J., 56 Pan, W., 62 Park, T S., 363, 402 Parmar, M K B., 94 Patterson, H D., 255, 262 Pawitan, Y., 94 Payne, R W., 276 Pearl, J., 557, 594, 595 Pearson, J D., 148, 244, 368 Pee, D., 39 Peel, D., 144, 152, 153, 160 Pepe, M S., 10, 53, 200, 293, 312 Pepper, J., 351, 355 Perelson, A S., 115 Perrier, D., 110, 112 Petersen, J H., 89 Petersen, M L., 585, 592 Pfeiffer, R M., 39 Pickles, A., 83, 90, 91, 92, 97, 98, 100, 102 Pierce, D A., 17, 18, 80 Pietra, M L., 210 Pinheiro, J C., 100, 126, 127, 128, 130, 135, 168, 292, 415 Platt, R., 93 Pletcher, S D., 279 Potthoff, R F., 5, 7, 503 Poursat, M.-A., 415 Pousse, A., 239 Prader, A., 191, 224, 228, 230, 231 Pregibon, D., 62 Preisler, H K., 80 Preisser, J S., 62 Prentice, R L., 12, 15, 17, 45, 50, 51, 58, 74, 328, 332, 373 Priestley, M B., 228 Prosser, R., 94 Pulkstenis, E P., 401, 424, 437 Q Qaqish, B F., 13, 45, 58, 62, 71, 74 Qu, A., 56 Qu, Y., 51 Quale, C M., 471 Quan, H., 424 Quan, J M., 293, 312 July 2, 2008 18:0 C6587 C6587˙C024 AUTHOR INDEX R Rabe-Hesketh, S., 81, 82, 83, 84, 86, 89, 90, 91, 92, 97, 98, 100, 102 Racine-Poon, A., 129, 415 Rae, A L., 80 Raftery, A E., 152 Raghunathan, T E., 479, 487 Ramsay, J O., 224, 226, 230, 231, 235, 237, 241, 242, 280, 282, 314 Ramsey, B W., 293, 312 Randolph, J F., 210 Rao, C R., 6, 7, 235 Rao, J N K., 415 Rasbash, J., 92, 93, 94 Rasch, G., 86 Ratcliffe, S J., 363 Rathouz, P J., 153 Raudenbush, S W., 18, 84, 94, 168, 169, 171, 172, 176, 371, 375 Raz, J., 191, 195, 205, 208, 210, 211, 212, 216, 255, 267 Rebok, G W., 144 Reboussin, B A., 382, 401, 424, 441 Reboussin, D M., 382 Regan, M M., 328, 329, 335 Reinfurt, D W., 13, 44 Reinsch, C., 304 Reinsel, G., 372, 376 Renard, D., 94 Ribaudo, H J., 377 Rice, J A., 191, 195, 201, 205, 207, 210, 224, 226, 235, 239, 246, 255, 257, 273, 291, 292, 307, 308, 314 Richard, J F., 10 Richardson, S., 486 Ridder, G., 355 Ripley, B D., 94 Ritov, Y., 454, 459 Ritter, L., 13 Ritz, J., 88 Rizopoulos, D., 546 Robins, J M., 10, 60, 61, 400, 405, 423, 454, 458, 459, 461, 462, 464, 466, 467, 468, 470, 471, 472–473, 482, 483, 490, 495, 502, 503, 546, 547, 554, 555, 557, 559, 560, 561, 563, 564, 565, 567, 568, 573, 579, 584, 585, 586, 587, 592, 593, 595, 596 Robinson, G K., 96, 292, 300 Rochon, J., 363, 374 Rodriguez, G., 93 Roeder, K., 100, 147, 152, 153 Roger, J H., 264, 274 Rogers, C E., 275 Romain, Y., 239 Rønn, B B., 230 609 Rosenbaum, P R., 400, 556, 573 Rosenberg, B., 125 Rosenberg, E S., 115 Rosenberger, W F., 505, 506, 508, 525 Rosenheck, R A., 471 Rosner, B A., 372 Rosner, G L., 128, 129 Rotnitzky, A G., 10, 45, 53, 55, 60, 61, 74, 400, 405, 423, 454, 461, 464, 466, 467, 468, 470, 471, 472–473, 490, 495, 502, 503, 546, 547, 555, 584, 585, 586, 587, 592 Rovine, M J., 378 Rowell, J G., Roy, J., 352, 383, 387, 409, 424 Roy, S N., 5, 7, 503 Royall, R M., 49 Rubin, D B., 8, 59, 65, 95, 148, 152, 171, 176, 292, 352, 353, 396, 399, 400, 401, 402, 404, 405, 410, 411, 413, 414, 416, 417, 421, 422, 424, 428, 433, 454, 477, 479, 480, 481, 482, 483, 484, 494, 502, 503, 504, 505, 506, 507, 508, 509, 512, 517, 525, 531, 556 Rudas, T., 45, 74 Ruppert, D., 133, 192, 193, 194, 205, 207, 257, 263, 267, 268, 283, 284, 285, 292, 297, 299, 304, 357 Rutledge, J H., 377, 378, 379 Ruud, P A., 92 Ryan, L M., 17, 114, 328, 374 S Sampson, R J., 147 Sandler, H M., 363 Sands, B R., 17, 18, 80 Sarda, P., 226, 235, 240 Sarma, A V., 487 Sarndal, C E., 455, 456 Sayer, A G., 382 Schafer, J L., 151, 413, 477, 482, 483, 484, 486, 487, 492, 496 Schall, R., 18 Scharfstein, D O., 61, 400, 454, 461, 468, 471, 472, 490, 503, 547, 555, 584, 592 Scheff´e, H., 4, Scheines, R., 557, 593 Schenker, N., 477, 484 Schilling, S G., 92, 151 Schluchter, M D., 8, 64, 65, 327, 363, 401, 415, 424, 433, 437, 503, 504 Schneyer, L., 427 Schoenfeld, D., 376 Schork, M A., 210 Schumitzky, A., 128 Schwarz, G., 152 Scott, A J., 51 July 2, 2008 18:0 C6587 C6587˙C024 610 Scott, E L., 86 Searle, S R., 93, 415 Seber, G A F., 110, 295 Secrest, D., 90 Seifert, B., 229 Self, S G., 21 Seltzer, M., 148 Sen, P K., 376 Service, S K., 226 Severini, T A., 56 Shah, A., 376 Shapiro, B., 210 Sharma, D., 371, 377 Shedden, K., 39, 143, 148, 378 Sheiner, L B., 125, 126–127, 131, 132, 135 Shi, M., 208, 235 Shih, M C., 135 Shih, W J., 424 Shock, N W., 367 Silverman, B W., 192, 193, 194, 205, 206, 224, 225, 226, 230, 231, 235, 237, 255, 260, 261, 280, 298, 304, 314 Singer, B., 355 Sinha, D., 363 Sivo, S A., 380, 381 Skellam, J G., 17, 80 Skinner, C., 402, 416, 546 Skrondal, A., 81, 82, 84, 86, 89, 90, 91, 92, 97, 98, 100, 102 Slate, E H., 148, 363 Smith, A F M., 129, 158, 168, 171, 415 Smith, A L., 293, 312 Smith, P W F., 13, 525 Smith, T J., 114 Snell, E J., 46 Snijders, T A B., 84 Song, P X K., 371 Song, X A., 363 Sopko, G., 56, 65 Sotto, C., 513, 514 Sousa, I., 351, 355 Sowden, R R., 12, 17, 18 Sowers, M F., 191, 195, 205, 208, 210, 211, 212, 216, 255, 267, 285, 307 Speckman, P., 192 Speed, T P., 255, 298 Speizer, F E., 21 Spencer, S., 492 Spiegelhalter, D J., 94, 95, 129, 486 Spiegelman, D., 88 Spiessens, B., 39, 90, 546 Spirtes, P., 557, 593 Stadtmă uller, U., 242 Stanish, W M., 13 Staniswalis, J G., 235 Stanski, D R., 130 AUTHOR INDEX Starc, T J., 56, 64, 65 Starmer, C F., 13, 44 Staudenmayer, J., 285, 379 Steele, F., 94 Stefanov, I., 255 Stegun, I A., 447 Steimer, J L., 125 Stein, M L., 354 Stern, H S., 506, 507, 508, 525 Stertz, B., 442 Stiratelli, R., 18, 168 Stokes, M E., 97 Stone, C J., 192, 194 Stoolmiller, M., 379 Storey, J D., 191 Stram, D O., 263, 267, 268 Strauss, D., 337, 338 Strawderman, R L., 471 Stroud, A H., 90 Stroup, W W., 125, 415 “Student” (Gosset, W S.), Su, T L., 547 Subramanian, S V., 89 Sued, M., 592 Sueyoshi, G., 355 Sugar, C A., 235, 239 Suh, E B., 424, 437, 448, 449 Sun, L., 371 Swensson, B., 455, 456 Sy, J P., 208, 377 Sylvestre, E A., 210, 235 T Tancredi, D J., 376 Tanner, M A., 95, 413 Tate, R F., 327 Taylor, H M., 449 Taylor, J M G., 208, 224, 235, 363, 377, 415, 486 Taylor, M G., 208, 487 Tchetgen, E., 472, 473 ten Berge, J M F., 381 Ten Have, T R., 148, 363, 374, 377, 401, 424, 437, 441, 450 Tharm, D., 258 Theodore, W H., 442 Theodorou, P., 351, 355 Therneau, T M., 351 Thi´ebaut, R., 377 Thijs, H., 400, 402, 479, 491, 502, 503, 521, 531, 534, 541, 546 Thomas, A., 95, 129 Thomas, D C., 322 Thompson, D J., 60, 405, 454, 455 July 2, 2008 18:0 C6587 C6587˙C024 AUTHOR INDEX Thompson, R., 255, 259, 260, 262, 263, 264, 265, 273, 276, 278, 279, 281, 282, 283, 285 Thompson, S G., 377 Thomson, D., 130 Thum, Y M., 378 Tibshirani, R J., 194, 209, 210, 255, 257, 258, 266, 291, 292, 297, 301, 302, 441 Timmerman, M E., 381 Tisak, J., 102, 378, 380 Titterington, D M., 158 Tobin, J D., 367 Tolboom, J T B M., 423 Tompkins, R G., 191 Tornoe, C W., 127 Tran, H T., 115 Tremblay, R E., 378, 382 Troxel, A B., 363, 503 Truong, Y K., 192, 194 Tseng, Y K., 363 Tsiatis, A A., 63, 322, 323, 352, 354, 355, 358, 363, 401, 437, 471, 482, 502 Tsonaka, R., 546 Tsutakawa, R D., 171, 176 Tu, X M., 322, 401, 424, 437 Tucker, L R., 80 Turkkan, J S., 144 Turnbull, B W., 148, 363 U Uebersax, J S., 100 Upsdell, M P., 286 Uryniak, T J., 97 V Vach, W., 400, 503, 531 van Buuren, S., 477, 487 van der Laan, M J., 61, 454, 458, 459, 462, 470, 471, 472, 473, 555, 585, 592, 593 van der Vaart, A W., 295, 454, 472, 473 van Houwelingen, H C., 363 Van Mechelen, I., 517, 547 Van Steen, K., 503, 531 Vangeneugden, T., 546 Vanrenterghem, Y., 369, 378 Vansteelandt, S., 471, 472–473, 522 Vasiljev, K M., 293, 312 Vasquez-Barquero, J L., 148 Vehovar, V., 506, 507, 508, 525 Venables, W N., 94 Verbeke, G., 8, 20, 39, 81, 92, 119, 132, 148, 158, 171, 264, 274, 321, 325, 331, 369, 373, 375, 377, 378, 384, 385, 387, 400, 402, 479, 490, 496, 502, 503, 504, 505, 512, 517, 531, 532, 533, 534, 541, 546, 547 611 Verbyla, A P., 195, 205, 255, 262, 265, 267, 269, 273, 291, 307 Verme, C N., 113 Verotta, D., 131 Vieu, P., 226 Vogel, J S., 237 Vonesh, E F., 127, 131, 135, 363, 415, 433, 437, 439 W Wadsworth, M E., 148 Wahba, G., 192, 193, 208, 216, 255, 257, 258, 279, 281, 298, 299, 314 Wakefield, J C., 113, 129, 130 Walker, S G., 128 Walters, D E., Wand, M P., 192, 193, 194, 207, 226, 257, 267, 268, 283, 284, 285, 292, 297, 299, 304 Wang, C P., 143, 145, 153 Wang, H., 131, 135, 437, 439 Wang, J L., 224, 225, 229, 239, 242, 243, 244, 245, 246, 314, 363 Wang, N Y., 135, 193, 195, 202, 203, 205, 206, 210, 213, 214, 224, 482 Wang, S., 144, 155, 210 Wang, S A., 424, 437, 448, 449 Wang, Y D., 56, 135, 195, 205, 210, 224, 231, 255, 268, 273, 275, 285, 291, 307, 314, 379, 401, 420, 525, 546, 592 Wang, Z., 74, 88 Wang-Clow, F., 427, 439 Ware, J H., 7, 8, 18, 21, 44, 79, 85, 119, 144, 168, 171, 176, 191, 351, 352, 375, 401, 415, 427, 437, 439 Wasserman, L., 563 Watson, G S., 229 Wedderburn, R W M., 9, 15, 48, 49, 73, 79 Wei, J T., 487 Wei, L J., 64 Weisberg, S., 62 Weiss, R E., 208, 235 Welham, S J., 195, 205, 255, 259, 263, 264, 265, 267, 269, 271, 273, 276, 281, 282, 283, 285, 291, 307 Wellner, J A., 454, 471 Wells, M T., 224 Welsch, R E., 62 Welsh, A H., 193, 195, 203, 205, 206, 224 Wermuth, N., 327 Werthamer-Larsson, L., 144, 155 West, M., 80 Wheeler, L., 144 White, H., 49 White, I M S., 260, 265, 273, 278, 279 White, I R., 479, 527 July 2, 2008 18:0 C6587 C6587˙C024 612 White, S., 442 Whittemore, A S., 18, 21 Wichern, D W., 327 Wild, C J., 110 Wild, P., 95 Wilkinson, C., 148 Wilkinson, G., 148 Wilkinson, G N., 275 Wilks, S S., 62 Willett, J B., 379 Williams, D., 17 Williams, G W., 51 Williamson, J M., 62 Williams-Warren, J., 293, 312 Willis, R J., 80 Wilson, R S., 376 Wishart, J., Witte, E A., 144 Wolfinger, R D., 18, 92, 125, 127, 268, 337, 339, 415 Wong, G Y., 80, 171 Wong, S P., 135 Wong, W H., 95 Wood, S N., 209, 285 Woodworth, G G., 402, 424, 437 Woolson, R F., 13, 402, 424, 437 Wretman, J H., 455, 456 Wright, R L., 455 Wu, C., 191, 207, 210, 224, 235 Wu, C O., 201, 207, 210, 242, 257, 307 Wu, H L., 115, 135, 209, 210 Wu, L., 135 Wu, M C., 352, 354, 401, 402, 403, 424, 427, 433, 437, 439, 446, 450, 503, 509 Wu, Y., 100 Wulfsohn, M S., 322, 352, 354, 355, 358, 401, 437 Wynne, S N., 115 X Xiao, W., 191 Xu, J., 351, 359 AUTHOR INDEX Y Yang, C C., 143, 145 Yang, H.-L., 18, 168 Yang, L.-P., 201, 210 Yang, M., 94 Yang, S., 83 Yang, Y C., 135 Yao, F., 224, 236, 237, 239, 240, 314 Yates, F., Yau, L H Y., 148, 479, 490, 491, 546 Ye, H., 56 Ying, Z., 64, 191, 210 Yosef, M., 18, 94, 168 Yu, K F., 242 Yu, M G., 363 Yule, G U., 17, 80 Z Zahner, G E P., 401 Zamar, R., 226 Zeger, S L., 13, 15, 19, 21, 22, 34, 39, 44, 45, 46, 48, 50, 51, 52, 55, 56, 57, 58, 71, 72, 73, 74, 85, 88, 94, 95, 100, 119, 121, 132, 153, 168, 169, 170, 172, 182, 183, 186, 191, 201, 208, 212, 213, 217, 223, 224, 351, 359, 373, 374, 375, 399, 457, 495 Zeng, D., 363 Zeng, L., 374 Zerbe, G O., 377, 378, 379 Zhang, B., 210 Zhang, D W., 39, 191, 195, 205, 208, 209, 210, 211, 212, 216, 255, 267, 268, 285, 291, 307, 314 Zhang, J T., 135, 201, 209, 210, 242, 247 Zhang, Y., 242 Zhao, H., 471 Zhao, L P., 45, 51, 58, 60, 61, 74, 373, 405, 423, 467, 468, 471, 472, 502, 546, 555 Zhao, X., 224 Zhao, Y., 285 Zhou, L., 191, 207, 210 Zimmerman, D L., 279 July 8, 2008 10:21 C6587 C6587˙C025 Subject Index A Accelerated EM algorithm (AEM), 152, 401, 404 AIC, see Akaike’s information criterion Akaike’s information criterion (AIC), 62, 130, 238, 257 Alternating logistic regression, see Generalized estimating equations (GEE) Autoregression, 8, 20–21, 50, 86, 132, 373–380 B Bahadur model, 12–14, 45, 67, 74 Bayesian information criterion (BIC), 130, 152, 238 Best linear unbiased estimator (BLUE), 205, 295 Best linear unbiased prediction (BLUP), 96, 205, 208, 212, 254, 292, 308 Beta-binomial model, 17, 23–25, 80 BUGS software, 129 C Causal inference, see Time-varying exposure Causal Markov assumption, 594 Clustered data, 7, 12, 15, 168 Coarsening at random, 454 Compartment model, 112–115, 132 Complete case, 413, 502 Complete data, 396–397 Compound symmetry, see Covariance Conditional model, joint, 321–322 Covariance, compound symmetry, 4, 6, 413, 505 unstructured, 50, 66, 117, 335, 372, 486, 532 Cross-validation, 193, 258 D Directed acyclic graph (DAG), 557 causal, 572, 575 conditional exchangeability and, 557 definition, 593 time-varying exposure scenario, 562 Double penalized quasi-likelihood, 209 Double robustness, see Inverse probability weighted method Dropout, see Incomplete data Dynamic regime, see Inverse probability of treatment weighting E EM algorithm, see Expectation–maximization algorithm Empirical Bayes estimate, 39 Empirical variance estimator, see Generalized estimating equations (GEE) Equivalent degrees of freedom, 257 Expectation–maximization (EM) algorithm accelerated, 152, 401, 404 generalized linear mixed model, 92 growth mixture model, 151, 152 linear mixed-effects model, non-linear mixed-effects model, 125, 128 random-effects model for joint analysis, 352, 356, 357 selection and pattern-mixture models, 412, 413, 424 External aliasing, 495 F Fully parametric likelihood-based estimator, 454 Functional data analysis, 223–251 B-spline, 235 curve registration, 230, 246 curve synchronization, 229 Fourier basis, 234 functional mixed model, 208, 211 functional normal equation, 242 functional principal component analysis, 224, 233–240 functional regression model, 240–245 Karhunen–Lo`eve representation, 234, 237, 243 kernel smoothing, 226 landmark identification, 231 local linear fitting, 228 non-parametric regression, 226–229 smoothing spline, 224 time synchronization, 230–233 time warping, 227, 229–233 varying-coefficient model, 242 July 8, 2008 10:21 C6587 C6587˙C025 614 wavelet basis, 234 wavelet expansion, 225 G Gaussian Ornstein–Uhlenbeck process, 449 GEE, see Generalized estimating equations GEE2, see Second-order generalized estimating equations Generalized additive mixed model, 208 Generalized cross-validation, 299 non-parametric regression, 207 penalized spline fit, 300 semi-parametric regression, 207 smoothing spline, 193, 255 Generalized estimating equations (GEE), 15, 43–78, 127, 223, 328, 495 alternating logistic regression, 51 empirical variance estimator, 49 Fisher scoring algorithm, 52 inverse probability weighted method, 457 goodness-of-fit and model diagnostic, 62–64 missing data, 58–62 population-averaged interpretation, 47 properties of GEE estimator, 52–55 quasi-likelihood, 46, 48, 49, 73 residuals, 56, 57, 67 robust variance estimator, see Sandwich variance estimator robustness property of, 16 sandwich variance estimator, 49, 51, 54 weighted estimating equations, 60, 61, 62 working correlation, 50, 51, 53, 54, 56, 58, 66, 70, 74 Generalized linear mixed model, 16, 33, 36, 43, 79–106, 331 empirical Bayes prediction, 96–97 endogeneity, 85–86 estimation, 89–95 expectation–maximization, 92 functional modelling, 223 Gauss–Hermite quadrature, 90 interpretation of model parameters, 87–89 latent-response formulation, 83–84 marginal likelihood, 18 marginal quasi-likelihood, 92, 93, 94 Markov chain Monte Carlo, 89, 94, 95 maximum likelihood estimation, 90–92, 96 multivariate, 377 non-parametric and semi-parametric regression, 209 penalized quasi-likelihood, 9, 82, 89 proportional odds model, 97, 98 quasi-likelihood, 82, 92–94 shared random-effects model, 102 SUBJECT INDEX targets of inference in, 19, 179, 184 two-stage formulation, 84–85 Generalized linear model, 8–9, 79, 80 characteristic feature of, extensions of, 9, 11, 16, 22 first-order autoregressive, 20 software, 21 Generalized smoothing spline estimator, 204–205 G-estimation, 561–586 Gibbs sampling, 95, 421, 486 Growth curve, 7–8, 84, 144–145, 191, 208 Growth mixture model, 143–165 accelerated EM algorithm, 152 between-level model, 159 clustering, 145, 148 EM algorithm, 151 estimation, 151–153 finite mixture, 143, 144 growth model, 161, 162 latent class, 144, 147, 153, 156, 162 H Hierarchical model, targets of inference in, 167–187 conditional covariance matrix, 174 conditional model, 170 generalized estimating equations, 168 generalized linear mixed model, 179, 184 link function, 168 marginalization, 171 population-averaged model, 170 structural model, 174 subject-specific model, 168, 169, 170, 172, 178, 180, 184 Horvitz–Thompson estimator, 454 Hosmer–Lemeshow goodness-of-fit test, 63 I Imputation, see Multiple imputation Incomplete data, 395–408 EM algorithm, 404 ignorability, 399, 400, 509 imputation, 403, 404, 405, 406, 429, 477–499 inverse probability weighting, 60, 405 joint model for non-ignorable missingness, 401–403 likelihood-based method, 399, 400, 404–405 missing completely at random, 397–398 missing-data mechanism, 396–400 missing at random, 398–400 missing not at random, 397, 400 July 8, 2008 10:21 C6587 C6587˙C025 SUBJECT INDEX monotone missingness, 60, 67, 400, 404–405, 471–473 non-response, 395, 401, 403, 405 pattern-mixture model, 400, 402, 403, 509 selection model, 401–403 sensitivity analysis, 400, 402, 403 Informative missingness, 433 Intention to treat (ITT) analysis, 490 Intraclass correlation, 4, 89–91, 98, 155–156 Inverse probability of treatment weighting, 554, 558 causal directed acyclic graph (DAG), 575 creation of pseudo-population, 559 dynamic regime, 576 marginal structural model, 574 robustness, 564 unbiased estimator, 564, 583 Inverse probability weighted method, 453–476 coarsening at random assumption, 457–460 counterfactual outcome, 454 double robustness, 460–462, 470, 472 efficiency consideration, 465–470 Horvitz–Thompson estimator, 454, 455, 456 locally efficient estimator, 468, 469 marginal structural model, 454 selection bias function, 460, 461 survey sampling, 455–456 Item response theory (IRT) model, 381 J Joint model, 319–391 association of evolutions, 369, 387 conditional model, 327 dimension reduction, 380 evolution in latent variable, 380–382 evolution in observed variable, 372–375 evolution of association, 369, 387 longitudinal mixed endpoints, 333–338 model for continuous and discrete data, 327–348 model for high-dimensional data, 367–391 model for longitudinal data, 319–326 model for repeated-measurement and time-to-event outcomes, 349–366 K Kernel GEE estimator, 203 Kernel smoothing, 192, 226 L Laplace approximation, 18, 26, 94, 127, 209 Last observation carried forward (LOCF), 427, 502 Linear mixed model, 7–8, 21, 292 615 growth curve analysis, joint model, 322, 384 penalized spline model, 300, 301 random-effects distribution, 39 random-effects model, 354, 356 two-stage formulation, 7, Local influence, see Incomplete data Local likelihood, 202, 218 Local polynomial kernel estimator, 193 M Marginal model, 33–36, 44 defining features, 46 estimation, 45 population-averaged model, 31 random-effects distribution, 38 regression coefficient, 34, 36, 40 Marginal quasi-likelihood (MQL), 18, 92, 93, 94 Marginal structural model, 454, 554, 564, 575 dynamic, 585 non-dynamic, 577 non-saturated misspecified, 576 positivity condition, 586 semi-linear, 586 variance estimator, 565 Markov chain Monte Carlo (MCMC), 89, 94, 95 Missing completely at random (MCAR), 397, 398 GEE, 59, 65, 397–398 missing-data mechanism, 397–398 multiple imputation, 490 selection and pattern-mixture models, 418 Missing at random (MAR), 398–400 bodyguard, 513, 520 multiple imputation, 478 selection and pattern-mixture models, 411 Missing not at random (MNAR), see Not missing at random (NMAR) Monotone missingness, see Incomplete data Multilevel model, see Hierarchical model Multiple imputation (MI), 429, 477–499 basic procedure, 478–481 between-imputation covariance matrix, 479 combining estimating equations and multiple imputation, 494–496 complete-data quantity, 478 drawing proper imputations, 482–483 external aliasing, 495 Gibbs sampling, 486 improper estimator, 482 monotone missingness pattern, 485 multiple chained equations, 487 multivariate missing data, 484 July 8, 2008 10:21 C6587 C6587˙C025 616 non-monotone missingness pattern, 483 not missing at random pattern-mixture model, 491 pattern-mixture model, 479, 490, 492 proper imputation, 481, 483–487 regression method, 485, 489, 490 selection model, 491 sensitivity analysis, 487–492 Multivariate analysis of variance, 5, N Nadaraya–Watson estimator, 192, 206 NMAR, see Not missing at random Non-linear mixed model, 37–38, 107–141 between-individual covariate, 116 first-order conditional method, 127 generalized estimating equations, 127 generalized linear mixed model, 123 Markov chain Monte Carlo (MCMC) method, 129 model formulation, 116–124 pharmacodynamics, 110 pharmacokinetics, 110, 126, 132, 135, 136 population-averaged model, 127 NONMEM, 126–127 Non-monotone missingness, see Incomplete data Non-parametric regression method, 191–197, 199–221 Non-parametric structural equation model, 595 Not missing at random (NMAR), 353, 400 bodyguard, 520 dropout model, 537, 542 multiple imputation, 479 pattern-mixture model, 411 random-effects model, 353 selection model, 411, 531 shared-parameter model, 433 Numerical integration, 90, 128, 439 O Observed-data likelihood, 411 Ordinal data, 51, 82–83, 97, 381 Ornstein–Uhlenbeck process, 208 Overdispersion, 49 P Parametric modeling, 31–41 Pattern-mixture model, 409–431, 490, 509 imputation model, 479 multiple imputation, 479, 490, 492 not missing at random, 487, 491, 492 Penalized likelihood, 192 Penalized quasi-likelihood (PQL), 9, 82, 89 SUBJECT INDEX generalized linear mixed model, 18 maximum likelihood estimation, 92 smoothing spline model, 285 Penalized spline model, 291–316 best linear unbiased estimator, 295 B-spline, 294, 297 linear mixed model, 292, 301, 306, 314 mixed model representation, 298–305 penalty, 302, 304, 311 prediction error variance, 292 P-spline, 297 regression spline, 294–295 roughness penalty, 296 smoothing spline, 297, 302, 304, 311 Sobolev space of functions, 308 Pharmacokinetics, 110 Plackett–Dale model, 332–333, 343 Principal component analysis, 380 Probit-normal model, 329, 334 Q Quasi-likelihood, 46, 48, 49, 73 R Random effect, 4, 7–8, 31–40, 79–82, 158–161 best linear unbiased predictor, 96, 205, 208, 212, 254, 292, 308 generalized linear mixed model, 16, 33, 36, 43, 79–106, 331 linear mixed model, 7–8, 80–81 normality assumption, 39, 161 shrinkage, 130, 176–177, 266 spline, 298–305 Regression spline, 194–195 Repeated-measures analysis of variance, univariate, 4, 6, Restricted maximum likelihood (REML), 205, 234, 298, 490–493 non-parametric and semi-parametric regression, 205 penalized spline model, 298 Robust variance estimator, see Generalized estimating equations (GEE), empirical variance estimator S Sandwich variance estimator, 49, 51, 54, 373 Second-order generalized estimating equations (GEE2), 57 Seemingly unrelated kernel estimator, 202–204 Selection model, 409–431 Bayesian inference, 410, 413, 423, 428 EM algorithm, 412, 413, 424, 426 missing completely at random, 418 missing at random, 411 July 8, 2008 10:21 C6587 C6587˙C025 SUBJECT INDEX multiple imputation, 429 non-ignorable non-response, 403 not missing at random, 411 Self-modeling regression model, 379 Semi-parametric regression method, 191–197, 199–221 Sensitivity analysis for incomplete data, 501–551 best–worst case interval, 523 direct-likelihood analysis, 510 global influence, 531–545 identifying restriction, 546 ignorability, 509 imprecision, 523 influence graph, 534 interval of ignorance, 503, 505, 527, 528, 529, 530 interval of uncertainty, 527, 529 last observation carried forward, 502 likelihood displacement, 533 local influence, 531–545 model assessment, 510 monotone pattern, 524 non-monotone pattern, 524, 546 protective assumption, 524 regions of ignorance and uncertainty, 522–531 selection model, 509, 524, 531 sensitivity parameter, 527 shared-parameter model, 503, 509 weighted generalized estimating equations, 502, 546 Shared-parameter model, 424, 433–452, 509 bootstrapping, 441 conditional independence, 436, 437 estimation, 438–441 informative missingness, 433, 446, 448 missing-data mechanism, 437, 448 model formulation, 436–438 monotone missing-data mechanism, 437 non-random missingness, 433, 440 numerical integration, 439 probit regression, 433, 440 random-effects model, 433, 434, 449 Shrinkage, 130, 176–177, 266 Smoothing spline model, 193–194, 204–205, 223–289 ante-dependence model, 279 basis function and properties of natural cubic spline, 258–261 best linear unbiased predictor, 254 cross-validation, 258 cubic spline, 256–258 diagnostic, 278–279 low-rank approximation, 283–285 617 L-spline, 279–283 mixed model representation 261, 264–274, 285, 286 penalized quasi-likelihood method, 285 P-spline and penalized spline, 254, 283–285 regression spline, 257 smoothing spline, 286 spline random effect, 269 Spline, see Smoothing spline model Stationary Gaussian process, 356 Structural equation modeling, 379 Structural nested mean model, 579 g-estimation, 582 non-dynamic, 584 optimal regime, 587, 588, 589, 591, 593 Structural nested model, 554, 577 T Time-to-event outcome, see Joint model for repeated-measurement and time-to-event outcomes Time-varying exposure, causal effect of, 553–599 causal directed acyclic graph, 593–596 causal inference, 554, 560, 571 choice among g-methods, 579–592 conditional exchangeability, 556–584 confounding, 554–573 directed acyclic graph, 557, 593 dynamic treatment regime, 555 fixed exposure, 555–560 g-estimation, 561–586 inverse probability of treatment weighting, 554, 558 marginal structural model, 554, 564, 575 Markov factorization, 594 non-dynamic regime, 561, 566, 579, 587, 588, 596 null hypothesis of no treatment effect, 582, 592 null paradox of estimated g-formula, 563 selection bias, 572 sequentially randomized experiment, 561, 580, 583, 586, 587 structural nested mean model, 579 time-dependent confounding, 554, 561, 562, 569 unconditional exchangeability, 561 Transitional model, 73 Two-stage model, 7–8, 15, 17, 37–39, 84–85, 117 U Unbalanced longitudinal data, 46 Unconditional exchangeability, 561 July 8, 2008 10:21 C6587 C6587˙C025 618 Uncongenial imputation model, 495 Unstructured covariance, see Covariance V Variance covariance matrix, 336 function, 10, 47 marginal structural model estimator, 565 Variance component, 5, 18, 23, 80, 169 Varying-coefficient model, functional modeling, 242 SUBJECT INDEX W Weighted generalized estimating equations, 502, 546 Weighted least squares (WLS), 44 WinBUGS software, 95, 129, 496 WLS, see Weighted least squares Working correlation, see Generalized estimating equations (GEE), Z Zero-inflated Poisson, 150, 153 ... models for longitudinal data analysis Linear mixed-effects model for longitudinal data Models for non-Gaussian longitudinal data ... the focus is on the current state of the art of longitudinal data analysis 1.2 Early origins of linear models for longitudinal data analysis The analysis of change is a fundamental component of... in the modeling of discrete longitudinal data Another issue that complicates the analysis is the inclusion of time-varying covariates in models for longitudinal data Longitudinal studies permit