Research Article
The parametric g‐formula to estimate the effect of highly active antiretroviral therapy on incident AIDS or death
Abstract
The parametric g‐formula can be used to contrast the distribution of potential outcomes under arbitrary treatment regimes. Like g‐estimation of structural nested models and inverse probability weighting of marginal structural models, the parametric g‐formula can appropriately adjust for measured time‐varying confounders that are affected by prior treatment. However, there have been few implementations of the parametric g‐formula to date. Here, we apply the parametric g‐formula to assess the impact of highly active antiretroviral therapy on time to acquired immune deficiency syndrome (AIDS) or death in two US‐based human immunodeficiency virus cohorts including 1498 participants. These participants contributed approximately 7300 person‐years of follow‐up (49% exposed to highly active antiretroviral therapy) during which 382 events occurred and 259 participants were censored because of dropout. Using the parametric g‐formula, we estimated that antiretroviral therapy substantially reduces the hazard of AIDS or death (hazard ratio = 0.55; 95% confidence limits [CL]: 0.42, 0.71). This estimate was similar to one previously reported using a marginal structural model, 0.54 (95% CL: 0.38, 0.78). The 6.5‐year difference in risk of AIDS or death was 13% (95% CL: 8%, 18%). Results were robust to assumptions about temporal ordering, and extent of history modeled, for time‐varying covariates. The parametric g‐formula is a viable alternative to inverse probability weighting of marginal structural models and g‐estimation of structural nested models for the analysis of complex longitudinal data. Copyright © 2012 John Wiley & Sons, Ltd.
Citing Literature
Number of times cited according to CrossRef: 58
- Tiffany L. Breger, Jessie K. Edwards, Stephen R. Cole, Daniel Westreich, Brian W. Pence, Adaora A. Adimora, Two-stage g-computation, Epidemiology, 10.1097/EDE.0000000000001233, 31, 5, (695-703), (2020).
- Alexander P. Keil, Jessie P. Buckley, Katie M. O’Brien, Kelly K. Ferguson, Shanshan Zhao, Alexandra J. White, A Quantile-Based g-Computation Approach to Addressing the Effects of Exposure Mixtures, Environmental Health Perspectives, 10.1289/EHP5838, 128, 4, (047004), (2020).
- Takuya Kawahara, Tomohiro Shinozaki, Yutaka Matsuyama, Doubly robust estimator of risk in the presence of censoring dependent on time-varying covariates: application to a primary prevention trial for coronary events with pravastatin, BMC Medical Research Methodology, 10.1186/s12874-020-01087-8, 20, 1, (2020).
- Andrew J. Spieker, Emily M. Ko, Jason A. Roy, Nandita Mitra, Nested g‐computation: a causal approach to analysis of censored medical costs in the presence of time‐varying treatment, Journal of the Royal Statistical Society: Series C (Applied Statistics), 10.1111/rssc.12441, 69, 5, (1189-1208), (2020).
- Salina P. Waddy, Allen J. Solomon, Adan Z. Becerra, Julia B. Ward, Kevin E. Chan, Chyng-Wen Fwu, Jenna M. Norton, Paul W. Eggers, Kevin C. Abbott, Paul L. Kimmel, Racial/Ethnic Disparities in Atrial Fibrillation Treatment and Outcomes among Dialysis Patients in the United States, Journal of the American Society of Nephrology, 10.1681/ASN.2019050543, 31, 3, (637-649), (2020).
- Eric J. Tchetgen Tchetgen, Isabel R. Fulcher, Ilya Shpitser, Auto-G-Computation of Causal Effects on a Network, Journal of the American Statistical Association, 10.1080/01621459.2020.1811098, (1-33), (2020).
- M. Schomaker, M.A. Luque‐Fernandez, V. Leroy, M.A. Davies, Using longitudinal targeted maximum likelihood estimation in complex settings with dynamic interventions, Statistics in Medicine, 10.1002/sim.8340, 38, 24, (4888-4911), (2019).
- Alexander Breskin, Daniel Westreich, Christopher B Hurt, Stephen R Cole, Michael G Hudgens, Eric C Seaberg, Chloe L Thio, Phyllis C Tien, Adaora A Adimora, The Effects of Hepatitis C Treatment Eligibility Criteria on All-cause Mortality Among People With Human Immunodeficiency Virus, Clinical Infectious Diseases, 10.1093/cid/ciz008, 69, 9, (1613-1620), (2019).
- Kathleen A McManus, Bianca Christensen, V Peter Nagraj, Renae Furl, Lauren Yerkes, Susan Swindells, Sharon Weissman, Anne Rhodes, Paul Targonski, Elizabeth Rogawski McQuade, Rebecca Dillingham, Evidence From a Multistate Cohort: Enrollment in Affordable Care Act Qualified Health Plans’ Association With Viral Suppression, Clinical Infectious Diseases, 10.1093/cid/ciz1123, (2019).
- Felicitas Kuehne, Beate Jahn, Annette Conrads-Frank, Marvin Bundo, Marjan Arvandi, Florian Endel, Niki Popper, Gottfried Endel, Christoph Urach, Michael Gyimesi, Eleanor J Murray, Goodarz Danaei, Thomas A Gaziano, Ankur Pandya, Uwe Siebert, Guidance for a causal comparative effectiveness analysis using ‘big real world’ evidence: when to start statin treatment, Journal of Comparative Effectiveness Research, 10.2217/cer-2018-0103, (2019).
- Bradley C. Saul, Michael G. Hudgens, Michael A. Mallin, Downstream Effects of Upstream Causes, Journal of the American Statistical Association, 10.1080/01621459.2019.1574226, (1-19), (2019).
- Jeffrey M Albert, Jang Ik Cho, Yiying Liu, Suchitra Nelson, Generalized causal mediation and path analysis: Extensions and practical considerations, Statistical Methods in Medical Research, 10.1177/0962280218776483, 28, 6, (1793-1807), (2018).
- Alexander P. Keil, Jessie K. Edwards, A Review of Time Scale Fundamentals in the g-Formula and Insidious Selection Bias, Current Epidemiology Reports, 10.1007/s40471-018-0153-0, 5, 3, (205-213), (2018).
- Alexander P. Keil, David B. Richardson, Daniel Westreich, Kyle Steenland, Estimating the Impact of Changes to Occupational Standards for Silica Exposure on Lung Cancer Mortality, Epidemiology, 10.1097/EDE.0000000000000867, 29, 5, (658-665), (2018).
- Elizabeth T Rogawski, Jie Liu, James A Platts-Mills, Furqan Kabir, Paphavee Lertsethtakarn, Mery Siguas, Shaila S Khan, Ira Praharaj, Arinao Murei, Rosemary Nshama, Buliga Mujaga, Alexandre Havt, Irene A Maciel, Darwin J Operario, Mami Taniuchi, Jean Gratz, Suzanne E Stroup, James H Roberts, Adil Kalam, Fatima Aziz, Shahida Qureshi, M Ohedul Islam, Pimmada Sakpaisal, Sasikorn Silapong, Pablo P Yori, Revathi Rajendiran, Blossom Benny, Monica McGrath, Jessica C Seidman, Dennis Lang, Michael Gottlieb, Richard L Guerrant, Aldo A M Lima, Jose Paulo Leite, Amidou Samie, Pascal O Bessong, Nicola Page, Ladaporn Bodhidatta, Carl Mason, Sanjaya Shrestha, Ireen Kiwelu, Estomih R Mduma, Najeeha T Iqbal, Zulfiqar A Bhutta, Tahmeed Ahmed, Rashidul Haque, Gagandeep Kang, Margaret N Kosek, Eric R Houpt, Angel Mendez Acosta, Rosa Rios de Burga, Cesar Banda Chavez, Julian Torres Flores, Maribel Paredes Olotegui, Silvia Rengifo Pinedo, Dixner Rengifo Trigoso, Angel Orbe Vasquez, Imran Ahmed, Didar Alam, Asad Ali, Muneera Rasheed, Sajid Soofi, Ali Turab, Aisha Yousafzai, Anita KM Zaidi, Binob Shrestha, Bishnu Bahadur Rayamajhi, Tor Strand, Geetha Ammu, Sudhir Babji, Anuradha Bose, Ajila T George, Dinesh Hariraju, M. Steffi Jennifer, Sushil John, Shiny Kaki, Priyadarshani Karunakaran, Beena Koshy, Robin P Lazarus, Jayaprakash Muliyil, Preethi Ragasudha, Mohan Venkata Raghava, Sophy Raju, Anup Ramachandran, Rakhi Ramadas, Karthikeyan Ramanujam, Anuradha Rose, Reeba Roshan, Srujan L Sharma, Shanmuga Sundaram, Rahul J Thomas, William K Pan, Ramya Ambikapathi, J Daniel Carreon, Viyada Doan, Christel Hoest, Stacey Knobler, Mark A Miller, Stephanie Psaki, Zeba Rasmussen, Stephanie A Richard, Karen H Tountas, Erling Svensen, Caroline Amour, Eliwaza Bayyo, Regisiana Mvungi, John Pascal, Ladislaus Yarrot, Leah Barrett, Rebecca Dillingham, William A Petri, Rebecca Scharf, AM Shamsir Ahmed, Md Ashraful Alam, Umma Haque, Md Iqbal Hossain, Munirul Islam, Mustafa Mahfuz, Dinesh Mondal, Baitun Nahar, Fahmida Tofail, Ram Krishna Chandyo, Prakash Sunder Shrestha, Rita Shrestha, Manjeswori Ulak, Aubrey Bauck, Robert Black, Laura Caulfield, William Checkley, Gwenyth Lee, Kerry Schulze, Samuel Scott, Laura E Murray-Kolb, A Catharine Ross, Barbara Schaefer, Suzanne Simons, Laura Pendergast, Cláudia B Abreu, Hilda Costa, Alessandra Di Moura, José Quirino Filho, Álvaro M Leite, Noélia L Lima, Ila F Lima, Bruna LL Maciel, Pedro HQS Medeiros, Milena Moraes, Francisco S Mota, Reinaldo B Oriá, Josiane Quetz, Alberto M Soares, Rosa MS Mota, Crystal L Patil, Cloupas Mahopo, Angelina Maphula, Emanuel Nyathi, Use of quantitative molecular diagnostic methods to investigate the effect of enteropathogen infections on linear growth in children in low-resource settings: longitudinal analysis of results from the MAL-ED cohort study, The Lancet Global Health, 10.1016/S2214-109X(18)30351-6, (2018).
- Michael Schomaker, Christian Heumann, Bootstrap inference when using multiple imputation, Statistics in Medicine, 10.1002/sim.7654, 37, 14, (2252-2266), (2018).
- Jessie K Edwards, Stephen R Cole, Richard D Moore, W Christopher Mathews, Mari Kitahata, Joseph J Eron, Sensitivity Analyses for Misclassification of Cause of Death in the Parametric G-Formula, American Journal of Epidemiology, 10.1093/aje/kwy028, 187, 8, (1808-1816), (2018).
- David Michael Vock, Laura Frances Boehm Vock, Estimating the effect of plate discipline using a causal inference framework: an application of the G-computation algorithm, Journal of Quantitative Analysis in Sports, 10.1515/jqas-2016-0029, 14, 2, (37-56), (2018).
- Marie C. D. Stoner, Jessie K. Edwards, William C. Miller, Allison E. Aiello, Carolyn T. Halpern, Aimée Julien, Katherine B. Rucinski, Amanda Selin, Rhian Twine, James P. Hughes, Jing Wang, Yaw Agyei, Francesc Xavier Gómez-Olivé, Ryan G. Wagner, Oliver Laeyendecker, Catherine Macphail, Kathleen Kahn, Audrey Pettifor, Does Partner Selection Mediate the Relationship Between School Attendance and HIV/Herpes Simplex Virus-2 Among Adolescent Girls and Young Women in South Africa, JAIDS Journal of Acquired Immune Deficiency Syndromes, 10.1097/QAI.0000000000001766, 79, 1, (20-27), (2018).
- Jon Michael Gran, Rune Hoff, Kjetil Røysland, Bruno Ledergerber, James Young, Odd O. Aalen, Estimating the treatment effect on the treated under time‐dependent confounding in an application to the Swiss HIV Cohort Study, Journal of the Royal Statistical Society: Series C (Applied Statistics), 10.1111/rssc.12221, 67, 1, (103-125), (2017).
- Alexander P Keil, Eric J Daza, Stephanie M Engel, Jessie P Buckley, Jessie K Edwards, A Bayesian approach to the g-formula, Statistical Methods in Medical Research, 10.1177/0962280217694665, 27, 10, (3183-3204), (2017).
- Cheng Wang, Katie R Mollan, Michael G Hudgens, Joseph D Tucker, Heping Zheng, Weiming Tang, Li Ling, Generalisability of an online randomised controlled trial: an empirical analysis, Journal of Epidemiology and Community Health, 10.1136/jech-2017-209976, 72, 2, (173-178), (2017).
- Sandro Galea, On the potential of academic epidemiology, European Journal of Epidemiology, 10.1007/s10654-017-0233-3, 32, 3, (169-171), (2017).
- Katherine M. Keyes, Melissa Tracy, Stephen J. Mooney, Aaron Shev, Magdalena Cerdá, Invited Commentary: Agent-Based Models—Bias in the Face of Discovery, American Journal of Epidemiology, 10.1093/aje/kwx090, 186, 2, (146-148), (2017).
- Catherine R. Lesko, Jonathan V. Todd, Stephen R. Cole, Andrew Edmonds, Brian W. Pence, Jessie K. Edwards, Wendy J. Mack, Peter Bacchetti, Anna Rubtsova, Stephen J. Gange, Adaora A. Adimora, Michael Saag, Mirjam-Colette Kempf, Deborah Konkle-Parker, Ighovwerha Ofotokun, Gina Wingood, Kathryn Anastos, Howard Minkoff, Deborah Gustafson, Mardge Cohen, Audrey French, Mary Young, Seble Kassaye, Margaret Fischl, Lisa Metsch, Adaora Adimora, Ruth Greenblatt, Bradley Aouizerat, Phyllis Tien, Stephen Gange, Elizabeth Golub, Joel Milam, Mortality under plausible interventions on antiretroviral treatment and depression in HIV-infected women: an application of the parametric g-formula, Annals of Epidemiology, 10.1016/j.annepidem.2017.08.021, 27, 12, (783-789.e2), (2017).
- John W. Jackson, Ian Schmid, Elizabeth A. Stuart, Propensity Scores in Pharmacoepidemiology: Beyond the Horizon, Current Epidemiology Reports, 10.1007/s40471-017-0131-y, 4, 4, (271-280), (2017).
- Katherine M. Keyes, Sandro Galea, Commentary, Epidemiology, 10.1097/EDE.0000000000000578, 28, 1, (1-5), (2017).
- Bradley C. Saul, Michael G. Hudgens, M. Elizabeth Halloran, Causal Inference in the Study of Infectious Disease, Disease Modelling and Public Health, Part A, 10.1016/bs.host.2017.07.002, (229-246), (2017).
- Daniel Westreich, Jordan Cates, Mardge Cohen, Kathleen M. Weber, Dominika Seidman, Karen Cropsey, Rodney Wright, Joel Milam, Mary A. Young, C. Christina Mehta, Deborah R. Gustafson, Elizabeth T. Golub, Margaret A. Fischl, Adaora A. Adimora, Smoking, HIV, and risk of pregnancy loss, AIDS, 10.1097/QAD.0000000000001342, 31, 4, (553-560), (2017).
- Catherine R Lesko, Stephen R Cole, H Irene Hall, Daniel Westreich, William C Miller, Joseph J Eron, Jianmin Li, Michael J Mugavero, The effect of antiretroviral therapy on all-cause mortality, generalized to persons diagnosed with HIV in the USA, 2009–11, International Journal of Epidemiology, 10.1093/ije/dyv352, 45, 1, (140-150), (2016).
- Jessie K. Edwards, Stephen R. Cole, Catherine R. Lesko, W. Christopher Mathews, Richard D. Moore, Michael J. Mugavero, Daniel Westreich, An Illustration of Inverse Probability Weighting to Estimate Policy-Relevant Causal Effects, American Journal of Epidemiology, 10.1093/aje/kwv339, 184, 4, (336-344), (2016).
- A.A. Akinkugbe, S. Sharma, R. Ohrbach, G.D. Slade, C. Poole, Directed Acyclic Graphs for Oral Disease Research, Journal of Dental Research, 10.1177/0022034516639920, 95, 8, (853-859), (2016).
- Joseph Kang, Wendy Chan, Mi-Ok Kim, Peter M. Steiner, Practice of causal inference with the propensity of being zero or one: assessing the effect of arbitrary cutoffs of propensity scores, Communications for Statistical Applications and Methods, 10.5351/CSAM.2016.23.1.001, 23, 1, (1-20), (2016).
- Michael Schomaker, Valeriane Leroy, Tom Wolfs, Karl-Günter Technau, Lorna Renner, Ali Judd, Shobna Sawry, Madeleine Amorissani-Folquet, Antoni Noguera-Julian, Frank Tanser, François Eboua, Maria Luisa Navarro, Cleophas Chimbetete, Clarisse Amani-Bosse, Josiane Warszawski, Sam Phiri, Sylvie N’Gbeche, Vivian Cox, Fla Koueta, Janet Giddy, Haby Sygnaté-Sy, Dorthe Raben, Geneviève Chêne, Mary-Ann Davies, Optimal timing of antiretroviral treatment initiation in HIV-positive children and adolescents: a multiregional analysis from Southern Africa, West Africa and Europe, International Journal of Epidemiology, 10.1093/ije/dyw097, (dyw097), (2016).
- Ashley I Naimi, Stephen R Cole, Edward H Kennedy, An Introduction to G Methods, International Journal of Epidemiology, 10.1093/ije/dyw323, (dyw323), (2016).
- Elizabeth T Rogawski, Steven R Meshnick, Sylvia Becker-Dreps, Linda S Adair, Robert S Sandler, Rajiv Sarkar, Deepthi Kattula, Honorine D Ward, Gagandeep Kang, Daniel J Westreich, Reduction in diarrhoeal rates through interventions that prevent unnecessary antibiotic exposure early in life in an observational birth cohort, Journal of Epidemiology and Community Health, 10.1136/jech-2015-206635, 70, 5, (500-505), (2015).
- Michael Schomaker, Mary-Ann Davies, Karen Malateste, Lorna Renner, Shobna Sawry, Sylvie N’Gbeche, Karl-Günter Technau, François Eboua, Frank Tanser, Haby Sygnaté-Sy, Sam Phiri, Madeleine Amorissani-Folquet, Vivian Cox, Fla Koueta, Cleophas Chimbete, Annette Lawson-Evi, Janet Giddy, Clarisse Amani-Bosse, Robin Wood, Matthias Egger, Valeriane Leroy, Growth and Mortality Outcomes for Different Antiretroviral Therapy Initiation Criteria in Children aged 1-5 Years, Epidemiology, 10.1097/EDE.0000000000000412, (1), (2015).
- Jessie P. Buckley, Alexander P. Keil, Leah J. McGrath, Jessie K. Edwards, Evolving Methods for Inference in the Presence of Healthy Worker Survivor Bias, Epidemiology, 10.1097/EDE.0000000000000217, 26, 2, (204-212), (2015).
- Daniel Westreich, Jessie K Edwards, Stephen R Cole, Robert W Platt, Sunni L Mumford, Enrique F Schisterman, Imputation approaches for potential outcomes in causal inference, International Journal of Epidemiology, 10.1093/ije/dyv135, 44, 5, (1731-1737), (2015).
- Aolin Wang, Onyebuchi A. Arah, G-computation demonstration in causal mediation analysis, European Journal of Epidemiology, 10.1007/s10654-015-0100-z, 30, 10, (1119-1127), (2015).
- Daniel Westreich, Jessie K. Edwards, Invited Commentary: Every Good Randomization Deserves Observation, American Journal of Epidemiology, 10.1093/aje/kwv200, 182, 10, (857-860), (2015).
- Katherine Keyes, Sandro Galea, What matters most: quantifying an epidemiology of consequence, Annals of Epidemiology, 10.1016/j.annepidem.2015.01.016, 25, 5, (305-311), (2015).
- Jessie K. Edwards, Stephen R. Cole, Daniel Westreich, Michael J. Mugavero, Joseph J. Eron, Richard D. Moore, William C. Mathews, Peter Hunt, Carolyn Williams, Age at Entry Into Care, Timing of Antiretroviral Therapy Initiation, and 10-Year Mortality Among HIV-Seropositive Adults in the United States, Clinical Infectious Diseases, 10.1093/cid/civ463, 61, 7, (1189-1195), (2015).
- S. R. Cole, M. G. Hudgens, M. A. Brookhart, D. Westreich, Risk, American Journal of Epidemiology, 10.1093/aje/kwv001, 181, 4, (246-250), (2015).
- Benjamin W. Chaffee, Jing Cheng, John DB Featherstone, Non-operative anti-caries agents and dental caries increment among adults at high caries risk: a retrospective cohort study, BMC Oral Health, 10.1186/s12903-015-0097-4, 15, 1, (2015).
- Jessie K. Edwards, Stephen R. Cole, Adaora Adimora, Jason Fine, Jeff Martin, Joseph Eron, Illustration of a Measure to Combine Viral Suppression and Viral Rebound in Studies of HIV Therapy, JAIDS Journal of Acquired Immune Deficiency Syndromes, 10.1097/QAI.0000000000000423, 68, 2, (241-244), (2015).
- M. R. Patel, D. Westreich, M. Yotebieng, M. Nana, J. J. Eron, F. Behets, A. Van Rie, The Impact of Implementation Fidelity on Mortality Under a CD4-Stratified Timing Strategy for Antiretroviral Therapy in Patients With Tuberculosis, American Journal of Epidemiology, 10.1093/aje/kwu338, 181, 9, (714-722), (2015).
- R. M. Daniel, B. L. De Stavola, S. N. Cousens, S. Vansteelandt, Causal mediation analysis with multiple mediators, Biometrics, 10.1111/biom.12248, 71, 1, (1-14), (2014).
- M. A. Hernan, Invited Commentary: Agent-Based Models for Causal Inference--Reweighting Data and Theory in Epidemiology, American Journal of Epidemiology, 10.1093/aje/kwu272, 181, 2, (103-105), (2014).
- D. Westreich, From Exposures to Population Interventions: Pregnancy and Response to HIV Therapy, American Journal of Epidemiology, 10.1093/aje/kwt328, 179, 7, (797-806), (2014).
- Alexander P. Keil, Jessie K. Edwards, David B. Richardson, Ashley I. Naimi, Stephen R. Cole, The Parametric g-Formula for Time-to-event Data, Epidemiology, 10.1097/EDE.0000000000000160, 25, 6, (889-897), (2014).
- Jessica G. Young, Eric J. Tchetgen Tchetgen, Simulation from a known Cox MSM using standard parametric models for the g‐formula, Statistics in Medicine, 10.1002/sim.5994, 33, 6, (1001-1014), (2013).
- Theis Lange, Mette Rasmussen, Lau Caspar Thygesen, Assessing Natural Direct and Indirect Effects Through Multiple Pathways, American Journal of Epidemiology, 10.1093/aje/kwt270, 179, 4, (513-518), (2013).
- Bibhas Chakraborty, Erica E. M. Moodie, Bibhas Chakraborty, Erica E.M. Moodie, Introduction, Statistical Methods for Dynamic Treatment Regimes, 10.1007/978-1-4614-7428-9_1, (1-8), (2013).
- Chelsea B. Polis, Daniel Westreich, Jennifer E. Balkus, Renee Heffron, Assessing the effect of hormonal contraception on HIV acquisition in observational data, AIDS, 10.1097/QAD.0000000000000036, 27, (S35-S43), (2013).
- Stephen R. Cole, David B. Richardson, Haitao Chu, Ashley I. Naimi, Analysis of Occupational Asbestos Exposure and Lung Cancer Mortality Using the G Formula, American Journal of Epidemiology, 10.1093/aje/kws343, 177, 9, (989-996), (2013).
- Martin Lajous, Walter C. Willett, James Robins, Jessica G. Young, Eric Rimm, Dariush Mozaffarian, Miguel A. Hernán, Changes in Fish Consumption in Midlife and the Risk of Coronary Heart Disease in Men and Women, American Journal of Epidemiology, 10.1093/aje/kws478, 178, 3, (382-391), (2013).
- Kohei Hasegawa, Yusuke Tsugawa, Carlos A. Camargo, Atsushi Hiraide, David F.M. Brown, Regional variability in survival outcomes of out-of-hospital cardiac arrest: The All-Japan Utstein Registry, Resuscitation, 10.1016/j.resuscitation.2013.03.007, 84, 8, (1099-1107), (2013).
