Analysis of non-ignorable missing and left-censored longitudinal data using a weighted random effects tobit model
In a longitudinal study with response data collected during a hospital stay, observations may be missing because of the subject's discharge from the hospital prior to completion of the study or the death of the subject, resulting in non‐ignorable missing data. In addition to non‐ignorable missi...
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| Published in | Statistics in medicine Vol. 30; no. 27; pp. 3167 - 3180 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
30.11.2011
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0277-6715 1097-0258 1097-0258 |
| DOI | 10.1002/sim.4344 |
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| Abstract | In a longitudinal study with response data collected during a hospital stay, observations may be missing because of the subject's discharge from the hospital prior to completion of the study or the death of the subject, resulting in non‐ignorable missing data. In addition to non‐ignorable missingness, there is left‐censoring in the response measurements because of the inherent limit of detection. For analyzing non‐ignorable missing and left‐censored longitudinal data, we have proposed to extend the theory of random effects tobit regression model to weighted random effects tobit regression model. The weights are computed on the basis of inverse probability weighted augmented methodology. An extensive simulation study was performed to compare the performance of the proposed model with a number of competitive models. The simulation study shows that the estimates are consistent and that the root mean square errors of the estimates are minimal for the use of augmented inverse probability weights in the random effects tobit model. The proposed method is also applied to the non‐ignorable missing and left‐censored interleukin‐6 biomarker data obtained from the Genetic and Inflammatory Markers of Sepsis study. Copyright © 2011 John Wiley & Sons, Ltd. |
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| AbstractList | In a longitudinal study with response data collected during a hospital stay, observations may be missing because of the subject's discharge from the hospital prior to completion of the study or the death of the subject, resulting in non‐ignorable missing data. In addition to non‐ignorable missingness, there is left‐censoring in the response measurements because of the inherent limit of detection. For analyzing non‐ignorable missing and left‐censored longitudinal data, we have proposed to extend the theory of random effects tobit regression model to weighted random effects tobit regression model. The weights are computed on the basis of inverse probability weighted augmented methodology. An extensive simulation study was performed to compare the performance of the proposed model with a number of competitive models. The simulation study shows that the estimates are consistent and that the root mean square errors of the estimates are minimal for the use of augmented inverse probability weights in the random effects tobit model. The proposed method is also applied to the non‐ignorable missing and left‐censored interleukin‐6 biomarker data obtained from the Genetic and Inflammatory Markers of Sepsis study. Copyright © 2011 John Wiley & Sons, Ltd. In a longitudinal study with response data collected during a hospital stay, observations may be missing because of the subject's discharge from the hospital prior to completion of the study or the death of the subject, resulting in non-ignorable missing data. In addition to non-ignorable missingness, there is left-censoring in the response measurements because of the inherent limit of detection. For analyzing non-ignorable missing and left-censored longitudinal data, we have proposed to extend the theory of random effects tobit regression model to weighted random effects tobit regression model. The weights are computed on the basis of inverse probability weighted augmented methodology. An extensive simulation study was performed to compare the performance of the proposed model with a number of competitive models. The simulation study shows that the estimates are consistent and that the root mean square errors of the estimates are minimal for the use of augmented inverse probability weights in the random effects tobit model. The proposed method is also applied to the non-ignorable missing and left-censored interleukin-6 biomarker data obtained from the Genetic and Inflammatory Markers of Sepsis study. In a longitudinal study with response data collected during a hospital stay, observations may be missing because of the subject's discharge from the hospital prior to completion of the study or the death of the subject, resulting in non-ignorable missing data. In addition to non-ignorable missingness, there is left-censoring in the response measurements because of the inherent limit of detection. For analyzing non-ignorable missing and left-censored longitudinal data, we have proposed to extend the theory of random effects tobit regression model to weighted random effects tobit regression model. The weights are computed on the basis of inverse probability weighted augmented methodology. An extensive simulation study was performed to compare the performance of the proposed model with a number of competitive models. The simulation study shows that the estimates are consistent and that the root mean square errors of the estimates are minimal for the use of augmented inverse probability weights in the random effects tobit model. The proposed method is also applied to the non-ignorable missing and left-censored interleukin-6 biomarker data obtained from the Genetic and Inflammatory Markers of Sepsis study. [PUBLICATION ABSTRACT] In a longitudinal study with response data collected during a hospital stay, observations may be missing because of the subject's discharge from the hospital prior to completion of the study or the death of the subject, resulting in non-ignorable missing data. In addition to non-ignorable missingness, there is left-censoring in the response measurements because of the inherent limit of detection. For analyzing non-ignorable missing and left-censored longitudinal data, we have proposed to extend the theory of random effects tobit regression model to weighted random effects tobit regression model. The weights are computed on the basis of inverse probability weighted augmented methodology. An extensive simulation study was performed to compare the performance of the proposed model with a number of competitive models. The simulation study shows that the estimates are consistent and that the root mean square errors of the estimates are minimal for the use of augmented inverse probability weights in the random effects tobit model. The proposed method is also applied to the non-ignorable missing and left-censored interleukin-6 biomarker data obtained from the Genetic and Inflammatory Markers of Sepsis study.In a longitudinal study with response data collected during a hospital stay, observations may be missing because of the subject's discharge from the hospital prior to completion of the study or the death of the subject, resulting in non-ignorable missing data. In addition to non-ignorable missingness, there is left-censoring in the response measurements because of the inherent limit of detection. For analyzing non-ignorable missing and left-censored longitudinal data, we have proposed to extend the theory of random effects tobit regression model to weighted random effects tobit regression model. The weights are computed on the basis of inverse probability weighted augmented methodology. An extensive simulation study was performed to compare the performance of the proposed model with a number of competitive models. The simulation study shows that the estimates are consistent and that the root mean square errors of the estimates are minimal for the use of augmented inverse probability weights in the random effects tobit model. The proposed method is also applied to the non-ignorable missing and left-censored interleukin-6 biomarker data obtained from the Genetic and Inflammatory Markers of Sepsis study. |
| Author | Molenberghs, Geert Sattar, Abdus Weissfeld, Lisa A. |
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| Cites_doi | 10.1080/01621459.1952.10483446 10.1002/sim.2560 10.2307/1907382 10.1111/j.0006-341X.2004.00240.x 10.1214/aos/1176345526 10.1080/01621459.1998.10473795 10.2307/2529876 10.1007/978-1-4757-1229-2_14 10.1111/1467-9876.00207 10.1111/1467-9876.00119 10.1111/j.0006-341X.1999.00625.x 10.1214/07-STS227D 10.1086/367924 10.1214/07-STS227 10.1111/1467-9868.00318 10.1111/1467-9868.00185 10.1111/j.0006-341X.2001.00007.x 10.1002/sim.3450 10.6339/JDS.2009.07(1).418 10.1111/j.1541-0420.2008.01102.x 10.1093/biostatistics/1.4.355 10.1001/archinte.167.15.1655 |
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| References_xml | – reference: Wu L. Mixed Effects Models for Complex Data, CRC Press:New York, 2010. – reference: Demirtas H, Hedeker D. Gaussianization-based quasi-imputation and expansion strategies for incomplete correlated binary responses. Statistics in Medicine 2007;26:782-799. – reference: Kellum JA, Kong L, Fink MP, Weissfeld LA, Yealy DM, Pinsky MR, Fine J, Krichevsky A, Delude RL, Angus DC. Understanding the inflammatory cytokine response in pneumonia and sepsis: results of the Genetic and Inflammatory Markers of Sepsis (GenIMS) Study. Archives of Internal Medicine 2007;167:1655-1663. – reference: Verbeke G, Molenberghs G, Thijs H, Lesaffre E, Kenward MG. Sensitivity analysis for nonrandom dropout: a local influence approach. Biometrics 2001;57:7-14. – reference: Gao S, Thiebaut R. Mixed effect models for truncated longitudinal outcomes with nonignorable missing data. Journal of Data Science 2009;7:13-25. – reference: Hogan JW, Lin X, Herman B. Mixtures of varying coefficient models for longitudinal data with discrete or continuous nonignorable dropout. Biometrics 2004;60:854-864. – reference: Laird NM, Ware JH. Random-effects models for longitudinal data. Biometrics 1982;38:963-974. – reference: Horvitz DG, Thompson DJ. A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association 1952;47:663-685. – reference: Rotnitzky A, Robins JM, Scharfstein DO. Semiparametric regression for repeated outcomes with nonignorable nonresponse. Journal of the American Statistical Association 1998;93:1321-1339. – reference: Lawless JF, Kalbfleisch JD, Wild CJ. Semiparametric methods for response-selective and missing data problems in regression. Journal of the Royal Statistical Society. Series B (Statistical Methodology) 1999;61:413-438. – reference: Troxel AB, Harrington DP, Lipsitz SR. Analysis of longitudinal data with non-ignorable non-monotone missing values. Journal of the Royal Statistical Society Series C-Applied Statistics 1998;47:425-438. – reference: Jacqmin-Gadda H, Thiebaut R, Chene G, Commenges D. Analysis of left-censored longitudinal data with application to viral load in HIV infection. Biostatistics 2000;1:355-368. – reference: Gong G, Samaniego FJ. Pseudo maximum likelihood estimation: theory and applications. The Annals of Statistics 1981;9:861-869. – reference: Epstein MP, Lin X, Boehnke M. A tobit variance-component method for linkage analysis of censored trait data. American Journal of Human Genetics 2003;72:611-620. – reference: Philipson PM, Ho WK, Henderson R. Comparative review of methods for handling drop-out in longitudinal studies. Statics in Medicine 2008;27:6276-6298. – reference: Yuan Y, Little RJA. Mixed-effect hybrid models for longitudinal data with nonignorable dropout. Biometrics 2009;65:478-486. – reference: Tobin J. Estimation of relationship for limited dependent variables. Econometrica 1958;26:24-36. – reference: Lyles RH, Lyles CM, Taylor DJ. Random regression models for human immunodeficiency virus ribonucleic acid data subject to left censoring and informative drop-outs. Journal of the Royal Statistical Society. Series C (Applied Statistics) 2000;49:485-497. – reference: Copas J, Eguchi S. Local sensitivity approximations for selectivity bias. Journal of the Royal Statistical Society Series B-Statistical Methodology 2001;63:871-895. – reference: Huges J. Mixed effects models with censored data with applications to HIV RNA levels. Biometrics 1999;55:625-629. – reference: Kang JDY, Schafer JL. Demystifying double robustness: a comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science 2007;22:523-539. – reference: Robins J, Sued M, Lei-Gomez Q, Rotnitzky A. Comment: performance of double-robust estimators when "inverse probability" weights are highly variable. 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| SubjectTerms | Biomarkers Biomarkers - blood Computer Simulation Data collection Data Interpretation, Statistical Humans Interleukin-6 - blood inverse probability weighting left-censoring longitudinal data Longitudinal Studies Mean square errors Medical statistics Models, Statistical non-ignorable missing pseudo-likelihood method Regression analysis Sepsis - blood Sepsis - genetics Sepsis - immunology |
| Title | Analysis of non-ignorable missing and left-censored longitudinal data using a weighted random effects tobit model |
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