Missing covariates in longitudinal data with informative dropouts: bias analysis and inference. (English) Zbl 1078.62073
Summary: We consider estimation in generalized linear mixed models (GLMM) for longitudinal data with informative dropouts. At the time a unit drops out, time-varying covariates are often unobserved in addition to the missing outcome. However, existing informative dropout models typically require covariates to be completely observed. This assumption is not realistic in the presence of time-varying covariates. We first study the asymptotic bias that would result from applying existing methods, where missing time-varying covariates are handled using naive approaches, which include: (1) using only baseline values; (2) carrying forward the last observation; and (3) assuming the missing data are ignorable.
Our asymptotic bias analysis shows that these naive approaches yield inconsistent estimators of model parameters. We next propose a selection/transition model that allows covariates to be missing in addition to the outcome variable at the time of dropout. The EM algorithm is used for inference in the proposed model. Data from a longitudinal study of human immunodeficiency virus (HIV)-infected women are used to illustrate the methodology.
Our asymptotic bias analysis shows that these naive approaches yield inconsistent estimators of model parameters. We next propose a selection/transition model that allows covariates to be missing in addition to the outcome variable at the time of dropout. The EM algorithm is used for inference in the proposed model. Data from a longitudinal study of human immunodeficiency virus (HIV)-infected women are used to illustrate the methodology.
MSC:
| 62J12 | Generalized linear models (logistic models) |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62F12 | Asymptotic properties of parametric estimators |
References:
| [1] | Booth, Maximizing generalized linear mixed models likelihoods with an automated Monte Carlo EM algorithm, Journal of the Royal Statistical Society, Series B 61 pp 265– (1999) · Zbl 0917.62058 · doi:10.1111/1467-9868.00176 |
| [2] | Breslow, Approximate inference in generalized linear mixed models, Journal of the American Statistical Association 88 pp 9– (1993) · Zbl 0775.62195 · doi:10.2307/2290687 |
| [3] | Diggle, Informative dropout in longitudinal data analysis (with discussion), Applied Statistics 43 pp 49– (1994) · Zbl 0825.62010 · doi:10.2307/2986113 |
| [4] | Ibrahim, Missing covariates in generalized linear models when the missing data mechanism is non-ignorable, Journal of the Royal Statistical Society, Series B 61 pp 173– (1999) · Zbl 0917.62060 · doi:10.1111/1467-9868.00170 |
| [5] | Ibrahim, Missing responses in generalised linear mixed models when the missing data mechanism is nonignorable, Biometrika 88 pp 551– (2001) · Zbl 0984.62047 · doi:10.1093/biomet/88.2.551 |
| [6] | Little, Modeling the drop-out mechanism in repeated measures studies, Journal of the American Statistical Association 90 pp 1112– (1995) · Zbl 0841.62099 · doi:10.2307/2291350 |
| [7] | Louis, Finding the observed information matrix when using the EM algorithm, Journal of the Royal Statistical Society, Series B 44 pp 226– (1982) · Zbl 0488.62018 |
| [8] | Rotnitzky, Semiparametric regression for repeated outcomes with nonignorable nonresponse, Journal of the American Statistical Association 93 pp 1321– (1998) · Zbl 1064.62520 · doi:10.2307/2670049 |
| [9] | Roy, Analysis of multivariate longitudinal outcomes with non-ignorable dropouts and missing covariates: Changes in methadone treatment practices, Journal of the American Statistical Association 97 pp 40– (2002) · Zbl 1073.62587 · doi:10.1198/016214502753479211 |
| [10] | Scharfstein, Adjusting for nonignorable drop-out using semiparametric nonresponse models (with discussions), Journal of the American Statistical Association 94 pp 1096– (1999) · Zbl 1072.62644 · doi:10.2307/2669923 |
| [11] | Smith, Design and baseline participant characteristics of human immunodeficiency virus epidemiology research (HER) study: A prospective cohort study of human immunodeficiency virus infection in US women, American Journal of Epidemiology 146 pp 459– (1997) · doi:10.1093/oxfordjournals.aje.a009299 |
| [12] | Stubbendick, Maximum likelihood methods for nonignorable missing responses and covariates in random effects models, Biometrics 59 pp 1140– (2003) · Zbl 1274.62174 · doi:10.1111/j.0006-341X.2003.00131.x |
| [13] | Tashima, A longitudinal analysis of hospitalization and emergency department use among human immunodeficiency virus-infected women reporting protease inhibitor use, Clinical Infectious Diseases 33 pp 2055– (2001) · doi:10.1086/323978 |
| [14] | Verbeke, Sensitivity analysis for nonrandom dropout: A local influence approach, Biometrics 57 pp 7– (2001) · Zbl 1209.62170 · doi:10.1111/j.0006-341X.2001.00007.x |
| [15] | Wei, A Monte Carlo implementation of the EM algorithm and the poor man’s data augmentation algorithms, Journal of the American Statistical Association 85 pp 699– (1990) · doi:10.2307/2290005 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
