Maximum Likelihood Estimation for the Pooled Repeated Partly Interval-Censored Observations Logistic Regression Model
- 1 Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR, USA
- 2 Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR, USA
Abstract
Often in longitudinal studies, some subjects complete their follow-up visits, but others miss their visits due to various reasons. For those who miss follow-up visits, some of them might learn that the event of interest has already happened when they come back. In this case, not only are their event times interval-censored, but also their time-dependent measurements are incomplete. This problem was motivated by a national longitudinal survey of youth data. Maximum likelihood estimation (MLE) method based on expectation-maximization (EM) algorithm is used for parameter estimation. Then missing information principle is applied to estimate the variance-covariance matrix of the MLEs. Simulation studies demonstrate that the proposed method works well in terms of bias, standard error, and power for samples of moderate size. The national longitudinal survey of youth 1997 (NLSY97) data is analyzed for illustration.
- Gao, F., Zeng, D.L. and Lin, D.Y. (2017) Semiparametric Estimation of the Accelerated Failure Time Model with Partly Interval-Censored Data. Biometrics, 73, 1161-1168. https://doi.org/10.1111/biom.12700
- Zhao, X.Q., Zhao, Q., Sun, J.G. and Kim, J.S. (2008) Generalized Log-Rank Tests for Partly Interval-Censored Failure Time Data. Biometrical Journal, 50, 375-385. https://doi.org/10.1002/bimj.200710419
- Kim, J.S. (2003) Maximum Likelihood Estimation for the Proportional Hazards Model with Partly Interval-Censored Data. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65, 489-502. https://doi.org/10.1111/1467-9868.00398
- Huang, J. (1999) Asymptotic Properties of Nonparametric Estimation Based on Partly Interval-Censored Data. Statistica Sinica, 9, 501-519.
- Adrienne Cupples, L., D’Agostino, R.B., Anderson, K. and Kannel, W.B. (1988) Comparison of Baseline and Repeated Measure Covariate Techniques in the Framingham Heart Study. Statistics in Medicine, 7, 205-218. https://doi.org/10.1002/sim.4780070122
- D’Agostino, R., Lee, M.L., Belanger, A., Cupples, L.A., Anderson, K. and Kannel, W.B. (1990) Relation of Pooled Logistic Regression to Time Dependent Cox Regression Analysis: The Framingham Heart Study. Statistics in Medicine, 9, 1501-1515. https://doi.org/10.1002/sim.4780091214
- Finkelstein, D.M., Wang, R., Ficociello, L.H. and Schoenfeld, D.A. (2010) A Score Test for Association of a Longitudinal Marker and an Event with Missing Data. Biometrics, 66, 726-732. https://doi.org/10.1111/j.1541-0420.2009.01326.x
- Dempster, A.P., Laird, N.M. and Rubin, D.B. (1997) Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society: Series B (Methodologica), 39, 1-22. https://doi.org/10.1111/j.2517-6161.1977.tb01600.x
- Masyn, K.E., Petras, H. and Liu, W. (2014) Growth Curve Models with Categorical Outcomes. In: Bruinsma, G. and Weisburd, D., Eds., Encyclopedia of Criminology and Criminal Justice, Springer, New York, 2013-2025. https://doi.org/10.1007/978-1-4614-5690-2_404
- Tanner, M.A. (1996) Tools for Statistical Inference. 3rd Edition, Springer-Verlag, New York. https://doi.org/10.1007/978-1-4612-4024-2
- Mongoué-Tchokoté, S. and Kim, J.S. (2008) New Statistical Software for the Proportional Hazards Model with Current Status Data. Computational Statistics and Data Analysis, 52, 4272-4286. https://doi.org/10.1016/j.csda.2008.02.007