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Analysis of longitudinal data with irregular, outcome-dependent follow-up. (English) Zbl 1046.62118
Summary: A frequent problem in longitudinal studies is that subjects may miss scheduled visits or be assessed at self-selected points in time. As a result, observed outcome data may be highly unbalanced and the availability of the data may be directly related to the outcome measure and/or some auxiliary factors that are associated with the outcome. If the follow-up visit and outcome processes are correlated, then marginal regression analyses will produce biased estimates.
Building on the work of J. M. Robins, A. Rotnitzky and L. P. Zhao [J. Am. Stat. Assoc. 90, No. 429, 106–121 (1995; Zbl 0818.62042)] we propose a class of inverse intensity-of-visit process-weighted estimators in marginal regression models for longitudinal responses that may be observed in continuous time. This allows us to handle arbitrary patterns of missing data as embedded in a subject’s visit process. We derive the large sample distribution for our inverse visit-intensity-weighted estimators and investigate their finite sample behaviour by simulation. Our approach is illustrated with a data set from a health services research study in which homeless people with mental illness were randomized to three different treatments and measures of homelessness (as percentage of days homeless in the past 3 months) and other auxiliary factors were recorded at follow-up times that are not fixed by design.

MSC:
62P10 Applications of statistics to biology and medical sciences; meta analysis
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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[1] DOI: 10.1111/j.0006-341X.2002.00631.x · Zbl 1210.62138 · doi:10.1111/j.0006-341X.2002.00631.x
[2] Anderson P. K., Statistical Models based on Counting Processes (1993) · doi:10.1007/978-1-4612-4348-9
[3] Bickel P. J., Efficient and Adaptive Estimation for Semiparametric Models (1993) · Zbl 0786.62001
[4] Daley D. J., An Introduction to the Theory of Point Processes: Elementary Theory and Methods (2002)
[5] DOI: 10.1111/j.0006-341X.1999.00565.x · Zbl 1059.62639 · doi:10.1111/j.0006-341X.1999.00565.x
[6] Diggle P., Appl. Statist. 43 pp 49– (1994)
[7] DOI: 10.1002/sim.718 · doi:10.1002/sim.718
[8] Fleming T. R., Counting Processes and Survival Analysis (1991) · Zbl 0727.62096
[9] Follmann D., Biometrics 51 pp 151– (1995)
[10] Gasser T., Lect. Notes Math. 757 pp 23– (1979)
[11] DOI: 10.1002/(SICI)1097-0258(19970215)16:3<239::AID-SIM483>3.0.CO;2-X · doi:10.1002/(SICI)1097-0258(19970215)16:3<239::AID-SIM483>3.0.CO;2-X
[12] Huber P. J., Ann. Statist. 13 pp 435– (1985)
[13] Kalbfleisch J. D., The Statistical Analysis of Failure Time Data (2002) · Zbl 1012.62104 · doi:10.1002/9781118032985
[14] Laan M. J., Unified Approach for Censored Longitudinal Data and Causality (2003) · Zbl 1013.62034 · doi:10.1007/978-0-387-21700-0
[15] Liang K.-Y., Biometrika 73 pp 13– (1986)
[16] DOI: 10.1111/j.0006-341X.2002.00621.x · Zbl 1210.62181 · doi:10.1111/j.0006-341X.2002.00621.x
[17] Little R. J. A., J. Am. Statist. Ass. 90 pp 1112– (1995)
[18] DOI: 10.1093/biomet/85.2.487 · Zbl 0931.62014 · doi:10.1093/biomet/85.2.487
[19] McCullagh P., Generalized Linear Models (1989) · Zbl 0744.62098 · doi:10.1007/978-1-4899-3242-6
[20] Newey W. K., J. Appl. Econ. 5 pp 99– (1990)
[21] Preisser J. S., J. Am. Statist. Ass. 95 pp 1021– (2000)
[22] Robins J. M., Biometrics 48 pp 479– (1992)
[23] DOI: 10.1002/(SICI)1097-0258(19970215)16:3<285::AID-SIM535>3.0.CO;2-# · doi:10.1002/(SICI)1097-0258(19970215)16:3<285::AID-SIM535>3.0.CO;2-#
[24] Robins J. M., AIDS Epidemiology-Methodological Issues pp 297– (1992) · doi:10.1007/978-1-4757-1229-2_14
[25] Robins J. M., J. Am. Statist. Ass. 90 pp 106– (1995)
[26] DOI: 10.1001/archpsyc.60.9.940 · doi:10.1001/archpsyc.60.9.940
[27] Rotnitzky A., J. Am. Statist. Ass. 93 pp 1321– (1998)
[28] Scharfstein D. O., J. Am. Statist. Ass. 94 pp 1096– (1999)
[29] DOI: 10.1093/biomet/85.3.661 · Zbl 0918.62088 · doi:10.1093/biomet/85.3.661
[30] Vaart A. W., Asymptotic Statistics (1998) · Zbl 0910.62001 · doi:10.1017/CBO9780511802256
[31] DOI: 10.1002/1521-4036(200203)44:2<175::AID-BIMJ175>3.0.CO;2-3 · doi:10.1002/1521-4036(200203)44:2<175::AID-BIMJ175>3.0.CO;2-3
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