Abstract
In a longitudinal study, an individual is followed up over a period of time. Repeated measurements on the response and some time-dependent covariates are taken at a series of sampling times. The sampling times are often irregular and depend on covariates. In this paper, we propose a sampling adjusted procedure for the estimation of the proportional mean model without having to specify a sampling model. Unlike existing procedures, the proposed method is robust to model misspecification of the sampling times. Large sample properties are investigated for the estimators of both regression coefficients and the baseline function. We show that the proposed estimation procedure is more efficient than the existing procedures. Large sample confidence intervals for the baseline function are also constructed by perturbing the estimation equations. A simulation study is conducted to examine the finite sample properties of the proposed estimators and to compare with some of the existing procedures. The method is illustrated with a data set from a recurrent bladder cancer study.
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References
Andersen PK, Gill RD (1982) Cox’x regression model for counting processes: a large sample study. Annal Stat 10: 1100–1120
Byar DP (1980) The veterans administration study of chemoprophylaxis for recurrent stage I bladder tumors: comparison of placebo, pyridoxine, and topical thiotepa. In: Pavone-Macaluso M, Smith PH, Edsmyn F (eds) Bladder tumors and other topics in urological oncology. Plenum, New York, pp 363–370
Cheng SC, Wei LJ (2000) Inferences for a semiparametric model with panel data. Biometrika 87: 89–97
Fan J, Li R (2004) New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis. J Am Stat Assoc 99: 710–723
Gilbert PB, Sun Y (2005) Failure time analysis of HIV vaccine effects on viral load and treatment initiation. Biostatistics 6: 374–394
Goffman C (1965) Calculus of several variables. Harper and Row, New York
Hoover DR, Rice JA, Wu CO, Yang LP (1998) Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika 85: 809–822
Hu XJ, Lagakos SW, Lockhart RA (2009) Generalized least squares estimation of the mean function of a counting process based on panel counts. Stat Sinica 19: 561–580
Hu XJ, Sun J, Wei LJ (2003) Regression parameter estimation from panel counts. Scand J Stat 30: 25–43
Jin Z, Ying Z, Wei LJ (2001) A simple resampling method by perturbing the minimand. Biometrika 88: 381–390
Lawless JF, Nadeau C (1995) Some simple robust methods for the analysis of recurrent events. Technometrics 37: 158–168
Liang H, Wu H, Carroll RJ (2003) The relationship between virologic and immunologic responses in AIDS clinical research using mixed-effects varying-coefficient semiparametric models with measurement error. Biostatistics 4: 297–312
Lin DY, Wei LJ, Yang I, Ying Z (2000) Semiparametric regression for the mean and rate functions of recurrent events. J Royal Stat Soc B 62: 711–730
Lin DY, Wei LJ, Ying Z (2001) Semiparametric transformation models for point processes. J Am Stat Assoc 96: 620–628
Lin DY, Ying Z (2001) Semiparametric and nonparametric regression analysis of longitudinal data (with discussion). J Am Stat Assoc 96: 103–113
Lu M, Zhang Y, Huang J (2007) Estimation of the mean function with panel count data using monotone polynomial splines. Biometrika 94: 705–718
Martinussen T, Scheike TH (1999) A semiparametric additive regression model for longitudinal data. Biometrika 86: 691–702
Martinussen T, Scheike TH (2000) A nonparametric dynamic additive regression model for longitudinal data. Annal Stat 28: 1000–1025
Martinussen T, Scheike TH (2001) Sampling adjusted analysis of dynamic additive regression models for longitudinal data. Scand J Stat 28: 303–323
Moyeed RA, Diggle PJ (1994) Rates of convergence in semiparametric modelling of longitudinal data. Aust J Stat 36: 75–93
Rice JA, Silverman B (1991) Estimating the mean and covariance structure nonparametrically when the data are curves. J Royal Stat Soc B 53: 233–243
Scheike TH (2002) The additive nonparametric and semiparametric Aalen model as the rate function for a counting process. Lifetime Data Anal 8: 247–262
Serfling RJ (1980) Approximation theorems of mathematical statistics. Wiley, New York
Sun J, Kalbfleisch JD (1995) Estimation of the mean function of point process based on panel count data. Stat Sinica 5: 279–289
Sun Y, Wu H (2005) Semiparametric time-varying coefficients regression model for longitudinal data. Scand J Stat 32: 21–47
Sun J, Wei LJ (2000) Regression analysis of panel count data with covariate-dependent observation and censoring times. J Royal Stat Soc B 62: 293–302
Van der Vaart AW (1998) Asymptotic statistics. Cambridge University Press, Cambridge
Wellner JA, Zhang Y (2000) Two estimators of the mean of a counting process with panel count data. Annal Stat 28: 779–814
Wu CO, Chiang CT, Hoover D (1998) Asymptotic confidence regions for kernel smoothing of a time-varying coefficient model with longitudinal data. J Am Stat Assoc 88: 1388–1402
Wu H, Liang H (2004) Backfitting random varying-coefficient models with time-dependent smoothing covariates. Scand J Stat 31: 3–19
Wu H, Zhang JT (2002) Local polynomial mixed-effects models for longitudinal data. J Am Stat Assoc 97: 883–897
Zeger SL, Diggle PJ (1994) Semiparametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters. Biometrics 55: 452–459
Zhang Y. (2002) A semiparametric pseudolikelihood estimation method for panel count data. Biometrika 89: 39–48
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Sun, Y. Estimation of semiparametric regression model with longitudinal data. Lifetime Data Anal 16, 271–298 (2010). https://doi.org/10.1007/s10985-009-9136-2
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DOI: https://doi.org/10.1007/s10985-009-9136-2