Abstract
Interval-censored time-to-event data occur in many medical areas, with dentistry or AIDS research being typical representatives. This article reviews methods for the analysis of such data, with an emphasis on the use of the accelerated failure time (AFT) model. A flexible AFT model (avoiding parametric assumptions on the distribution of the error term) is described in greater detail and is used to solve a typical dental question in a longitudinal oral health study.
|
Vanobbergen J , Martens L , Lesaffre E , Declerck D. The Signal-Tandmobiel® project - a longitudinal intervention health promotion study in Flanders (Belgium): baseline and first year results . European Journal of Paediatric Dentistry 2000; 2: 87-96 . Google Scholar | |
|
Komárek A , Lesaffre E , Hilton JF. Accelerated failure time model for arbitrarily censored data with smoothed error distribution . Journal of Computational and Graphical Statistics 2005; 14, inpress. Google Scholar | Crossref | ISI | |
|
Rücker G , Messerer D. Remission duration: an example of interval-censored observations . Statistics in Medicine 1988; 7: 1139-1145 . Google Scholar | Crossref | Medline | ISI | |
|
Law CG , Brookmeyer R. Effects of mid-point imputation on the analysis of doubly censored data . Statistics in Medicine 1992; 11: 1569-1578 . Google Scholar | Crossref | Medline | ISI | |
|
Odell PM , Anderson KM , D’Agostino RB. Maximum likelihood estimation for interval-censored data using a Weibull-based accelerated failure time model . Biometrics 1992; 48: 951-959 . Google Scholar | Crossref | Medline | ISI | |
|
Dorey FJ , Little RJ , Schenker N. Multiple imputation for threshold-crossing data with interval censoring . Statistics in Medicine 1993; 12: 1589-1603 . Google Scholar | Crossref | Medline | ISI | |
|
Kaplan EL , Meier P. Nonparametric estimation from incomplete observations . Journal of the American Statistical Association 1958; 53: 457-481 . Google Scholar | Crossref | ISI | |
|
Peto R. Experimental survival curves for interval-censored data . Applied Statistics 1973; 22: 86-91 . Google Scholar | Crossref | |
|
Turnbull BW. The empirical distribution function with arbitrarily grouped, censored and truncated data . Journal of the Royal Statistical Society, Series B 1976; 38: 290-295 . Google Scholar | |
|
Dempster AP , Laird NM , Rubin DB. Maximum likelihood from incomplete data via the EM algorithm . Journal of the Royal Statistical Society, Series B 1977; 39: 1-38 . Google Scholar | |
|
Kooperberg C , Stone CJ. Logspline density estimation for censored data . Journal of Computational and Graphical Statistics 1992; 1: 301-328 . Google Scholar | |
|
Rosenberg PS. Hazard function estimation using B-splines . Biometrics 1995; 51: 874-887 . Google Scholar | Crossref | Medline | ISI | |
|
Mantel N. Evaluation of survival data and two new rank order statistics arising in its consideration . Cancer Chemotherapy Reports 1966; 50: 163-170 . Google Scholar | Medline | |
|
Gehan EA. A generalized Wilcoxon test for comparing arbitrarily singly-censored samples . Biometrika 1965; 52: 203-223 . Google Scholar | Crossref | Medline | ISI | |
|
Peto R , Peto J. Asymptotically efficient rank-invariant test procedures . Journal of the Royal Statistical Society, Series A 1972; 135: 185-206 (with discussion). Google Scholar | Crossref | ISI | |
|
Prentice RL. Linear rank tests with right censored data . Biometrika 1978; 65: 167-179 . Google Scholar | Crossref | ISI | |
|
Pepe MS , Fleming TR. Weighted Kaplan-Meier statistics: a class of distance tests for censored survival data . Biometrics 1989; 45: 497-507 . Google Scholar | Crossref | Medline | ISI | |
|
Mantel N. Ranking procedures for arbitrarily restricted observations . Biometrics 1967; 23: 65-78 . Google Scholar | Crossref | Medline | ISI | |
|
Self SG , Grossman EA. Linear rank tests for interval-censored data with application to PCB levels in adipose tissue of transformer repair workers . Biometrics 1986; 42: 521-530 . Google Scholar | Crossref | Medline | ISI | |
|
Finkelstein DM. A proportional hazards model for interval-censored failure time data . Biometrics 1986; 42: 845-854 . Google Scholar | Crossref | Medline | ISI | |
|
Petroni GR , Wolfe RA. A Sample test for stochastic ordering with interval-censored data . Biometrics 1994; 50: 77-87 . Google Scholar | Crossref | Medline | ISI | |
|
Fay MP. Rank invariant tests for interval censored data under grouped continuous model . Biometrics 1996; 52: 811-822 . Google Scholar | Crossref | Medline | ISI | |
|
Fang H-B , Sun J , Lee M-LT. Nonparametric survival comparisons for interval-censored continuous data . Statistica Sinica 2002; 12: 1073-1083 . Google Scholar | ISI | |
|
Pan W. A two-sample test with interval censored data via multiple imputation . Statistics in Medicine 2000; 19: 1-11 . Google Scholar | Crossref | Medline | ISI | |
|
Cox DR. Regression models and life-tables . Journal of the Royal Statistical Society, Series B 1972; 34: 187-220 (with discussion). Google Scholar | |
|
Cox DR. Partial likelihood . Biometrika 1975; 62: 269-276 . Google Scholar | Crossref | ISI | |
|
Breslow NE. Covariance analysis of censored survival data . Biometrics 1974; 30: 89-99 . Google Scholar | Crossref | Medline | ISI | |
|
Satten GA. Rank-based inference in the proportional hazards model for interval censored data . Biometrika 1996; 83: 355-370 . Google Scholar | Crossref | ISI | |
|
Satten GA , Datta S , Williamson JM. Inference based on imputed failure times for the proportional hazards model with interval-censored data . Journal of the American Statistical Association 1998; 93: 318-327 . Google Scholar | Crossref | ISI | |
|
Goggins WB , Finkelstein DM , Schoenfeld DA , Zaslavsky AM. A Markov chain Monte Carlo EM algorithm for analyzing interval-censored data under the Cox proportional hazards model . Biometrics 1998; 54: 1498-1507 . Google Scholar | Crossref | Medline | ISI | |
|
Pan W. A multiple imputation approach to Cox regression with interval-censored data . Biometrics 2000; 56: 199-203 . Google Scholar | Crossref | Medline | ISI | |
|
Goetghebeur E , Ryan L. Semiparametric regression analysis of interval-censored data . Biometrics 2000; 56: 1139-1144 . Google Scholar | Crossref | Medline | ISI | |
|
Kooperberg C , Clarkson DB. Hazard regression with interval-censored data . Biometrics 1997; 53: 1485-1494 . Google Scholar | Crossref | Medline | ISI | |
|
Betensky RA , Lindsey JC , Ryan LM , Wand MP. Local EM estimation of the hazard function for interval-censored data . Biometrics 1999; 55: 238-245 . Google Scholar | Crossref | Medline | ISI | |
|
Kalbfleisch JD , Prentice RL. The statistical analysis of failure time data, second edition. Hoboken: John Wiley & Sons , 2002. Google Scholar | Crossref | |
|
Rabinowitz D , Tsiatis A , Aragon J. Regression with interval-censored data . Biometrika 1995; 82: 501-513 . Google Scholar | Crossref | ISI | |
|
Betensky RA , Rabinowitz D , Tsiatis AA. Computationally simple accelerated failure time regression for interval censored data . Biometrika 2001; 88: 703-711 . Google Scholar | Crossref | ISI | |
|
Pan W , Louis TA. A linear mixed-effects model for multivariate censored data . Biometrics 2000; 56: 160-166 . Google Scholar | Crossref | Medline | ISI | |
|
Pan W , Connett JE. A multiple imputation approach to linear regression with clustered censored data . Lifetime Data Analysis 2001; 7: 111-123 . Google Scholar | Crossref | Medline | ISI | |
|
Pan W , Kooperberg C. Linear regression for bivariate censored data via multiple imputation . Statistics in Medicine 1999; 18: 3111-3121 . Google Scholar | Crossref | Medline | ISI | |
|
Hougaard P. Fundamentals of survival data . Biometrics 1999; 55: 13-22 . Google Scholar | Crossref | Medline | ISI | |
|
Eilers PHC , Marx BD. Flexible smoothing with B-splines and penalties . Statistical Science 1996; 11: 89-121 . Google Scholar | Crossref | ISI | |
|
Akaike H. A new look at the statistical model identification . IEEE Transactions on Automatic Control 1974; AC-19: 716-723 . Google Scholar | Crossref | ISI | |
|
Pourahmadi M. Joint mean-covariance models with applications to longitudinal data: unconstrained parametrisation . Biometrika 1999; 86: 677-690 . Google Scholar | Crossref | ISI | |
|
Pan J , MacKenzie G. On modelling mean-covariance structures in longitudinal studies . Biometrika 2003; 90: 239-244 . Google Scholar | Crossref | ISI | |
|
R Development Core Team . R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing , 2004, ISBN 3-900051-00-3, URL http://www.R-project.org. Accessed 17 October 2005. Google Scholar |
