Estimation and comparison of changes in the presence of informative right censoring: conditional linear model.

A general linear regression model for the usual least squares estimated rate of change (slope) on censoring time is described as an approximation to account for informative right censoring in estimating and comparing changes of a continuous variable in two groups. Two noniterative estimators for the group slope means, the linear minimum variance unbiased (LMVUB) estimator and the linear minimum mean squared error (LMMSE) estimator, are proposed under this conditional model. In realistic situations, we illustrate that the LMVUB and LMMSE estimators, derived under a simple linear regression model, are quite competitive compared to the pseudo maximum likelihood estimator (PMLE) derived by modeling the censoring probabilities. Generalizations to polynomial response curves and general linear models are also described.

[1]  Strother H. Walker,et al.  Estimation of the probability of an event as a function of several independent variables. , 1967, Biometrika.

[2]  J. Ware,et al.  Random-effects models for longitudinal data. , 1982, Biometrics.

[3]  E. Vonesh,et al.  Efficient inference for random-coefficient growth curve models with unbalanced data. , 1987, Biometrics.

[4]  Gail Gong,et al.  Pseudo Maximum Likelihood Estimation: Theory and Applications , 1981 .

[5]  J. Koziol,et al.  A distribution-free test for tumor-growth curve analyses with application to an animal tumor immunotherapy experiment. , 1981, Biometrics.

[6]  Calyampudi R. Rao,et al.  The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves. , 1965, Biometrika.

[7]  Genesis and interpretation of differences in distribution of baseline characteristics between cases and non-cases in cohort studies. , 1979, Journal of chronic diseases.

[8]  Tom Fearn,et al.  A Bayesian approach to growth curves , 1975 .

[9]  Raymond J. Carroll,et al.  On errors-in-variables for binary regression models , 1984 .

[10]  J. Schlesselman,et al.  Planning a longitudinal study. II. Frequency of measurement and study duration. , 1973, Journal of chronic diseases.

[11]  R. D. Bock,et al.  A multivariate correction for attenuation , 1975 .

[12]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[13]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .

[14]  Intermittent positive pressure breathing therapy of chronic obstructive pulmonary disease. A clinical trial. , 1983, Annals of internal medicine.

[15]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[16]  Raymond J. Carroll,et al.  Estimation and comparison of changes in the presence of informative right censoring by modeling the censoring process , 1988 .

[17]  Frederick E. Smith,et al.  Matrix Algebra for the Biological Sciences , 1966 .