Regression models for truncated survival data

Right truncated survival data measured in discrete time are considered. A simple derivation of Turnbull's (1976) non-parametric maximum likelihood estimate of the cumulative distribution function is given. Regression models in discrete time are considered for the analysis of right truncated and left censored survival data when categorical or ordered categorical covariates are present. Standard programs, with risk sets appropriately defined, that compute maximum likelihood estimates for regression coefficients from discrete data, may be used to compute maximum likelihood estimates of the proposed model parameters. Dynamic asymptotic methods of Arjas & Haara (1987) permit the establishment of asymptotic joint normality of the estimates. In the continuous case, an extension of Cox's model to retro-hazard functions is established using a time transformation. Asymptotic properties are derived following Andersen et al. (1985) and Andersen & Gill (1982).

[1]  Niels Keiding,et al.  Random truncation models and Markov processes , 1990 .

[2]  B. Turnbull.  The Empirical Distribution Function with Arbitrarily Grouped, Censored, and Truncated Data , 1976 .

[3]  Nicholas P. Jewell,et al.  Asymptotic Properties of the Product Limit Estimate Under Random Truncation , 1986 .

[4]  S W Lagakos,et al.  Analysis of doubly-censored survival data, with application to AIDS. , 1989, Biometrics.

[5]  Mads Melbye,et al.  USE OF A LOG-LINEAR MODEL TO COMPUTE THE EMPIRICAL SURVIVAL CURVE FROM INTERVAL-CENSORED DATA, WITH APPLICATION TO DATA ON TESTS FOR HIV POSITIVITY , 1991 .

[6]  R. Prentice,et al.  Regression analysis of grouped survival data with application to breast cancer data. , 1978, Biometrics.

[7]  Zhiliang Ying,et al.  Estimating a distribution function with truncated and censored data , 1991 .

[8]  L. Billard,et al.  Incubation period of AIDS in patients infected via blood transfusion , 1987, Nature.

[9]  M. Woodroofe.  Estimating a Distribution Function with Truncated Data , 1985 .

[10]  Jerald F. Lawless,et al.  Inference Based on Retrospective Ascertainment: An Analysis of the Data on Transfusion-Related AIDS , 1989 .

[11]  Nan M. Laird,et al.  Covariance Analysis of Censored Survival Data Using Log-Linear Analysis Techniques , 1981 .

[12]  V. De Gruttola,et al.  Nonparametric analysis of truncated survival data, with application to AIDS , 1988 .

[13]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[14]  N Keiding,et al.  Confirmatory analysis of survival data using left truncation of the life times of primary survivors. , 1987, Statistics in medicine.

[15]  R Brookmeyer,et al.  The analysis of delays in disease reporting: methods and results for the acquired immunodeficiency syndrome. , 1990, American journal of epidemiology.

[16]  Niels Keiding,et al.  Age‐Specific Incidence and Prevalence: A Statistical Perspective , 1991 .

[17]  Kwok-Leung Tsui,et al.  A Nonparametric Approach to the Truncated Regression Problem , 1988 .

[18]  Elja Arjas,et al.  A logistic regression model for hazard: asymptotic results , 1987 .

[19]  N Keiding,et al.  A Cox regression model for the relative mortality and its application to diabetes mellitus survival data. , 1985, Biometrics.

[20]  Mei-Cheng Wang,et al.  Nonparametric Estimation from Cross-Sectional Survival Data , 1991 .

[21]  Nicholas P. Jewell,et al.  A note on the product-limit estimator under right censoring and left truncation , 1987 .

[22]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[23]  K. Lui,et al.  A model-based approach for estimating the mean incubation period of transfusion-associated acquired immunodeficiency syndrome. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[24]  L Ryan,et al.  Survival analysis in natural history studies of disease. , 1989, Statistics in medicine.

[25]  R. Gill,et al.  Cox's regression model for counting processes: a large sample study : (preprint) , 1982 .

[26]  B. Efron.  Logistic Regression, Survival Analysis, and the Kaplan-Meier Curve , 1988 .

[27]  Zhiliang Ying,et al.  Rank Regression Methods for Left-Truncated and Right-Censored Data , 1991 .