Logistic Regression, Survival Analysis, and the Kaplan-Meier Curve

Abstract We discuss the use of standard logistic regression techniques to estimate hazard rates and survival curves from censored data. These techniques allow the statistician to use parametric regression modeling on censored data in a flexible way that provides both estimates and standard errors. An example is given that demonstrates the increased structure that can be seen in a parametric analysis, as compared with the nonparametric Kaplan-Meier survival curves. In fact, the logistic regression estimates are closely related to Kaplan-Meier curves, and approach the Kaplan-Meier estimate as the number of parameters grows large.

[1]  Calyampudi Radhakrishna Rao,et al.  Linear Statistical Inference and its Applications , 1967 .

[2]  David R. Cox.  The analysis of binary data , 1970 .

[3]  Calyampudi R. Rao,et al.  Linear Statistical Inference and Its Applications. , 1975 .

[4]  T. Holford.  Life tables with concomitant information. , 1976, Biometrics.

[5]  B. Efron.  The Efficiency of Cox's Likelihood Function for Censored Data , 1977 .

[6]  Thompson Wa.  On the treatment of grouped observations in life studies. , 1977 .

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

[8]  D A Pierce,et al.  Distribution-free regression analysis of grouped survival data. , 1979, Biometrics.

[9]  W. J. Padgett,et al.  Maximum likelihood estimation of a distribution function with increasing failure rate based on censored observations , 1980 .

[10]  J. Anderson,et al.  Smooth Estimates for the Hazard Function , 1980 .

[11]  N. L. Johnson,et al.  Survival Models and Data Analysis , 1982 .

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

[13]  J. Friedman,et al.  Projection Pursuit Regression , 1981 .

[14]  Thomas J. Santner,et al.  Maximum likelihood estimation of the survival function based on censored data under hazard rate assumptions , 1981 .

[15]  Rupert G. Miller,et al.  Survival Analysis , 2022, The SAGE Encyclopedia of Research Design.

[16]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[17]  J. Anderson,et al.  A Two-step Regression Model for Hazard Functions , 1982 .

[18]  Martin A. Tanner,et al.  The Estimation of the Hazard Function from Randomly Censored Data by the Kernel Method , 1983 .

[19]  R. G. Miller,et al.  What price Kaplan-Meier? , 1983, Biometrics.

[20]  David Clayton,et al.  Fitting a General Family of Failure-Time Distributions using GLIM , 1983 .

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

[22]  Wing Hung Wong,et al.  Data-Based Nonparametric Estimation of the Hazard Function with Applications to Model Diagnostics and Exploratory Analysis , 1984 .

[23]  D. Cox,et al.  Analysis of Survival Data. , 1985 .

[24]  R. Tibshirani,et al.  Generalized additive models for medical research , 1986, Statistical methods in medical research.

[25]  Wei-Yann Tsai,et al.  Estimation of the survival function with increasing failure rate based on left truncated and right censored data , 1988 .