Problems and prediction in survival-data analysis.

Twenty-one years after its appearance, Cox's 1972 paper on 'Regression models and life tables' continues to be one of the most frequently cited publications in the scientific and medical literature. The proportional-hazards model and partial-likelihood technique have been applied to thousands of data sets, not always appropriately, and have motivated hundreds of theoretical studies, not always relevant. Recent developments are reviewed and continuing problems discussed, especially with respect to predictive inference. The accuracy of model-based predictions, and how they compare with consultants' judgements are investigated by means of an example.

[1]  M. Schemper The relative importance of prognostic factors in studies of survival , 1993 .

[2]  P. J. Verweij,et al.  Cross-validation in survival analysis. , 1993, Statistics in medicine.

[3]  O. Aalen,et al.  Further results on the non-parametric linear regression model in survival analysis. , 1993, Statistics in medicine.

[4]  Adrian F. M. Smith,et al.  Bayesian Inference for Generalized Linear and Proportional Hazards Models Via Gibbs Sampling , 1993 .

[5]  R. Tibshirani,et al.  Varying‐Coefficient Models , 1993 .

[6]  Z. Ying,et al.  Checking the Cox model with cumulative sums of martingale-based residuals , 1993 .

[7]  Jens Perch Nielsen,et al.  A framework for consistent prediction rules based on markers , 1993 .

[8]  P. Sasieni Maximum weighted partial likelihood estimators for the Cox model , 1993 .

[9]  T. Bednarski Robust estimation in Cox's regression model , 1993 .

[10]  Robin Henderson,et al.  Influence in Linear Hazard Models , 1993 .

[11]  M. Schemper Cox Analysis of Survival Data with Non‐Proportional Hazard Functions , 1992 .

[12]  D. Lin Sequential log rank tests adjusting for covariates with the accelerated life model , 1992 .

[13]  K. Yamaguchi Accelerated Failure-Time Regression Models with a Regression Model of Surviving Fraction: An Application to the Analysis of “Permanent Employment” in Japan , 1992 .

[14]  James M. Robins,et al.  Semiparametric estimation of an accelerated failure time model with time-dependent covariates , 1992 .

[15]  J. Robins Estimation of the time-dependent accelerated failure time model in the presence of confounding factors , 1992 .

[16]  Joel L. Horowitz,et al.  A Generalized Moments Specification Test of the Proportional Hazards Model , 1992 .

[17]  Michael Schemper,et al.  Further results on the explained variation in proportional hazards regression , 1992 .

[18]  J. Simonoff,et al.  Prediction in censored survival data: a comparison of the proportional hazards and linear regression models. , 1992, Biometrics.

[19]  P. Sasieni,et al.  Non-orthogonal projections and their application to calculating the information in a partly linear Cox model , 1992 .

[20]  M Schumacher,et al.  A bootstrap resampling procedure for model building: application to the Cox regression model. , 1992, Statistics in medicine.

[21]  P. Oman A note on last case influence using the partial likelihood approach under heavy censoring. , 1992, Statistics in medicine.

[22]  P. Andersen,et al.  Survival analysis 1982-1991: the second decade of the proportional hazards regression model. , 1991, Statistics in medicine.

[23]  R. Gentleman,et al.  Local full likelihood estimation for the proportional hazards model. , 1991, Biometrics.

[24]  Robin Henderson,et al.  Aalen Plots under Proportional Hazards , 1991 .

[25]  Danyu Lin,et al.  Goodness-of-Fit Analysis for the Cox Regression Model Based on a Class of Parameter Estimators , 1991 .

[26]  R. Gentleman,et al.  Graphical Methods for Censored Data , 1991 .

[27]  On residual plots for relative risk regression , 1991 .

[28]  C H Chen,et al.  Diagnostic plots in Cox's regression model. , 1991, Biometrics.

[29]  Richard Simon,et al.  Explained Residual Variation, Explained Risk, and Goodness of Fit , 1991 .

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

[31]  D G Clayton,et al.  A Monte Carlo method for Bayesian inference in frailty models. , 1991, Biometrics.

[32]  D. Harrington,et al.  Counting Processes and Survival Analysis , 1991 .

[33]  D. Gamerman Dynamic Bayesian Models for Survival Data , 1991 .

[34]  Ian W. McKeague,et al.  Weighted Least Squares Estimation for Aalen's Additive Risk Model , 1991 .

[35]  K. Anderson,et al.  A nonproportional hazards Weibull accelerated failure time regression model. , 1991, Biometrics.

[36]  Zhiliang Ying,et al.  Linear regression analysis of censored survival data based on rank tests , 1990 .

[37]  R. Tibshirani,et al.  Exploring the nature of covariate effects in the proportional hazards model. , 1990, Biometrics.

[38]  A. Pettitt,et al.  Investigating Time Dependence in Cox's Proportional Hazards Model , 1990 .

[39]  J. C. van Houwelingen,et al.  Predictive value of statistical models , 1990 .

[40]  N. Hjort Goodness of fit tests in models for life history data based on cumulative hazard rates , 1990 .

[41]  Klaus J. Utikal,et al.  Inference for a Nonlinear Counting Process Regression Model , 1990 .

[42]  K. L. Q. Read,et al.  Proportional Hazards Changepoint Models in Survival Analysis , 1990 .

[43]  J. F. Bjørnstad Predictive Likelihood: A Review , 1990 .

[44]  R Simon,et al.  Measures of explained variation for survival data. , 1990, Statistics in medicine.

[45]  Michael Schemper,et al.  The explained variation in proportional hazards regression , 1990 .

[46]  A. Karr,et al.  Nonparametric Survival Analysis with Time-Dependent Covariate Effects: A Penalized Partial Likelihood Approach , 1990 .

[47]  A. Tsiatis Estimating Regression Parameters Using Linear Rank Tests for Censored Data , 1990 .

[48]  P. Grambsch,et al.  Martingale-based residuals for survival models , 1990 .

[49]  R. Gray Some diagnostic methods for Cox regression models through hazard smoothing. , 1990, Biometrics.

[50]  O. Aalen A linear regression model for the analysis of life times. , 1989, Statistics in medicine.

[51]  Anthony N. Pettitt,et al.  Case-Weighted Measures of Influence for Proportional Hazards Regression , 1989 .

[52]  J O'Quigley,et al.  Score tests for homogeneity of regression effect in the proportional hazards model. , 1989, Biometrics.

[53]  John T. Kent,et al.  Measures of dependence for censored survival data , 1988 .

[54]  W. Barlow,et al.  Residuals for relative risk regression , 1988 .

[55]  Elja Arjas,et al.  A Graphical Method for Assessing Goodness of Fit in Cox's Proportional Hazards Model , 1988 .

[56]  Douglas G. Altman,et al.  A note on the uncertainty of a survival probability estimated from Cox's regression model , 1986 .

[57]  J. Mau,et al.  On a Graphical Method for the Detection of Time‐Dependent Effects of Covariates in Survival Data , 1986 .

[58]  R. Butler Predictive Likelihood Inference with Applications , 1986 .

[59]  A. Davison Approximate predictive likelihood , 1986 .

[60]  Mounir Mesbah,et al.  A Global Goodness‐Of‐Fit Statistic for the Proportional Hazards Model , 1985 .

[61]  Jack Cuzick,et al.  The EM Algorithm for Cox's Regression Model Using Glim , 1985 .

[62]  Nancy Reid,et al.  Influence functions for proportional hazards regression , 1985 .

[63]  J. Crowley,et al.  A Diagnostic for Cox Regression and General Conditional Likelihoods , 1985 .

[64]  N. Lange,et al.  Approximate case influence for the proportional hazards regression model with censored data. , 1984, Biometrics.

[65]  Ørnulf Borgan,et al.  Counting process models for life history data: a review , 1984 .

[66]  C. Link,et al.  Confidence intervals for the survival function using Cox's proportional-hazard model with covariates. , 1984, Biometrics.

[67]  David A. Schoenfeld,et al.  Partial residuals for the proportional hazards regression model , 1982 .

[68]  Per Kragh Andersen,et al.  Testing Goodness of Fit of Cox's Regression and Life Model , 1982 .

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

[70]  Odd Aalen,et al.  A Model for Nonparametric Regression Analysis of Counting Processes , 1980 .

[71]  David A. Schoenfeld,et al.  Chi-squared goodness-of-fit tests for the proportional hazards regression model , 1980 .

[72]  O. Aalen Nonparametric Inference for a Family of Counting Processes , 1978 .

[73]  J. Kalbfleisch Non‐Parametric Bayesian Analysis of Survival Time Data , 1978 .

[74]  D. Cox Regression Models and Life-Tables , 1972 .