Least squares type estimation for Cox regression model and specification error

A new estimation procedure for the Cox proportional hazards model is introduced. The method proposed employs the sample covariance matrix of model covariates and alternates between estimating the baseline cumulative hazard function and estimating model coefficients. It is shown that the estimating equation for model parameters resembles the least squares estimate in a linear regression model, where the outcome variable is the transformed event time. As a result an explicit expression for the difference in the parameter estimates between nested models can be derived. Nesting occurs when the covariates of one model are a subset of the covariates of the other. The new method applies mainly to the uncensored data, but its extension to the right censored observations is also proposed.

[1]  Jerald F. Lawless,et al.  Statistical Models and Methods for Lifetime Data. , 1983 .

[2]  Z. Ying,et al.  Analysis of transformation models with censored data , 1995 .

[3]  C. Huber-Carol,et al.  Effects of omitting covariates in Cox's model for survival data , 1988 .

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

[5]  Gordon Johnston,et al.  Statistical Models and Methods for Lifetime Data , 2003, Technometrics.

[6]  John D. Kalbfleisch,et al.  Misspecified proportional hazard models , 1986 .

[7]  Kjell A. Doksum,et al.  An extension of partial likelihood methods for proportional hazard models to general transformation models , 1987 .

[8]  J. Jett,et al.  Placebo-controlled trial of hydrazine sulfate in patients with newly diagnosed non-small-cell lung cancer. , 1994, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[9]  M. Gail,et al.  Biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates , 1984 .

[10]  Thomas A. Gerds,et al.  On functional misspecification of covariates in the Cox regression model , 2001 .

[11]  Nader Ebrahimi,et al.  A semi-parametric generalization of the Cox proportional hazards regression model: Inference and applications , 2011, Comput. Stat. Data Anal..

[12]  Zhiliang Ying,et al.  Predicting Survival Probabilities with Semiparametric Transformation Models , 1997 .

[13]  Roger M. Cooke,et al.  Competing risk and the Cox proportional hazard model , 2006 .

[14]  N. Breslow.  Covariance analysis of censored survival data. , 1974, Biometrics.

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

[16]  R. Prentice,et al.  Commentary on Andersen and Gill's "Cox's Regression Model for Counting Processes: A Large Sample Study" , 1982 .

[17]  Zhiliang Ying,et al.  On the linear transformation model for censored data , 1998 .

[18]  J. Kalbfleisch,et al.  Marginal likelihoods based on Cox's regression and life model , 1973 .

[19]  Zhiliang Ying,et al.  Semiparametric analysis of transformation models with censored data , 2002 .

[20]  A. Tsiatis.  A Large Sample Study of Cox's Regression Model , 1981 .

[21]  Collin Carbno,et al.  Uncertainty Analysis With High Dimensional Dependence Modelling , 2007, Technometrics.

[22]  Gillian Bartlett,et al.  Bias due to aggregation of individual covariates in the Cox regression model. , 2003, American journal of epidemiology.