Assessment of stratum-covariate interactions in Cox's proportional hazards regression model.

We assess stratum (e.g. treatment) interactions with covariates and with the baseline hazard function in the proportional hazards (PH) regression model for lifetime data. We consider models incorporating stratum interactions both with and without stratification of the risk sets in the likelihood function, and describe likelihood ratio statistics for tests of the presence of these interactions. We also present step-down methods for building reduced models which include stratum-specific parameters corresponding to covariates which interact with treatment. We apply PH models with such interactions to a clinical trial of DES in the treatment of prostate cancer to determine optimal treatment conditional on each patient's covariates.

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

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

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

[4]  D. Byar,et al.  Selecting optimal treatment in clinical trials using covariate information. , 1977, Journal of chronic diseases.

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

[6]  A. V. Peterson,et al.  On the regression analysis of multivariate failure time data , 1981 .

[7]  D. Oakes,et al.  Survival Times: Aspects of Partial Likelihood , 1981 .

[8]  On the comparison of procedures for testing the equality of Survival curves , 1983 .

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

[10]  Richard D. Gill,et al.  Understanding Cox's regression model: a martingale approach : (preprint) , 1984 .

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

[12]  James H. Ware,et al.  On distribution-free tests for equality of survival distributions , 1977 .

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

[14]  V. Farewell.  An Application of Cox's Proportional Hazard Model to Multiple Infection Data , 1979 .

[15]  Niels Keiding,et al.  Linear Nonparametric Tests for Comparison of Counting Processes, with Applications to Censored Survival Data, Correspondent Paper , 1982 .

[16]  R. Kay.  The analysis of transition times in multistate stochastic processes using proportional hazard regression models , 1982 .

[17]  D. Byar,et al.  Estrogen treatment for cancer of the prostate. Early results with 3 doses of diethylstilbestrol and placebo , 1970, Cancer.

[18]  S. Johansen.  An Extension of Cox's Regression Model , 1983 .

[19]  V T Farewell,et al.  The analysis of failure times in the presence of competing risks. , 1978, Biometrics.