Selecting Concomitant Variables Using a Likelihood Ratio Step-Down Procedure and a Method of Testing Goodness of Fit in an Exponential Survival Model

In 1960, the Veterans Administration Co-operative Urological Research Group (VACURG) undertook a study designed to compare several standard modes of treatment for cancer of the prostate. In 1967 the group analyzed, by treatment, survival experience through August 15, 1966 and published these data along with a detailed description of the study design (Mellinger [1967]). Meanwhile, Feigl and Zelen [1965] published a paper dealing with follow-up studies using an exponential model with concomitant information to estimate survival probabilities. This model was extended in 1966 to censored data by Zippen and Armitage [1966]. A more recent paper by the VACURG group (Huse et al. [1974]) modified this model to determine the relative importance of presenting signs and symptoms in relation to survival and to suggest optimum treatment depending upon symptoms presented at diagnosis. Using the same basic model (see Appendix 1), we have reanalyzed the VACURG data to obtain estimates of the parameters of eight variables (Table 1) felt to be important in predicting survival of patients with prostatic cancer and have evaluated the fit of the model to the data. We also introduce a log likelihood ratio step-down procedure for elimination of variables.