Hi, I'm interested in building a Cox PH model for survival modeling, using 2 covariates (x1 and x2). x1 represents a 'baseline' covariate, whereas x2 represents a 'new' covariate, and my goal is to figure out where x2 adds significant predictive information over x1. Ideally, I could get a p-value for doing this. Originally, I thought of doing some kind of likelihood ratio test (LRT), where i measure the (partial) likelihood of the model with just x1, then with x1 and x2, then it becomes a LRT with 1 degree of freedom. But when i use the summary() function for coxph(), i get the following output (shown at the bottom). I have two questions: 1) What exactly are the p-values in the Pr(>|z|) representing? I understand that the coefficients have standard errors, etc., but i'm not sure how the p-value there is calculated. 2) At the bottom, where it shows the results of an LRT with 2df, i don't quite understand what model the ratio is being tested against. If the current model has two variables (x1 and x2), and those are the extra degrees of freedom, then the baseline should then have 0 variables, but that's not really a Cox model? thanks for any help. Brian> summary(coxph(Surv(myTime,Event)~x1+x2))Call: coxph(formula = Surv(myTime, Event) ~ x1 + x2) n= 211 coef exp(coef) se(coef) z Pr(>|z|) x1 0.03594 1.03660 0.17738 0.203 0.83942 x2 0.53829 1.71308 0.17775 3.028 0.00246 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 exp(coef) exp(-coef) lower .95 upper .95 x1 1.037 0.9647 0.7322 1.468 x2 1.713 0.5837 1.2091 2.427 Rsquare= 0.111 (max possible= 0.975 ) Likelihood ratio test= 21.95 on 2 df, p=1.714e-05 Wald test = 20.29 on 2 df, p=3.924e-05 Score (logrank) test = 22.46 on 2 df, p=1.328e-05 [[alternative HTML version deleted]]
1) The p values in the printout are a Wald test. The Wald, score, and likelihood ratio tests are asymptotically equivalent, but may differ somewhat in finite samples. (The Wald and score are both Taylor series approximations to the LR). If you want to do an LR test, fit the two models and use the anova command. But beware if your second variable has missing values: the two fits have to be on the same sample. 2) Yes, coxph(Surv(time, status) ~1) is a valid Cox model. Not a particularly interesting one -- it's the LR for the overall fit of the baseline hazard which is equivalent to a Kaplan Meier when there are no covariates. Terry T. -------begin inclusion ------ I'm interested in building a Cox PH model for survival modeling, using 2 covariates (x1 and x2). x1 represents a 'baseline' covariate, whereas x2 represents a 'new' covariate, and my goal is to figure out where x2 adds significant predictive information over x1. Ideally, I could get a p-value for doing this. Originally, I thought of doing some kind of likelihood ratio test (LRT), where i measure the (partial) likelihood of the model with just x1, then with x1 and x2, then it becomes a LRT with 1 degree of freedom. But when i use the summary() function for coxph(), i get the following output (shown at the bottom). I have two questions: 1) What exactly are the p-values in the Pr(>|z|) representing? I understand that the coefficients have standard errors, etc., but i'm not sure how the p-value there is calculated. 2) At the bottom, where it shows the results of an LRT with 2df, i don't quite understand what model the ratio is being tested against. If the current model has two variables (x1 and x2), and those are the extra degrees of freedom, then the baseline should then have 0 variables, but that's not really a Cox model? thanks for any help.