In R, I am doing survival data analysis of cancer patients.
I have been reading very helpful stuff about survival analysis in CrossValidated and other places and think I understood how to interpret the Cox regression results. However, one result still bugs me...
I am comparing survival vs. gender. The Kaplan-Meier curves are in clear favour of female patients (I have checked several times that the legend I have added is correct, the patient with the maximum survival, 4856 days, is indeed a woman):
And the Cox regression is returning:
Call: coxph(formula = survival ~ gender, data = Clinical) n= 348, number of events= 154 coef exp(coef) se(coef) z Pr(>|z|) gendermale -0.3707 0.6903 0.1758 -2.109 0.035 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 exp(coef) exp(-coef) lower .95 upper .95 gendermale 0.6903 1.449 0.4891 0.9742 Concordance= 0.555 (se = 0.019 ) Rsquare= 0.012 (max possible= 0.989 ) Likelihood ratio test= 4.23 on 1 df, p=0.03982 Wald test = 4.45 on 1 df, p=0.03499 Score (logrank) test = 4.5 on 1 df, p=0.03396
So Hazards Ratio (HR) for male patients (
gendermale) is 0.6903. The way I would interpret that (without looking at the Kaplan-Meier curve) is: as the HR is <1, being a patient of male gender is protective. Or more precisely, a female patient is 1/0.6903 = exp(-coef) = 1.449 more likely to die at any specific time than a male.
But that does not seem like what the Kaplan-Meier curves say! What's wrong with my interpretation?