What does a negative Somers' D say about model discriminative power?

Question

I developed a Cox proportional hazard regression model in R. Then I tried using validate in Professor Harrell's rms package to validate it:

> v <- validate(f5, B=200, dxy=TRUE)

I got dxy = -0.5510. Which got me confused. I was told that D can be computed from c index using the formula $2(c - 0.5)$, where $c$ estimates the probability of concordance between predicted and observed responses (p. 371 in Harrell, Lee and Mark 1996). A value of $0.5$ indicates no predictive discrimination and a value of $1.0$ indicates perfect separation of patients with different outcomes.

My question is: according to the formula, a negative $D$ would imply that $c$ is less than $0.5$, i.e. if A is predicted to live longer than B, then it is more likely than not that B would live longer than A(?!) Does it mean that my model is doing worse than random prediction? Or I am missing something here? Any help would be greatly appreciated.

1. Harrell, Lee and Mark (1996) Multivariable Prognostic Models: Issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors

Answer 1

For the Cox model, large predictions (large $X\hat{\beta}$) means high hazard rate which means short survival time. If instead of computing the correlation between relative log hazard and survival time you want to compute the correlation between survival probability and survival time, just negate $D_{xy}$.