Description

Computes quantile treatment effects comparable to those of crq model from a coxph object.

Usage

Arguments

Details

Estimates of the Cox QTE, (d/dx_j) Q( t | x ) at x=xbar, can be expressed as a function of t as follows:

(d/dx_j) Q( t | x ) = (d/dx_j)t * (d/dt) Q(t | x)

The Cox survival function, S( y | x ) = exp{ - H_o(y) exp(b'x) }

(d/dx_j) S( y | x ) = S( y | x ) log(S( y | x )) b_j

where (d/dt) Q(t | x) can be estimated by - (diff(t)/diff(S) (1-t) where $S$ and $t$ denote the surv and time components of the survfit object. Note that since t = 1 - S( y | x ), the above is the value corresponding to the argument $(1-t)$; and furthermore

(d/dx_j)t = - (d/dx_j) S( y | x ) = - (1-t) log(1-t) b_j

Thus the QTE at the mean of x's is:

(1 - S) = (diff(t)/diff(S) S log(S) b_j

Since diff(S) is negative and $log (S)$ is also negative this has the same sign as b_{j} The crq model fits the usual AFT form Surv(log(Time),Status), then

(d/dx_j) log(Q( t | x )) = (d/dx_j) Q( t | x ) / Q( t | x )

This is the matrix form returned.

Value

Author(s)

Roger Koenker Stephen Portnoy & Tereza Neocleous

References

Koenker, R. and Geling, O. (2001). Reappraising Medfly longevity: a quantile regression survival analysis, J. Amer. Statist. Assoc., 96, 458-468

See Also

crq