Computes quantile treatment effects comparable to those of
crq model from a coxph object.
Usage
QTECox(x, smooth = TRUE)
Arguments
x
An object of class coxph produced by coxph.
smooth
Logical indicator if TRUE (default)
then Cox survival function is smoothed.
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
taus
points of evaluation of the QTE.
QTE
matrix of QTEs, the ith column contains the QTE for the
ith covariate effect. Note that there is no intercept effect.
see plot.summary.crqs for usage.
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