| QTECox {quantreg} | R Documentation |
Computes quantile treatment effects comparable to those of crq model from a coxph object.
QTECox(x, smooth = TRUE)
x |
An object of class coxph produced by |
smooth |
Logical indicator if TRUE (default) then Cox survival function is smoothed. |
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.
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 |
Roger Koenker Stephen Portnoy & Tereza Neocleous
Koenker, R. and Geling, O. (2001). Reappraising Medfly longevity: a quantile regression survival analysis, J. Amer. Statist. Assoc., 96, 458-468