| QTECox {quantreg} | R Documentation |
Function to obtain QTE from a Cox model
Description
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 |
smooth |
Logical indicator if TRUE (default) then Cox survival function is smoothed. |
Details
Estimates of the Cox QTE, \frac{dQ(t|x)}{dx_{j}}
at x=\bar{x}, can be expressed as a function of t as follows:
\frac{dQ(t|x)}{dx_{j}}=\frac{dt}{dx_{j}}\frac{dQ(t|x)}{dt}
The Cox survival function, S(y|x)=\exp \{-H_{0}(y)\exp (b^{\prime
}x)\}
\frac{dS(y|x)}{dx_{j}}=S(y|x)log \{S(y|x)\}b_{j}
where \frac{dQ(t|x)}{dx_{j}}
can be estimated by \frac{\Delta (t)}{\Delta (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
\frac{dt}{dx_{j}}=-\frac{dS(y|x)}{dx_{j}}=-(1-t) log (1-t)b_{j}
Thus the QTE at the mean of x's is:
(1-S)= \frac{\Delta (t)}{\Delta (S)}S ~log
(S)b_{j}
Since \Delta 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
\frac{d log (Q(t|x))}{dx_{j}}=\frac{dQ(t|x)}{dx_{j}}/
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 |
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