QTECox: Function to obtain QTE from a Cox model

In quantreg: Quantile Regression

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 coxph.
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 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

See Also

crq

quantreg documentation built on Oct. 22, 2024, 5:07 p.m.