R: Function to obtain QTE from a Cox model

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 `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

### See Also

`crq`

[Package quantreg version 5.70 Index]