tauhat_func {QTOCen}

Kernel-based Local Kaplan-Meier Estimator for the Conditional Probability of the Survival Time

Description

This function estimates the value of

F(T <= y_0 \mid x_0),

the conditional cumulative distribution function of a survival time T given covaraites vector x_0 at value y_0. This estimator is described in detail in (Wang and Wang 2009).

Usage

tauhat_func(y0, x0, z, x, delta, bw)

Arguments

y0

the vector of censored outcome of a single observation

x0

the vector of given covariate of a single observation

z

observed vector of response variable from observed data

x

the observed matrix of covariates, the dimension is # of observations by number of covariates. Note that the vector of ones should NOT be included in x.

delta

the vector of censoring indicators

bw

the scalar bandwidth parameter in kernel

Details

For cases with multivariate covariates, we adopted a product kernel. For example, in the bivariate case we use

K(x_1, x_2) = K_1(x_1) K_2(x_2),

where K_1 and K_2 are both biquadratickernel functions.

References

Wang HJ, Wang L (2009). “Locally weighted censored quantile regression.” Journal of the American Statistical Association, 104(487), 1117–1128.

Examples

tauhat_func(y0=10, x0=c(2,3), z=c(10, 12, 11), 
            x=matrix(c(1,1,2,2,3,3), nrow=3, byrow=TRUE), 
            delta=c(1,1,0), bw=10)