kmc.bjtest | R Documentation |
Use the empirical likelihood ratio and Wilks theorem to test if the regression coefficient equals beta.
El(F)=∏_{i=1}^{n}(Δ F(T_i))^{δ_i}(1-F(T_i))^{1-δ_i}
with constraints
∑_i g(T_i)Δ F(T_i)=0,\quad,i=1,2,…
Instead of EM algorithm, this function calculates the Kaplan-Meier estimator with mean constraints recursively to test H_0:~β=β_0 in the accelerated failure time model:
\log(T_i) = y_i = x_iβ^\top + ε_i,
where ε is distribution free.
kmc.bjtest(y, d, x, beta,init.st="naive")
y |
Response variable vector (length n). |
d |
Status vector (length n), 0: right censored; 1 uncensored. |
x |
n by p explanatory variable matrix. |
beta |
The value of the regression coeffiecnt vector (length p) to be tested. |
init.st |
Type of methods to initialize the algorithm. By default, init.st is set to 1/n |
The empirical likelihood is the likelihood of the error term when the coefficients are specified. Model assumptions are the same as requirements of a standard Buckley-James estimator.
a list with the following components:
prob |
the probabilities that max the empirical likelihood under estimating equation. |
logel1 |
the log empirical likelihood without constraints, i.e. under Kaplan-Merier of residuals' |
logel2 |
the log empirical likelihood with constraints, i.e. under null hypotheses or estimation equations. |
"-2LLR" |
the -2 loglikelihood ratio; have approximate chisq distribution under null hypotheses |
convergence |
an indicator: 0: fails to converge 1: converged |
Mai Zhou(mai@ms.uky.edu), Yifan Yang(yfyang.86@hotmail.com)
Buckley, J. and James, I. (1979). Linear regression with censored data. Biometrika, 66 429-36
Zhou, M., & Li, G. (2008). Empirical likelihood analysis of the Buckley-James estimator. Journal of multivariate analysis, 99(4), 649-664.
Zhou, M. and Yang, Y. (2015). A recursive formula for the Kaplan-Meier estimator with mean constraints and its application to empirical likelihood Computational Statistics. Online ISSN 1613-9658.
plotkmc2D
, bjtest
.
library(survival) stanford5 <- stanford2[!is.na(stanford2$t5), ] y <- log10(stanford5$time) d <- stanford5$status oy <- order(y, -d) d <- d[oy] y <- y[oy] x <- cbind(1, stanford5$age)[oy,] beta0 <- c(3.2, -0.015) ss <- kmc.bjtest(y, d, x=x, beta=beta0, init.st="naive")
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