trans_m {transmdl}

Regression Analysis of Right-censored Data using Semiparametric Transformation Models.

Description

This function is used to conduct the regression analysis of right-censored data using semiparametric transformation models. It calculates the estimators, standard errors and p values. A plot of estimated baseline cumulative hazard function and confidence intervals can be produced.

Usage

trans_m(
  X,
  delta,
  Y,
  plot.Lamb = TRUE,
  alpha = seq(0.1, 1.1, by = 0.1),
  trsmodel = TRUE,
  EM_itmax = 250,
  show_res = TRUE
)

Arguments

X

design matrix

delta

censoring indicator. If Y_i is censored, delta=0. If not, delta=1.

Y

observed event times

plot.Lamb

If TRUE, plot the estimated baseline cumulative hazard function and confidence intervals. The default is TRUE.

alpha

parameter in transformation function. Generally, \alpha can not be observed in medical applications. In that situation, alpha indicates the scale of choosing \alpha. The default is (0.1,0.2,...,1.1). If \alpha is known, alpha indicates the true value of \alpha.

trsmodel

logical value indicating whether to implement transformation models. The default is TRUE.

EM_itmax

maximum iteration of EM algorithm. Defaults to 250.

show_res

show results after trans_m.

Details

If \alpha is unknown, we firse set \alpha=alpha. Then, for each \alpha, we estimate the parameters and record the value of observed log-likelihood function. The \alpha that maximizes the observed log-likelihood function and the corresponding \hat\beta and \hat\Lambda(\cdot) are chosen as the best estimators. Nonparametric maximum likelihood estimators are developed for the regression parameters and cumulative intensity functions of these models based on censored data.

Value

a list containing

beta.est			estimators of \beta
SE.beta			standard errors of the estimated \beta
SE.Ydot			standard errors of the estimated \Lambda(Y')
Ydot			vector of sorted event times with duplicate values removed
Lamb.est			estimated baseline cumulative hazard
lamb.est			estimated jump sizes of baseline cumulative hazard function
choose.alpha			the chosen \alpha
Lamb.upper			upper confidence limits for the estimated baseline cumulative hazard function
Lamb.lower			lower confidence limits for the estimated baseline cumulative hazard function
p.beta			P values of estimated \beta
p.Lamb			P values of estimated baseline cumulative hazard
p.beta

References

Cheng, S.C., Wei, L.J., and Ying, Z. (1995). Analysis of transformation models with censored data. Biometrika 82, 835-845.

Zeng, D. and Lin, D.Y. (2007). Maximum likelihood estimation in semiparametric regression models with censored data. J. R. Statist. Soc. B 69, 507-564.

Abramowitz, M., and Stegun, I.A. (1972). Handbook of Mathematical Functions (9th ed.). Dover Publications, New York.

Evans, M. and Swartz, T. (2000). Approximating Integrals via Monte Carlo and Deterministic Methods. Oxford University Press.

Liu, Q. and Pierce, D.A. (1994). A note on Gauss-Hermite quadrature. Biometrika 81, 624-629.

Louis, T. (1982). Finding the Observed Information Matrix when Using the EM Algorithm. Journal of the Royal Statistical Society. Series B (Methodological), 44(2), 226-233.

See Also

EM_est

Examples

 gen_data = generate_data(200, 1, 0.5, c(-0.5,1))
 delta = gen_data$delta
 Y = gen_data$Y
 X = gen_data$X
 res.trans = trans_m(X, delta,  Y, plot.Lamb = TRUE, show_res = FALSE)