BCA1SG_interval_censor {BCA1SG}

BCA1SG algorithm for interval-censored survival data

Description

This function implements the BCA1SG algorithm on the semiparametric proportional hazard model for interval-censored data to solve the ML estimates of the model parameters.

Usage

BCA1SG_interval_censor(input_data, initial_beta, initial_Lambda = function(x){x},
threshold = 1e-05, max_iter = 5000, max_stepsize = 10000, xi = 0.3, contraction = 0.5)

Arguments

input_data

An object of class data.frame. The structure of the data frame must be {lower bound of the survival time,upper bound of the survival time,covariate_1,...,covariate_p}. This data frame cannot contain missing values. See the dataset "duser" for an example.

initial_beta

The initial value of the regression coefficients. The dimension of this input should comply with the dimension of the covariates.

initial_Lambda

An R function which serves as the initial value of the baseline cumulative hazard function.

threshold

Convergence threshold. The algorithm is terminated when the infinity norm of the difference between successive iterates is less than the convergence threshold.

max_iter

Maximum number of iterations allowed.

max_stepsize

Maximum stepsize allowed.

xi

The xi parameter in the inexact backtracking line search algorithm. See Wang et al. (2020) for details.

contraction

The contraction parameter in the inexact backtracking line search algorithm. See Wang et al. (2020) for details.

Details

Details about the BCA1SG algorithm can be found in Wang et al. (2020), and the details concerning the semiparametric proportional hazard model can be found in Section 4 of Huang and Wellner (1997).

Value

distinct_time

The set of distinct observation time points.

est_Lambda

The estimated baseline cumulative hazard function at the set of distinct observation time points.

est_beta

The estimated regression coefficients.

iteration

The number of iterations.

timecost

The computational time in seconds.

Note

If we directly run this function on the data set "duser", we may get a different result from that presented in Section 6.2 of Wang et al. (2020). This is because the settings about the initial values of the nonparametric baseline cumulative hazard function are different.

Author(s)

Wang Y., Ye Z., and Cao H.

References

Wang Y., Ye, Z.-S., and Cao, H.(2020). On Computation of Semi-Parametric Maximum Likelihood Estimators with Shape Constraints. Submitted.

Huang J. and Wellner, J.A.(1997). Interval-Censored Survival Data: A Review of Recent Progress. Proceedings of the Fifth Seattle Symposium in Biostatistics, 123-169.

Examples

data(adapt_duser)
res<-BCA1SG_interval_censor(adapt_duser, initial_beta = rep(0,2), threshold = 5e-3)
res$est_beta
res$iteration
res$timecost
plot(res$distinct_time,res$est_Lambda,type="s",lwd=3,
xlab="time",ylab="Baseline cumulative hazard function")