BCA1SG_NHPP {BCA1SG}

BCA1SG algorithm for panel count data

Description

This function implements the BCA1SG algorithm on the semiparametric nonhomogeneous Poisson process model for panel count data to solve the ML estimates of the model parameters.

Usage

BCA1SG_NHPP(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 {patient ID, time of measurement, measurement(cumulative counts),covariate_1,...,covariate_p}. This data frame cannot contain missing values. See the dataset "skiTum" 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 mean cumulative 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 NHPP model can be found in Wellner and Zhang (2007).

Value

distinct_time

The set of distinct observation time points.

est_Lambda

The estimated baseline mean cumulative 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.

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.

Wellner J.A. and Zhang Y.(2007). Two Likelihood-Based Semiparametric Estimation Methods for Panel Count Data with Covariates. The Annals of Statistics, 35(5), 2106-2142.

Examples

data(adapt_skiTum)
res<-BCA1SG_NHPP(adapt_skiTum, initial_beta = rep(0,4), threshold = 2e-3)
res$est_beta
res$iteration
res$timecost
plot(res$distinct_time,res$est_Lambda,type="s",lwd=3,
xlab="Time",ylab="Baseline mean cumulative function")