Description Usage Arguments Details Value Author(s) References Examples
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.
1 2 | 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)
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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 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).
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. |
Wang Y., Ye Z., and Cao H.
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.
1 2 3 4 5 6 7 | 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")
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