| Title: | Block Coordinate Ascent with One-Step Generalized Rosen Algorithm |
|---|---|
| Description: | Implementing the Block Coordinate Ascent with One-Step Generalized Rosen (BCA1SG) algorithm on the semiparametric models for panel count data, interval-censored survival data, and degradation data. A comprehensive description of the BCA1SG algorithm can be found in Wang et al. (2020) <https://github.com/yudongstat/BCA1SG/blob/master/BCA1SG.pdf>. For details of the semiparametric models for panel count data, interval-censored survival data, and degradation data, please see Wellner and Zhang (2007) <doi:10.1214/009053607000000181>, Huang and Wellner (1997) <ISBN:978-0-387-94992-5>, and Wang and Xu (2010) <doi:10.1198/TECH.2009.08197>, respectively. |
| Authors: | Wang Yudong, Ye Zhisheng, and Cao Hongyuan |
| Maintainer: | Wang Yudong <[email protected]> |
| License: | GPL-2 |
| Version: | 0.1.0 |
| Built: | 2024-10-31 06:21:40 UTC |
| Source: | CRAN |
Data set of 763 drug users in Badalona (Spain). The data come from the detoxification unit of Hospital Universitari Germans Trias i Pujol in Badalona, Spain. See Gómez et al. (2000) for details.
data("adapt_duser")data("adapt_duser")
A data frame with 763 observations on the following 4 variables.
leftleft endpoint of time to HIV-infection.
rightright endpoint of time to HIV-infectio.n
zgengender (0: male; 1: female).
agepatient's age.
The "FHtest" package.
Gómez, G., Calle, M. L., Egea, J. M., and Muga, R.(2000). Risk of HIV infection as a function of the duration of intravenous drug use: A non-parametric Bayesian approach. Statistics in Medicine 19(19), 2641–2656.
A data frame containing the recurrence of skin tumors. See Chiou et al. (2017) for details.
data("adapt_skiTum")data("adapt_skiTum")
A data frame with 894 observations on the following 7 variables.
idpatient id (repeated for each recurrence).
timeobservation time.
countcumulative number of tumors till the current observation time.
agepatient's age at enrollment; age = 1 if greater than 65, age = 0 otherwise.
malegender; male = 1, female = 0.
dfmotreatment (DFMO) group = 1; placebo = 0.
priorTumornumber of prior tumor from diagnosis to randomization.
The "spef" package.
Chiou S. H., Xu G., Yan J., and Huang C.(2018). Semiparametric Estimation of the Accelerated Mean Model with Panel Count Data under Informative Examination Times. Biometrics, 74(3), 944-953.
This function implements the BCA1SG algorithm on the semiparametric random-effects inverse Gaussian process model for degradation data to solve the ML estimates of the model parameters.
BCA1SG_degradation(input_data, initial_delta, initial_r, initial_Lambda = function(x){x}, threshold = 1e-05, max_iter = 5000, max_stepsize = 1e+05, xi = 0.3, contraction = 0.5)BCA1SG_degradation(input_data, initial_delta, initial_r, initial_Lambda = function(x){x}, threshold = 1e-05, max_iter = 5000, max_stepsize = 1e+05, xi = 0.3, contraction = 0.5)
input_data |
An object of class data.frame. The structure of the data frame must be {subject ID, time of measurement, measurement}.. This data frame cannot contain missing values. See the dataset "liner" for an example. |
initial_delta |
The initial value of the shape parameter of the gamma distributed scale parameter in the random-effects inverse Gaussian process. See Wang and Xu (2010) for details. |
initial_r |
The initial value of the rate parameter of the gamma distributed scale parameter in the random-effects inverse Gaussian process. See Wang and Xu (2010) for details. |
initial_Lambda |
An R function which serves as the initial value of the baseline mean 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 random-effects inverse Gaussian process model can be found in Section 3 of Wang and Xu (2010).
distinct_time |
The set of distinct observation time points. |
est_Lambda |
The estimated baseline mean function at the set of distinct observation time points. |
est_delta |
The estimated shape parameter of the gamma distributed scale parameter in the random-effects inverse Gaussian process. |
est_r |
The estimated rate parameter of the gamma distributed scale parameter in the random-effects inverse Gaussian process. |
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.
Wang X. and Xu, D.(2010). An Inverse Gaussian Process Model for Degradation Data. Technometrics, 52(2), 188-197.
data(liner) res<-BCA1SG_degradation(liner, initial_delta = 1, initial_r = 1, threshold = 5e-2) res$est_delta res$est_r res$iteration res$timecost plot(res$distinct_time,res$est_Lambda,type="s",lwd=3,xlab="time",ylab="Baseline mean function")data(liner) res<-BCA1SG_degradation(liner, initial_delta = 1, initial_r = 1, threshold = 5e-2) res$est_delta res$est_r res$iteration res$timecost plot(res$distinct_time,res$est_Lambda,type="s",lwd=3,xlab="time",ylab="Baseline mean function")
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.
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)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)
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 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).
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. |
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.
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.
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.
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$est_Lambda,type="s",lwd=3, xlab="time",ylab="Baseline cumulative hazard function")data(adapt_duser) res<-BCA1SG_interval_censor(adapt_duser, initial_beta = rep(0,2), threshold = 5e-3) res$est_beta res$iteration res$timecost plot(res$distinct_time,res$est_Lambda,type="s",lwd=3, xlab="time",ylab="Baseline cumulative hazard function")
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.
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)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)
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.
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$est_Lambda,type="s",lwd=3, xlab="Time",ylab="Baseline mean cumulative function")data(adapt_skiTum) res<-BCA1SG_NHPP(adapt_skiTum, initial_beta = rep(0,4), threshold = 2e-3) res$est_beta res$iteration res$timecost plot(res$distinct_time,res$est_Lambda,type="s",lwd=3, xlab="Time",ylab="Baseline mean cumulative function")
The degradation data measured on 32 marine engine cylinder liners from January 1999 to August 2006. See Giorgio et al. (2012) for details.
data("liner")data("liner")
A data frame with 64 observations on the following 3 variables.
IDliner ID.
Timepointsthe time of measurement (in years).
Measurementsthe measurement (in mm).
Giorgio M., Guida M., and Pulcini G.(2012). A State-Dependent Wear Model with an Application to Marine Engine Cylinder Liners. Technometrics, 52(2), 172-187.
Giorgio M., Guida M., and Pulcini G.(2012). A State-Dependent Wear Model with an Application to Marine Engine Cylinder Liners. Technometrics, 52(2), 172-187.