For the purposes of the package examples, the dataset was adapted from the numerical simulations of the original manuscript.
X is a data frame with 400 observations on the following 3 variables.
IDpatient identifier, there are 400 patients.
Timethe time to event or censoring
Deltaa numeric vector with 0 denoting censoring and 1 event
Z is a data frame with 3237 observations on the following 3 variables.
IDpatient identifier, there are 400 patients.
obsTimethe covariate observation times.
x1the covariate generated through a piecewise constant function.
Data was generated for 400 subjects. The total number of covariate observation times was Poisson distributed with intensity rate 8. The covariate observation times are generated from a uniform distribution Unif(0,1) independently. The covariate process is piecewise constant, with values being multivariate normal with mean 0, variance 1 and correlation \(\exp(-|i - j|/20)\). The survival time were generated from the Cox model \(\lambda(t | Z(r), r \le t) = \lambda_0 \exp(\beta Z(t))\), where \(\beta\) = 1.5, and \(\lambda_0\) = 1.0. Covariates are dataset Z. Event times and indicators are dataset X.
Cao H., Churpek M. M., Zeng D., Fine J. P. (2015). Analysis of the proportional hazards model with sparse longitudinal covariates. Journal of the American Statistical Association, 110, 1187-1196.