In tbalan/dynfrail: Fitting Dynamic Frailty Models with the EM Algorithm

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This is an R package for fitting semiparametric dynamic frailty models with the EM algorithm. The hazard for individual $j$ from cluster $i$ is specified as: $$ \lambda_{ij}(t | Z_i(t)) = Z_i(t) \exp(\beta^\top x_{ij}(t)) \lambda_0(t). $$ The model used here is described in detail in Putter & van Houwelingen (2015). The distribution of $Z_i(t)$ is described by two parameters: $\theta$, that is an inverse-variability parameter of $Z_i(t)$ for a fixed $t$, and $\lambda$, that describes the autocorrelation of the process, so that for $t_1 \leq t_2$ $$ \mathrm{cor}(Z_i(t_1), Z_i(t_2)) = \exp(\lambda (t_2 - t_1)). $$

The estimation process is that for fixed $(\theta, \lambda)$ the maximized profile likelihood is calculated, i.e. maximized with respect to $(\beta, \lambda_0)$. This profile likelihood is finally maximized itself.

Installation

The development version from GitHub:

devtools::install_github("tbalan/dynfrail")

The following packages are needed to build dynfrail:

install.packages(c("RcppArmadillo", "tibble", "magrittr", "dplyr", "tidyr"))

The functioning of the package is described in the documentation of the main fitting function, dynfrail().

Features

• gamma, PVF, compount Poisson, inverse Gaussian distributions
• flexible adjustment of estimation parameters
• semiparametric $Z(t)$ that changes values at every $t$ or piecewise constant $Z(t)$
• clustered survival data & recurrent events (calendar time or gaptime) ar supported

Functions

• dynfrail() has a friendly syntax very similar to the frailtyEM package: next to a formula and data argument, the distribution argument is used to specify the distribution parameters and the control parameter is used for controling the precision of the estimation.
• dynfrail_prep() and dynfrail_fit() are used internally by dynfrail() but are made user-available. The first one prepares the input of dynfrail() to make it suitable for the actual EM algorithm. The second one performs one EM algorithm for fixed $(\theta, \lambda)$ to estimate the maximum ($\beta$, $\lambda_0$).

Limitations

• slow even for medium sized data sets. It is recommended to start with a small number of piecewise constant intervals and/or a subset of the data
• no direct standard errors for $(\theta, \lambda)$.

tbalan/dynfrail documentation built on May 3, 2019, 4:30 p.m.