bandyopd / fastcrrc

Introduction to the fastCRRC R package

Introduction

fastCRRC implements a fast and efficient clustered competing risks (CCR) regression model for large correlated clustered data. This regression model assesses the marginal effects of covariates on the respective cumulative incidence functions while accommodating the correlation induced due to clustering. Parameter estimation utilizes the ‘forward-backward scan’ algorithm to drastically reduce the computation time for large clustered competing risk datasets. Variance estimation is efficiently handled using a clustered bootstrap approach.

CCR Model

Let $i=1,2,\ldots,n$ denote the clusters where each cluster has $k=1, \ldots, M_i$ observations. For the $k$th member in cluster $i$, let $T_{ik}$ and $C_{ik}$ denote the failure and right censoring times, respectively. Then for right censored data, the corresponding observable random variables become $X_{ik}= \min(T_{ik}, C_{ik})$ and $\xi_{ik} = I(T_{ik} \leq C_{ik})\epsilon_{ik}$ where $\epsilon_{ik} \in {1, \ldots,l}$ denotes the cause of failure, $I(\cdot)$ is the indicator function, and $Z_{ik} = (Z_{ik1},...,Z_{ikp})^{\top}$ is a $p \times 1$ vector of time-independent covariates for individual $k$ in cluster $i$.

The marginal cumulative incidence function conditional on the covariates is defined as $F_1(t;Z_{ik}) = P(T_{ik} \leq t, , \epsilon_{ik} = 1|Z_{ik})$ and the marginal subdistribution hazard is modeled as

$$\lambda_1(t; Z_{ik}) = \lambda_{10}(t) \exp(\beta^\top_{0}Z_{ik}),$$

where $\lambda_{10}(\cdot)$ is a completely unspecified baseline subdistribution hazard function and $\beta_0$ is a $p \times 1$ vector of unknown regression parameters.

Vignettes is available here

Installation

You can install the development version of fastCRRCfrom GitHub with:

# install.packages("devtools")
devtools::install_github("edemprd/fastCRRC")

Example

This is a basic example which shows you how to simulate data and fit the CCR model using the package.

library(fastCRRC)
set.seed(1)
dat <- simCR(n = 10, al = .3, ga = .6, clsize = 2:10, summary = TRUE)
#> Call: 
#> simCR(n = 10, al = 0.3, ga = 0.6, clsize = 2:10, summary = TRUE)
#> 
#> Number of clusters generated:                    10 
#> Average number of observations per cluster:     7.9 
#> Overall observed censoring rate:                0.722 
#> 
#> Before censoring:
#> Proportion of event 1:                          0.772 
#> Proportion of event 2:                          0.228 
#> Before censoring:
#> Proportion of event 1:                          0.253 
#> Proportion of event 2:                          0.025 
#> Average proportion of event 1 per cluster:      0.235 
#> Average proportion of event 2 per cluster:      0.029

fit1 <- fastCrrC(Surv(time, status) ~ Z.1 + Z.2, data = dat, B = 100, fitter = "fastCrr")

summary(fit1)
#> Call:
#> fastCrrC(formula = Surv(time, status) ~ Z.1 + Z.2, data = dat, 
#>     fitter = "fastCrr", B = 100)
#> 
#> fastCrrC Estimator
#>     estimate std.Error z.value p.value
#> Z.1   0.4390    0.2709   1.621  0.1050
#> Z.2   0.0181    1.2406   0.015  0.9884

References

• Zhou, B., Fine, J., Latouche, A., & Labopin, M. (2012). Competing risks regression for clustered data. Biostatistics, 13(3), 371-383.

• Kawaguchi, E. S., Shen, J. I., Suchard, M. A., & Li, G. (2021). Scalable algorithms for large competing risks data. Journal of Computational and Graphical Statistics, 30(3), 685-693.