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MultiFrailty: Shared Frailty Regression Models in R

MultiFrailty is a comprehensive R package designed for shared frailty survival regression analysis. It unifies five frailty distributions (Inverse Gaussian, Generalized Lindley Type 1, Generalized Lindley Type 2, Gamma, and No-Frailty) across two flexible baseline hazards (2-parameter Weibull and 3-parameter Generalized Weibull).

Key Features

10 Model Combinations: Supports all combinations of 5 frailty families × 2 baseline hazards.
Robust Estimation: Frequentist Maximum Likelihood Estimation via maxLik / optim with log-domain numerical stability and analytical Laplace derivatives.
Formula Interface: Seamless survival::Surv(time, status) ~ x1 + x2 interface.
8 Censoring Schemes: Data generation under exact, right, left, interval, Type-I, Type-II, progressive, and progressive Type-I censoring.
Model Comparison: AIC, BIC, AICc, HQIC, bootstrapped WAIC, and k-fold cross-validation.
Diagnostics & Plots: Residual analysis (Cox-Snell, Martingale, Deviance, K-S test), influence diagnostics (Leverage, Cook’s D, DFBETAS, DFFITS), and frailty density overlay plots.

Installation

# Install locally
install.packages("MultiFrailty", repos = NULL, type = "source")

Quick Start Example

library(MultiFrailty)

# Generate synthetic survival data with GL Type 1 frailty & Weibull baseline
set.seed(123)
dat <- r_frailty(n = 100, baseline = "weibull", bpar = c(2, 1.5),
                 frailty = "gl1", fpar = c(1.2, 0.5),
                 x = matrix(rnorm(100), ncol = 1), beta = 0.5,
                 cen_type = "right", cen_rate = 0.1)

# Fit Shared Frailty Model via Formula Interface
fit <- multifrailty(Surv(time, status) ~ X1, data = dat,
                    baseline = "weibull", frailty = "gl1")

# Print Summary & Diagnostic Plots
summary(fit)
plot_all(fit)

References

Pandey, A., Hanagal, D. D., & Tyagi, S. (2022). Shared Frailty Models Based on Cancer Data. International Journal of Statistics and Reliability Engineering, 9(3), 461–474.
Pandey, A., & Tyagi, S. (2021). Comparison of Multiplicative Frailty Models Under Weibull Baseline Distribution. Lobachevskii Journal of Mathematics, 42(13), 3184–3195.
Hougaard, P. (1984). Life table methods for heterogeneous populations: distributions of frailties. Biometrika, 71(1), 75–83.
Mudholkar, G. S., & Srivastava, D. K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability, 42(2), 299–302.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.