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Introduction to MultiFrailty: Shared Frailty Regression Models

Shikhar Tyagi, Arvind Pandey, Bhupendra Singh, Vrijesh Tripathi

2026-07-31

Overview

The MultiFrailty package provides tools for fitting and analyzing shared frailty survival regression models. Shared frailty models incorporate unobserved individual heterogeneity into proportional hazard settings.

Supported Frailty & Baseline Distributions

MultiFrailty supports 10 model combinations across 5 frailty families and 2 baseline hazard functions:

Basic Usage Example

library(MultiFrailty)
library(survival)

# Generate synthetic survival data under Gamma frailty with Weibull baseline
set.seed(123)
dat <- r_frailty(n = 80, baseline = "weibull", bpar = c(2.0, 1.5),
                 frailty = "gamma", fpar = c(0.8),
                 x = matrix(rnorm(80), ncol = 1), beta = 0.5)

# Fit model using formula interface
fit <- multifrailty(Surv(time, status) ~ X1, data = dat,
                    baseline = "weibull", frailty = "gamma")

# Summarize fit
summary(fit)
#> 
#> =========================================================
#>  MultiFrailty Regression Model Fit (MLE)
#> =========================================================
#> Baseline Hazard : weibull 
#> Frailty Family  : gamma 
#> Sample Size (n) : 80 
#> Log-Likelihood  : -163.14 
#> AIC / BIC       : 334.28 / 343.81 
#> Frailty Var (SE): 0.2093 ( 0.1925 )
#> Optimizer       : Converged 
#> ---------------------------------------------------------
#> Parameter Estimates (Natural Scale):
#>        Estimate StdErr z_stat p_value   CI_lower  CI_upper Signif
#> lambda   2.6499 0.3788 6.9954  0.0000  1.9074434 3.3923778    ***
#> gamma    1.2771 0.1744 7.3249  0.0000  0.9353857 1.6188461    ***
#> theta    0.2093 0.1925 1.0875  0.2768 -0.1679262 0.5865439       
#> X1       0.2427 0.1472 1.6489  0.0992 -0.0457808 0.5311039      .
#> =========================================================

# Predict survival probabilities
pred_surv <- predict_frailty(fit, type = "survival", newtime = c(1, 2, 3))

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They may not be fully stable and should be used with caution. We make no claims about them.
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