GammaFrailty - Gamma Frailty Regression Models with Multiple Baseline Distributions

Implements univariate gamma frailty regression models for survival data with six different baseline distributions: the Arvind distribution (Pandey et al., 2024), the Lindley distribution (Lindley, 1958), the Linear Failure Rate distribution (Bain, 1974), the Power Xgamma distribution (Tyagi et al., 2022), the Modified Topp-Leone distribution (Singh et al., 2025), and the Power Failure Rate distribution (Mugdadi, 2005). The package supports uncensored (complete) and censored data (right, left, interval, and progressive censoring) with and without covariates. It provides maximum likelihood estimation, standard errors, confidence intervals, t-statistics, p-values, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), a bootstrap approximation of the Widely Applicable Information Criterion (WAIC), k-fold cross-validation, variance inflation factors, R-squared, adjusted R-squared, Mean Squared Error (MSE), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), an overall model F-test, frailty variance estimation, survival probabilities at user-specified time points, median survival, expected survival within a fixed window, risk predictions, marginal predictions, martingale and deviance residuals, standardized and studentized residuals, leverage values, Cook's distance, Difference in Fits (DFFITS), Difference in Betas (DFBETAS), and a comprehensive suite of diagnostic and survival plots including Kaplan-Meier overlays and coefficient forest plots. Random number generation is available for each baseline distribution and the full frailty model, and a simulation study function evaluates parameter recovery across sample sizes and censoring scenarios. References are Lindley (1958) <doi:10.1111/j.2517-6161.1958.tb00278.x>, Mugdadi (2005) <doi:10.1016/j.amc.2004.09.064>, Bain (1974) <doi:10.1080/00401706.1974.10489237>, Singh, Tyagi, Singh, and Tyagi (2025) <https://ph02.tci-thaijo.org/index.php/thaistat/article/view/257215>, Pandey, Singh, Tyagi, and Tyagi (2024) <https://ssca.org.in/journal.html>, and Tyagi, Kumar, Pandey, Saha, and Bagariya (2022) <https://ijsreg.com/>.