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  "Title": "Gamma Frailty Regression Models with Multiple Baseline\nDistributions",
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  "Description": "Implements univariate gamma frailty regression models for\nsurvival data with six different baseline distributions: the\nArvind distribution (Pandey et al., 2024), the Lindley\ndistribution (Lindley, 1958), the Linear Failure Rate\ndistribution (Bain, 1974), the Power Xgamma distribution (Tyagi\net al., 2022), the Modified Topp-Leone distribution (Singh et\nal., 2025), and the Power Failure Rate distribution (Mugdadi,\n2005). The package supports uncensored (complete) and censored\ndata (right, left, interval, and progressive censoring) with\nand without covariates. It provides maximum likelihood\nestimation, standard errors, confidence intervals,\nt-statistics, p-values, Akaike Information Criterion (AIC),\nBayesian Information Criterion (BIC), a bootstrap approximation\nof the Widely Applicable Information Criterion (WAIC), k-fold\ncross-validation, variance inflation factors, R-squared,\nadjusted R-squared, Mean Squared Error (MSE), Mean Absolute\nError (MAE), Root Mean Squared Error (RMSE), an overall model\nF-test, frailty variance estimation, survival probabilities at\nuser-specified time points, median survival, expected survival\nwithin a fixed window, risk predictions, marginal predictions,\nmartingale and deviance residuals, standardized and studentized\nresiduals, leverage values, Cook's distance, Difference in Fits\n(DFFITS), Difference in Betas (DFBETAS), and a comprehensive\nsuite of diagnostic and survival plots including Kaplan-Meier\noverlays and coefficient forest plots. Random number generation\nis available for each baseline distribution and the full\nfrailty model, and a simulation study function evaluates\nparameter recovery across sample sizes and censoring scenarios.\nReferences are Lindley (1958)\n<doi:10.1111/j.2517-6161.1958.tb00278.x>, Mugdadi (2005)\n<doi:10.1016/j.amc.2004.09.064>, Bain (1974)\n<doi:10.1080/00401706.1974.10489237>, Singh, Tyagi, Singh, and\nTyagi (2025)\n<https://ph02.tci-thaijo.org/index.php/thaistat/article/view/257215>,\nPandey, Singh, Tyagi, and Tyagi (2024)\n<https://ssca.org.in/journal.html>, and Tyagi, Kumar, Pandey,\nSaha, and Bagariya (2022) <https://ijsreg.com/>.",
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    "compare_models",
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    "forecast_frailty",
    "gamma_frailty",
    "gamma_frailty_functions",
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    "loglik_gamma_frailty",
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    "plot_dfbetas",
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    "plot_scale_location",
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    "predict_frailty",
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    "r_gamma_frailty",
    "r_lfr",
    "r_lindley",
    "r_mtl",
    "r_pfr",
    "r_pxg",
    "residuals_frailty",
    "risk_predict",
    "simulate_mle_performance",
    "simulation_study",
    "survival_at"
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      "page": "baseline_hazard",
      "title": "Baseline Cumulative Hazard and Hazard Functions",
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      "page": "bootstrap_waic",
      "title": "Bootstrap WAIC for the Gamma Frailty Model",
      "topics": [
        "bootstrap_waic"
      ]
    },
    {
      "page": "compare_models",
      "title": "Compare Multiple Gamma Frailty Models",
      "topics": [
        "compare_models"
      ]
    },
    {
      "page": "cv_frailty",
      "title": "K-Fold Cross-Validation for the Gamma Frailty Model",
      "topics": [
        "cv_frailty"
      ]
    },
    {
      "page": "diagnostics_table",
      "title": "Summary Diagnostics Table",
      "topics": [
        "diagnostics_table"
      ]
    },
    {
      "page": "fit_gamma_frailty",
      "title": "Fit a Gamma Frailty Regression Model",
      "topics": [
        "fit_gamma_frailty"
      ]
    },
    {
      "page": "forecast_frailty",
      "title": "Forecast Survival Curves",
      "topics": [
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      ]
    },
    {
      "page": "gamma_frailty",
      "title": "Gamma Frailty Regression Model (Formula Interface)",
      "topics": [
        "gamma_frailty"
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    },
    {
      "page": "gamma_frailty_functions",
      "title": "Gamma Frailty Model Functions",
      "topics": [
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    },
    {
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      "title": "Influence Diagnostics for the Gamma Frailty Model",
      "topics": [
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    {
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      "title": "Log-Likelihood for the Gamma Frailty Model",
      "topics": [
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    {
      "page": "plot_all",
      "title": "Plot All Diagnostics",
      "topics": [
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      ]
    },
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      "title": "Plot Baseline Distribution Functions",
      "topics": [
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      "topics": [
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    },
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    },
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      "topics": [
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    },
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      "title": "Kaplan-Meier vs Model-Based Survival Plot",
      "topics": [
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      "page": "predict_frailty",
      "title": "Predictions from a Gamma Frailty Model",
      "topics": [
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    {
      "page": "r_arvind",
      "title": "Random samples from the Arvind distribution",
      "topics": [
        "r_arvind"
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    },
    {
      "page": "r_gamma_frailty",
      "title": "Generate Random Survival Times from the Gamma Frailty Model",
      "topics": [
        "r_gamma_frailty"
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    },
    {
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    },
    {
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      "title": "GammaFrailty: Gamma Frailty Regression Models with Multiple Baseline Distributions",
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