Predictive Analytics Using Statistics and Big Data: Concepts and Modeling

Analysis of Bivariate Survival Data using Shared Inverse Gaussian Frailty Models: A Bayesian Approach

Author(s): Arvind Pandey, Shashi Bhushan, Lalpawimawha and Shikhar Tyagi

Pp: 75-88 (14)

DOI: 10.2174/9789811490491120010008

* (Excluding Mailing and Handling)

Abstract

Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks of disease and death. The shared frailty models have been suggested to analyze the bivariate data on related survival times (e.g., matched pairs experiments, twin or family data). This paper introduces the shared Inverse Gaussian (IG) frailty model with baseline distribution as Weibull exponential, Lomax, and Logistic exponential. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the actual values of the parameters with the estimated values. Also, we apply these models to a real-life bivariate survival data set of McGilchrist and Aisbett [1] related to the kidney infection data, and a better model is suggested for the data.


Keywords: Bayesian model comparison, Inverse gaussian frailty, Lomax distribution, Logistic exponential distribution, MCMC, Shared frailty, Weibull exponential distribution.

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      320μsalphaeurekaselec_live_10_06_2022Subject.php#255
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      300μsalphaeurekaselec_live_10_06_2022ContentAccess.php#647
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      • 11. app/Models/ContentAccess.php:647
      • 12. app/Http/Controllers/ChapterController.php:1478
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      630μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1518
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
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      590μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 2930 and `b`.`banner_from_date` <= 1740515632 and `b`.`banner_to_date` >= 1740515632 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.09msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 2930
      • 3: 1740515632
      • 4: 1740515632
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='cb7b2324a80b8034485bcd4724b93b66'
      230μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Keywords
    7Keywords.php#?
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        LhBWncKhEcRIe3gwc5ax120LAE7x0PPgROh702MJ
        uc_cart_id
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        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/14416" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
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        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:17 [ "x-https" => array:1 [ 0 => "1" ] "host" => array:1 [ 0 => "alpha.eurekaselect.com" ] "priority" => array:1 [ 0 => "u=0, i" ] "cookie" => array:1 [ 0 => "wayfindertarget=eyJpdiI6ImFVcWk0MnNHcVdtblFLYytiZE5BNXc9PSIsInZhbHVlIjoiSXlVVW5WWlBLWXZSc1ZCUWJCT05BQ3piZEpPZzVRZUpnNlRDcXFuUmN5RT0iLCJtYWMiOiI1NTAyMjk3YTY5YmJhMDRjYTViMjA0ZGYxOWYyZTBlOGViNTdiZjg1N2YxYmJmNjcyZmU4ZDVkOThmYThjMTc3IiwidGFnIjoiIn0%3Dwayfindertarget=eyJpdiI6ImFVcWk0MnNHcVdtblFLYytiZE5BNXc9PSIsInZhbHVlIjoiSXlVVW5WWlBLWXZSc1ZCUWJCT05BQ3piZEpPZzVRZUpnNlRDcXFuUmN5RT0iLCJtYWMiOiI1NTAyMjk3YTY5YmJh" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] ]
        request_cookies
        0 of 0
        array:1 [ "wayfindertarget" => null ]
        response_headers
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        ClearShow all
        Date ↕MethodURLData
        #12025-02-25 20:33:52GET/chapter/14416112189