INSTITUTIONAL REPOSITORY

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Bivariate Current Status Data with Competing Risks using Frailty Models
(Indian Statistical Institute, 2026-07-21) Ghosh, Biswadeep
Bivariate current status data with competing risks arises in many application areas, for example, carcinogenicity studies, epidemiological studies, reliability studies, etc..As par of our knowledge, bivariate current status data with competing risks has not received much attention in literature. We initiate this research focusing on modeling and estimation of quantities of interest in absence of any covariate. We model bivariate current status data with competing risks through different frailty structures in order to describe different kinds of association. We consider multiplicative frailty effect on different cause-specific baseline hazard functions. One important part of our analysis is to investigate the identifiability of a proposed model. It has been shown that, when both the cause-specific baseline hazard function and frailty distribution are non-parametric, then the model is not identifiable. Motivated by the previous result, we consider the analysis of following three different combinations of cause-specific baseline hazard and frailty distributions, namely, (a) both the cause-specific baseline hazard and frailty distribution are parametric, (b) the cause-specific baseline hazard functions are parametric and the frailty distribution is non-parametric, (c) the cause-specific baseline hazard functions are non-parametric and the frailty distribution is parametric. For the parametric frailty distribution, we have considered Gamma distribution of different kinds. We have used the maximum likelihood estimation method to estimate the parameters when both the cause-specific baseline hazard functions and frailty distribution are assumed to be parametric. In case of parametric cause-specific baseline hazard and non-parametric frailty, we have implemented an algorithm to estimate mixing distribution in order to obtain the NPMLE of frailty distribution. We have used the Bernstein polynomials to model the non-parametric cause-specific baseline hazard functions, and using sieve maximum likelihood estimation, we have estimated the non-parametric cause-specific baseline hazard function and relevant frailty parameter(s). In every case, simulation studies have been carried out in order to investigate the finite sample properties of the proposed methodologies. We have illustrated the proposed methods through the analyses of a hearing loss data.
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M. Stat 2 nd year Second Semester Exam 2024 - Statistical Computing II
(Indian Statistical Institute, 2025-05-07) Indian Statistical Institute
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M. Stat 1 st year Second Semester Final Exam 2024 - Sample Survey & Design of Experiments
(Indian Statistical Institute, 2025-05-07) Indian Statistical Institute
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M. Stat 2 nd year Second Semester Exam 2024 - Risk Management
(Indian Statistical Institute, 2025-04-28) Indian Statistical Institute
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M. Stat 1 st year Second Semester Exam 2024 - Resampling Techniques
(Indian Statistical Institute, 2025-04-30) Indian Statistical Institute