arXiv subjects

Sandip Barui

Publications and source records attributed to Sandip Barui.

6 recordsLinked to original sources

arXiv2026

Bivariate inverse Gaussian degradation processes with shared random effects and an application to fatigue cracks

The inverse Gaussian (IG) process is a widely used model for univariate degradation data. For bivariate degradation data involving two performance characteristics (PCs), dependence is often introduced through an unobserved shared frailty factor combined with IG processes. Previous studies typically assume a specific frailty distribution, such as normal or gamma, although such choices are difficult to justify because the frailty is unobserved. This paper proposes a general IG GG framework for modeling bivariate degradation data with dependent PCs. Each degradation process is modeled using an IG process, while the shared frailty follows the generalized gamma (GG) family, which includes exponential, gamma, Weibull, and lognormal distributions as special cases. The proposed framework allows flexible selection of an appropriate frailty distribution within the GG family, leading to improved model fitting. Convenient parameter estimation procedures are developed and evaluated through simulation studies, demonstrating satisfactory performance. The proposed model is applied to fatigue crack data and compared with several existing frailty based and copula based models. Results show that the IG GG model provides a superior fit. System reliability estimation under the IG GG framework is also discussed.

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arXiv2026

Optimal Accelerated Life Testing Sampling Plan Design with Piecewise Linear Function based Modeling of Lifetime Characteristics

Researchers have widely used accelerated life tests to determine an optimal inspection plan for lot acceptance. All such plans are proposed by assuming a known relationship between the lifetime characteristic(s) and the accelerating stress factor(s) under a parametric framework of the product lifetime distribution. As the true relationship is rarely known in practical scenarios, the assumption itself may produce biased estimates that may lead to an inefficient sampling plan. To this endeavor, an optimal accelerating life test plan is designed under a Type-I censoring scheme with a generalized link structure similar to a spline regression, to capture the nonlinear relationship between the lifetime characteristics and the stress levels. Product lifetime is assumed to follow Weibull distribution with non-identical scale and shape parameters linked with the stress factor through a piecewise linear function. The elements of the Fisher information matrix are computed in detail to formulate the acceptability criterion for the conforming lots. The decision variables of the sampling plan including sample size, stress factors, and others are determined using a constrained aggregated cost minimization approach and variance minimization approach. A simulated case study demonstrates that the nonlinear link-based piecewise linear approximation model outperforms the linear link-based model.

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arXiv2023

Likelihood-Based Inference for Semi-Parametric Transformation Cure Models with Interval Censored Data

A simple yet effective way of modeling survival data with cure fraction is by considering Box-Cox transformation cure model (BCTM) that unifies mixture and promotion time cure models. In this article, we numerically study the statistical properties of the BCTM when applied to interval censored data. Time-to-events associated with susceptible subjects are modeled through proportional hazards structure that allows for non-homogeneity across subjects, where the baseline hazard function is estimated by distribution-free piecewise linear function with varied degrees of non-parametricity. Due to missing cured statuses for right censored subjects, maximum likelihood estimates of model parameters are obtained by developing an expectation-maximization (EM) algorithm. Under the EM framework, the conditional expectation of the complete data log-likelihood function is maximized by considering all parameters (including the Box-Cox transformation parameter $\alpha$) simultaneously, in contrast to conventional profile-likelihood technique of estimating $\alpha$. The robustness and accuracy of the model and estimation method are established through a detailed simulation study under various parameter settings, and an analysis of real-life data obtained from a smoking cessation study.

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arXiv2021

Destructive cure models with proportional hazards lifetimes and associated likelihood inference

In survival analysis, cure models have gained much importance due to rapid advancements in medical sciences. More recently, a subset of cure models, called destructive cure models, have been studied extensively under competing risks scenario wherein initial competing risks undergo a destructive process, such as under a chemotherapy. In this article, we study destructive cure models by assuming a flexible weighted Poisson distribution (exponentially weighted Poisson, length biased Poisson and negative binomial distributions) for the initial number of competing causes and with lifetimes of the susceptible individuals following proportional hazards. The expectation-maximization (EM) algorithm and profile likelihood approach are made use of for estimating the model parameters. An extensive simulation study is carried out under various parameter settings to examine the properties of the models, and the accuracy and robustness of the proposed estimation technique. Effects of model misspecification on the parameter estimates are also discussed in detail. Finally, for the illustration of the proposed methodology, a real-life cutaneous melanoma data set is analyzed.

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arXiv2021

A Support Vector Machine Based Cure Rate Model For Interval Censored Data

The mixture cure rate model is the most commonly used cure rate model in the literature. In the context of mixture cure rate model, the standard approach to model the effect of covariates on the cured or uncured probability is to use a logistic function. This readily implies that the boundary classifying the cured and uncured subjects is linear. In this paper, we propose a new mixture cure rate model based on interval censored data that uses the support vector machine (SVM) to model the effect of covariates on the uncured or the cured probability (i.e., on the incidence part of the model). Our proposed model inherits the features of the SVM and provides flexibility to capture classification boundaries that are non-linear and more complex. Furthermore, the new model can be used to model the effect of covariates on the incidence part when the dimension of covariates is high. The latency part is modeled by a proportional hazards structure. We develop an estimation procedure based on the expectation maximization (EM) algorithm to estimate the cured/uncured probability and the latency model parameters. Our simulation study results show that the proposed model performs better in capturing complex classification boundaries when compared to the existing logistic regression based mixture cure rate model. We also show that our model's ability to capture complex classification boundaries improve the estimation results corresponding to the latency parameters. For illustrative purpose, we present our analysis by applying the proposed methodology to an interval censored data on smoking cessation.

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arXiv2021

A Stochastic Version of the EM Algorithm for Mixture Cure Rate Model with Exponentiated Weibull Family of Lifetimes

Handling missing values plays an important role in the analysis of survival data, especially, the ones marked by cure fraction. In this paper, we discuss the properties and implementation of stochastic approximations to the expectation-maximization (EM) algorithm to obtain maximum likelihood (ML) type estimates in situations where missing data arise naturally due to right censoring and a proportion of individuals are immune to the event of interest. A flexible family of three parameter exponentiated-Weibull (EW) distributions is assumed to characterize lifetimes of the non-immune individuals as it accommodates both monotone (increasing and decreasing) and non-monotone (unimodal and bathtub) hazard functions. To evaluate the performance of the SEM algorithm, an extensive simulation study is carried out under various parameter settings. Using likelihood ratio test we also carry out model discrimination within the EW family of distributions. Furthermore, we study the robustness of the SEM algorithm with respect to outliers and algorithm starting values. Few scenarios where stochastic EM (SEM) algorithm outperforms the well-studied EM algorithm are also examined in the given context. For further demonstration, a real survival data on cutaneous melanoma is analyzed using the proposed cure rate model with EW lifetime distribution and the proposed estimation technique. Through this data, we illustrate the applicability of the likelihood ratio test towards rejecting several well-known lifetime distributions that are nested within the wider class of EW distributions.

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