Summary of current and next issues

Abstract: When modeling time-to-event data that are subject to right censoring, it is commonly assumed that the survival time T and the censoring time C are independent. However, this assumption frequently fails in practice, leading to biased estimators and testing procedures having invalid type 1 error rates. To overcome this issue, several models relaxing the independent censoring assumption have been proposed in the literature. Among these, copula-based approaches have become popular due to their ability to separately model the marginal distributions of T and C and their dependence structure. This review paper gives a comprehensive overview of recent advances in copula-based methods for dependent censoring, along with a discussion of the most important historical papers on this topic. As it is well known that the distribution of (T, C) (and hence of T) is not identified in a fully nonparametric way, we examine different strategies to achieve model identifiability. These strategies consist of imposing assumptions on either the copula or the marginal distributions of T and C. Both of these approaches will be discussed, with and without covariates. We also consider the case where a dependent censoring time is accompanied by an additional latent independent censoring time. Lastly, we briefly explain alternative approaches that are not based on copulas.

Keywords: copula, dependent censoring, identifiability, survival analysis

Pages: 3–42

DOI: 10.57645/20.8080.02.21

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Abstract: The maxima and the minima of a randomly stopped sample of a random variable, X, together with two newly defined random variables that make X into the maxima or minima of a randomly stopped sample of them, can be used to define statistical model transformation mechanisms. These transformations can be used to define models for extreme-value data that are not grounded on large sample theory. The relationship between the stopping model and characteristics of the corresponding model transformations obtained is investigated. In particular, one looks into which stopping models make these model transformations into model extensions, and which stopping models lead to statistically stable extensions in the sense that using the model extension a second time leaves the extended model unchanged. The stopping models under which the extensions based on randomly stopped maxima and their inverses coincide with the extensions based on randomly stopped minima and their inverses are also characterized. The advantages of using models obtained through these model extension mechanisms instead of resorting to extreme-value models grounded on asymptotic arguments is illustrated by way of examples.

Keywords: Marshall-Olkin extension, extreme value, randomly stopped maximum, randomly stopped minimum, statistical stability, stopping model

Pages: 43–72

DOI: 10.57645/20.8080.02.22

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Abstract: The comparison of investments in financial derivatives is an appealing topic in the optimization of resources. A relevant derivative is the call ratio backspread. Motivated by the need to compare investments in such derivatives, a new family of stochastic orders is introduced. That permits to reach decisions on the allocations of funds in those derivatives under general conditions and without assuming specific probability distributions of the asset prices. Characterizations of the orders are developed. Special emphasis is placed on the existence of infima and suprema in such dominance criteria, which leads to lattice structures on some special spaces and to the reduction of some optimization problems with stochastic dominance constraints. The method is illustrated with an application using real data from financial markets.

Keywords: call ratio backspread derivative, integrated survival function, lattice, stochastic order

Pages: 73–92

DOI: 10.57645/20.8080.02.23

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Abstract: We propose the geometric mean spatial conditional model for fitting spatial public Health data, assuming that the disease incidence in one region depends on that of neighbouring regions, and incorporating an autoregressive spatial term based on their geometric mean. We explore alternative spatial weights matrices, including those based on contiguity, distance, covariate differences and individuals’ mobility. A simulation study assesses the model’s performance with mobility-based spatial correlation. We illustrate our proposals by analysing the COVID-19 spread in Flanders, Belgium, and comparing the proposed model with other commonly used spatial models. Our approach demonstrates advantages in interpretability, computational efficiency, and flexibility over the commonly used and previously existing methods.

Keywords: Bayesian approaches, COVID-19 incidence, epidemiology, spatial modelling

Pages: 93–120

DOI: 10.57645/20.8080.02.24

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Abstract: Evaluating the predictive performance of a statistical model is commonly done using cross-validation. Among the various methods, leave-one-out cross-validation (LOOCV) is frequently used. Originally designed for exchangeable observations, LOOCV has since been extended to other cases such as hierarchical models. However, it focuses primarily on short-range prediction and may not fully capture long-range prediction scenarios. For structured hierarchical models, particularly those involving multiple random effects, the concepts of short-and long-range predictions become less clear, which can complicate the interpretation of LOOCV results. In this paper, we propose a complementary cross-validation framework specifically tailored for longer-range prediction in latent Gaussian models, including those with structured random effects. Our approach differs from LOOCV by excluding a carefully constructed set from the training set, which better emulates longer-range prediction conditions. Furthermore, we achieve computational efficiency by adjusting the full joint posterior for this modified cross-validation, thus eliminating the need for model refitting. This method is implemented in the R-INLA package (www.r-inla.org) and can be adapted to a variety of inferential frameworks.

Keywords: Bayesian Cross-Validation, Latent Gaussian Models, R-INLA

Pages: 121–146

DOI: 10.57645/20.8080.02.25

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