We present a new class of survival models that combine unobserved population heterogeneity and cured individuals by incorporating frailty terms from the Power Variance Function (PVF) family, referred to as PVF-Induced Defective (PVF-ID) models. This structure broadens classic frailty theory and defective lifetimes under a proportional-hazards lens, letting researchers flexibly track long-term survivors in mixed cohorts. Inference follows a full-Bayesian routine run via Hamiltonian Monte Carlo, and key frequentist properties are cross-checked using simulation studies. When applied to HIV/AIDS records, the model reliably pinpoints important covariates and quantifies the fraction of cured patients. In this case study, among several baseline hazards, the simple exponential form wins by both leave-plus-one marginal likelihood (LPML) and raw marginal likelihood. Together, these findings position the PVF-ID framework as a robust, versatile toolbox for studying survival data with immune subpopulations.
The relationship between a noise exposure level of a supersonic flight event and the probability of an individual being highly annoyed by the event is quantified by a dose-response curve. Dose-response curve estimation is based on logistic regression modeling, and it is subject to bias when the dose is measured with error. The National Aeronautics and Space Administration (NASA) is planning to conduct a set of supersonic aircraft annoyance surveys in select communities in the U.S., to measure public perception of reduced sonic boom. Unavoidable amounts of estimation error are expected in these upcoming noise measurements. Hence, the development of an estimation approach that accounts for such error when estimating the dose-response curve is imperative. In this paper, an evaluation study is conducted to assess the impact of measurement error on dose-response curve estimation. For this, hierarchical Bayes models are fit to data collected by NASA in 2018, as part of a risk-reduction study of supersonic flights at Galveston, Texas. Then, the models are evaluated using a simulation study built on features that are expected in the survey data to be collected in the new study. It is observed that the estimated dose-response curve is indeed highly sensitive to uncertainty in dose measurements, being subject to attenuation bias. The results show that the proposed models are effective in correcting a substantial portion of the attenuation bias.
Robust inference for overdispersed count data is crucial in applications where outliers may substantially distort classical likelihood-based estimation of both the mean and dispersion. We develop robust estimation procedures for independent and identically distributed negative binomial data and provide practical guidelines on the choice of the estimator. We propose a combined robust M-estimator that jointly estimates the mean and dispersion parameter through an alternating updating scheme based on bounded score functions. The mean update relies on a bias-corrected Tukey-type M-estimator, extending the Poisson framework of Elsaied and Fried (2016) to the negative binomial setting, while the dispersion update follows a robust modification of score-based estimation in the spirit of Aeberhard et al. (2014). Under standard regularity conditions, we establish key theoretical guarantees for the proposed estimator, including consistency, local convergence of the alternating algorithm, asymptotic normality, and robustness to outliers through bounded influence. Extensive simulation studies compare the proposed method with maximum likelihood estimation, minimum disparity estimators, and weighted maximum likelihood approaches under both clean and contaminated sampling. The results show that classical likelihood procedures can be highly sensitive to additive contamination, particularly in dispersion estimation, whereas the proposed estimator achieves a favorable efficiency–robustness trade-off across a broad range of sample sizes and contamination regimes, while retaining high efficiency under the nominal model. An analysis of epileptic seizure count data further illustrates the practical relevance of the approach and the stability of the resulting inference without relying on ad hoc data cleaning.
Compositional data, which capture relative contributions of parts to a whole, are constrained by a constant sum. They arise in various fields such as geochemistry, soil science, and paleoecology, describing data typically affected by measurement errors. We discuss the kernel method for contaminated compositional data, using a deconvolution approach. Some numerical experiments are provided using both simulated and real data.
Simulation studies are often carried out to study theoretical properties of a statistical procedure that cannot be derived analytically. Oftentimes, simulation studies can be very extensive, including various factors with various levels. This makes the results of such studies often difficult to report, and difficult for readers to interpret the general picture in the overabundance of results. Additionally, in many cases such extensive studies may not even be necessary. This work aims to explore and discuss some general guidelines on when (not) to include a simulation factor. Depending on the research question, oftentimes varying only one or two factors may suffice for answering the research question. In the current paper two different types of simulation studies are defined, namely proof of principle studies and robustness studies. Next, for a number of quality measures it is argued which factors are and are not useful to vary, both in proof of principle studies and robustness studies. Finally, the results of a literature study are presented confirming the need for guidelines on what factors to vary in a simulation study. A general recommendation is to not vary too many factors, especially for proof of principle studies.
