Volume 21, Issue 2

The binary classification problem (BCP) aims to correctly allocate subjects in one of two possible groups. The groups are frequently defined as having or not one characteristic of interest. With this goal, we are allowed to use different types of information. There is a huge number of methods dealing with this problem; including standard binary regression models, or complex machine learning techniques such as support vector machine, boosting, or perceptron, among others. When this information is summarized in a continuous score, we have to define classification regions (or subsets) which will determine whether the subjects are classified as positive, with the characteristic under study, or as negative, otherwise. The standard (or regular) receiver-operating characteristic (ROC) curve assumes that higher values of the marker are associated with higher probabilities of being positive and considers as positive those patients with values within the intervals [ c , ∞) ( c ∈ R ) $(c\in \mathbb{R})$ , and plots the true- against the false- positive rates (sensitivity against one minus specificity) for all potential c . The so-called generalized ROC curve, gROC, allows that both higher and lower values of the score are associated with higher probabilities of being positive. The efficient ROC curve, eROC, considers the best ROC curve based on a transformation of the score. In this manuscript, we are interested in studying, comparing and approximating the transformations leading to the eROC and to the gROC curves. We will prove that, when the optimal transformation does not have relative maximum, both curves are equivalent. Besides, we investigate the use of the gROC curve on some theoretical models, explore the relationship between the gROC and the eROC curves, and propose two non-parametric procedures for approximating the transformation leading to the gROC curve. The finite-sample behavior of the proposed estimators is explored through Monte Carlo simulations. Two real-data sets illustrate the practical use of the proposed methods.

Variable selection is challenging for high-dimensional data, in particular when sample size is low. It is widely recognized that external information in the form of complementary data on the variables, ‘co-data’, may improve results. Examples are known variable groups or p -values from a related study. Such co-data are ubiquitous in genomics settings due to the availability of public repositories, and is likely equally relevant for other applications. Yet, the uptake of prediction methods that structurally use such co-data is limited. We review guided adaptive shrinkage methods: a class of regression-based learners that use co-data to adapt the shrinkage parameters, crucial for the performance of those learners. We discuss technical aspects, but also the applicability in terms of types of co-data that can be handled. This class of methods is contrasted with several others. In particular, group-adaptive shrinkage is compared with the better-known sparse group-lasso by evaluating variable selection. Moreover, we demonstrate the versatility of the guided shrinkage methodology by showing how to ‘do-it-yourself’: we integrate implementations of a co-data learner and the spike-and-slab prior for the purpose of improving variable selection in genetics studies. We conclude with a real data example.

In observational studies, the treatment assignment is typically not random. Even in randomized clinical trials, the randomization may be imperfect given the limitation of sample size. In these cases, traditional statistical methods may lead to biased estimates of treatment effects, and causal inference methods are needed to obtain unbiased estimates. The doubly robust estimator (DRE) is a recent development in causal inference, but the literature on DRE for survival data is very limited, and existing methods tend to have complicated forms and may not have double robustness in the original sense. Some are constructed based on the Nelson–Aalen estimator, and to our knowledge no DRE is constructed based on the Kaplan–Meier estimator. Furthermore, in these methods, the propensity score model is often subjectively specified with a logistic model. DRE can be seriously biased if the propensity score and outcome models are slightly misspecified. Here we propose a new semiparametric robust estimator that utilizes the Kaplan–Meier estimator and Stute weighted empirical form to address these issues. Our proposed estimator is not only doubly robust in the original sense but also enhances robustness with the use of semiparametric specification. The asymptotic properties of the proposed estimator are derived, and extensive simulation studies are conducted to evaluate its finite sample performance and compare it with existing methods. Finally, we apply our proposed method to a real clinical study.

In this paper, a two-sample empirical likelihood method for right censored data is established. This method allows for comparisons between various functionals of survival distributions, such as mean lifetimes, survival probabilities at a fixed time, restricted mean survival times, and other parameters of interest. It is demonstrated that under some regularity conditions, the scaled empirical likelihood statistic converges to a chi-squared distributed random variable with one degree of freedom. A consistent estimator for the scaling constant is proposed, involving the jackknife estimator of the asymptotic variance of the Kaplan-Meier integral. A simulation study is carried out to investigate the coverage accuracy of confidence intervals. Finally, two real datasets are analyzed to illustrate the application of the proposed method.

This paper discusses regression analysis of interval-censored failure time data arising from semiparametric transformation models in the presence of covariates that are missing at random (MAR). We define a specific formulation of the MAR mechanism tailored to the interval censoring, where the timing of observation adds complexity to handling missing covariates. To overcome the limitations and computational challenges present in the existing methods, we propose a multiple imputation procedure that can be easily implemented with the use of the standard software. The proposed method makes use of two predictive scores for each individual and the distance defined by these scores. Furthermore, it utilizes partial information from incomplete observations and thus yields more efficient estimators than the complete-case analysis and the inverse probability weighting approach. An extensive simulation study is conducted to assess the performance of the proposed method and indicates that it performs well in practical situations. Finally we apply the proposed approach to an Alzheimer’s Disease study that motivated this work.

A disease of interest can often be classified into subtypes based on its various molecular or pathological characteristics. Recent epidemiological studies have increasingly provided evidence that some molecular subtypes in a disease may have distinct etiologies, by assessing whether the associations of a potential risk factor vary by disease subtypes (i.e., etiologic heterogeneity). Case-control and case-case studies are popular study designs in molecular epidemiology, and both can be validly applied in studies of etiologic heterogeneity. This study compared the efficiency of the etiologic heterogeneity parameter estimation between these two study designs by theoretical and numerical examinations. In settings where the two study designs have the same number of cases, the results showed that, compared with the case-case study, case-control studies always provided more efficient estimates or estimates with at least equivalent efficiency for heterogeneity parameters. In addition, we illustrated both approaches in a study for aiming to evaluate the association between plasma free estradiol and breast cancer risk according to the status of tumor estrogen and progesterone receptors, the results of which were originally provided through case-control study data.

The quantification of overlap between two distributions has applications in various fields of biology, medical, genetic, and ecological research. In this article, new overlap and containment indices are considered for quantifying the niche overlap between two species/populations. Some new properties of these indices are established and the problem of estimation is studied, when the two distributions are exponential with different scale parameters. We propose several estimators and compare their relative performance with respect to different loss functions. The asymptotic normality of the maximum likelihood estimators of these indices is proved under certain conditions. We also obtain confidence intervals of the indices based on three different approaches and compare their average lengths and coverage probabilities. The point and confidence interval procedures developed here are applied on a breast cancer data set to analyze the similarity between the survival times of patients undergoing two different types of surgery. Additionally, the similarity between the relapse free times of these two sets of patients is also studied.

Traditional survival analysis typically assumes that all subjects will eventually experience the event of interest given a sufficiently long follow-up period. Nevertheless, due to advancements in medical technology, researchers now frequently observe that some subjects never experience the event and are considered cured. Furthermore, traditional survival analysis assumes independence between failure time and censoring time. However, practical applications often reveal dependence between them. Ignoring both the cured subgroup and this dependence structure can introduce bias in model estimates. Among the methods for handling dependent censoring data, the numerical integration process of frailty models is complex and sensitive to the assumptions about the latent variable distribution. In contrast, the copula method, by flexibly modeling the dependence between variables, avoids strong assumptions about the latent variable structure, offering greater robustness and computational feasibility. Therefore, this paper proposes a copula-based method to handle dependent current status data involving a cure fraction. In the modeling process, we establish a logistic model to describe the susceptible rate and a Cox proportional hazards model to describe the failure time and censoring time. In the estimation process, we employ a sieve maximum likelihood estimation method based on Bernstein polynomials for parameter estimation. Extensive simulation experiments show that the proposed method demonstrates consistency and asymptotic efficiency under various settings. Finally, this paper applies the method to lymph follicle cell data, verifying its effectiveness in practical data analysis.

Phase I trials aim to identify the maximum tolerated dose (MTD) early and proceed quickly to an expansion cohort or a Phase II trial to assess the efficacy of the treatment. We present an early completion method based on multiple dosages (adjacent dose information) to accelerate the identification of the MTD in model-assisted designs. By using not only toxicity data for the current dose but also toxicity data for the next higher and lower doses, the MTD can be identified early without compromising accuracy. The early completion method is performed based on dose-assignment probabilities for multiple dosages. These probabilities are straightforward to calculate. We evaluated the early completion method using from an actual clinical trial. In a simulation study, we evaluated the percentage of correct MTD selection and the impact of early completion on trial outcomes. The results indicate that our proposed early completion method maintains a high level of accuracy in MTD selection, with minimal reduction compared to the standard approach. In certain scenarios, the accuracy of MTD selection even improves under the early completion framework. We conclude that the use of this early completion method poses no issue when applied to model-assisted designs.

Multi-stage models for cohort data are widely used in various fields, including disease progression, the biological development of plants and animals, and laboratory studies of life cycle development. However, the likelihood functions of these models are often intractable and complex. These complexities in the likelihood functions frequently result in significant biases and high computational costs when estimating parameters using current Bayesian methods. This paper aims to address these challenges by applying the enhanced Sequential Monte Carlo approximate Bayesian computation (ABC-SMC) method, which does not rely on explicit likelihood functions, to stage-structured development models with non-hazard rates and stage-wise constant hazard rates. Instead of using a likelihood function, the proposed method determines parameter estimates based on matching vector summary statistics. It incorporates stage-wise parameter estimations and retains accepted parameters across stages. This approach not only reduces model biases but also improves the computational efficiency of parameter estimations, despite the computational intractability of the likelihood functions. The proposed ABC-SMC method is validated through simulation studies on stage-structured development models and applied to a case study of breast development in New Zealand schoolgirls. The results demonstrate that the proposed methods effectively reduce biases in later-stage estimates for stage-structured models, enhance computational efficiency, and maintain accuracy and reliability in parameter estimations compared to the current methods.

Competing risks models are survival models with several events of interest acting in competition and whose occurrence is only observed for the event that occurs first in time. This paper presents a Bayesian approach to these models in which the issue of model selection is treated in a special way by proposing generalizations of some of the Bayesian procedures used in univariate survival analysis. This research is motivated by a study on the survival of patients with heart failure undergoing cardiac resynchronization therapy, a procedure which involves the implant of a device to stabilize the heartbeat. Two different causes of death have been considered: cardiovascular and non-cardiovascular, and a set of baseline covariates are examined in order to better understand their relationship with both causes of death. Model selection, model checking, and model comparison procedures have been implemented and assessed. The posterior distribution of some relevant outputs such as the overall survival function, cumulative incidence functions, and transition probabilities have been computed and discussed.

Hyponatremia, characterized by a serum sodium concentration below 135 mEq/L, is a prevalent electrolyte imbalance associated with increased morbidity and mortality across various clinical conditions. This study employs the Holt-Winters seasonal method, a robust time series forecasting model, to predict mortality rates attributed to hyponatremia. Leveraging retrospective mortality data from a cohort of hospitals in the United States, our analysis aims to elucidate temporal patterns and trends in hyponatremia-related deaths. The findings underscore the critical role of statistical forecasting in healthcare, facilitating proactive resource allocation and targeted interventions to mitigate mortality risks associated with electrolyte imbalances. Integrating predictive analytics into clinical practice holds promise for enhancing patient care and optimizing health outcomes in populations vulnerable to hyponatremia-related complications.