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Competing risks data are commonly encountered in randomized clinical trials and observational studies. This paper considers the situation where the ending statuses of competing events have different clinical interpretations and/or are of simultaneous interest. In clinical trials, often more than one competing event has meaningful clinical interpretations even though the trial effects of different events could be different or even opposite to each other. In this paper, we develop estimation procedures and inferential properties for the joint use of multiple cumulative incidence functions (CIFs). Additionally, by incorporating longitudinal marker information, we develop estimation and inference procedures for weighted CIFs and related metrics. The proposed methods are applied to a COVID‐19 in‐patient treatment clinical trial, where the outcomes of COVID‐19 hospitalization are either death or discharge from the hospital, two competing events with completely different clinical implications. [ABSTRACT FROM AUTHOR]

Background Racial and ethnic differences in survival after a first cancer are well established but have not been examined after a second primary cancer (SPC) despite the increasing incidence among survivors. Methods We examined 39 029 female breast cancer survivors who developed an SPC between 2000 and 2014 in the Surveillance, Epidemiology, and End Results 18 database. Multivariable Cox proportional hazards regression for competing risks data was used to estimate hazard ratios (HR) and 95% confidence intervals (CI) for cancer and cardiovascular disease mortality after SPCs comparing Hispanic, Non-Hispanic Asian, and Non-Hispanic Black survivors with Non-Hispanic White survivors. Models were adjusted for sociodemographics, tumor characteristics, and treatments of the first and second cancer. Analyses were stratified by SPC type. Results During 17 years of follow-up, there were 15 117 deaths after SPCs. The risk of cancer death was 12% higher among Non-Hispanic Black survivors (HR = 1.12, 95% CI = 1.05 to 1.19) and 8% higher among Hispanic survivors (HR = 1.08, 95% CI = 1.00 to 1.16) compared with Non-Hispanic White survivors. In subgroup analyses, the strongest associations were observed among Non-Hispanic Black survivors with a second breast or uterine cancer and among Hispanic survivors with a second breast cancer. Non-Hispanic Black survivors also experienced a 44% higher risk of cardiovascular disease death after SPC diagnosis than Non-Hispanic White survivors (HR = 1.44, 95% CI = 1.20 to 1.74). Conclusions Higher cancer mortality among Non-Hispanic Black and Hispanic survivors and higher cardiovascular mortality among Non-Hispanic Black survivors exist among women who survive a first breast cancer to develop an SPC. Studies focused on identifying the contributors to these disparities are needed to enable implementation of effective mitigation strategies. [ABSTRACT FROM AUTHOR]

In biomedical practices, multiple biomarkers are often combined using a prespecified classification rule with tree structure for diagnostic decisions. The classification structure and cutoff point at each node of a tree are usually chosen on an ad hoc basis, depending on decision makers' experience. There is a lack of analytical approaches that lead to optimal prediction performance, and that guide the choice of optimal cutoff points in a pre‐specified classification tree. In this paper, we propose to search for and estimate the optimal decision rule through an approach of rank correlation maximization. The proposed method is flexible, theoretically sound, and computationally feasible when many biomarkers are available for classification or prediction. Using the proposed approach, for a prespecified tree‐structured classification rule, we can guide the choice of optimal cutoff points at tree nodes and estimate optimal prediction performance from multiple biomarkers combined. [ABSTRACT FROM AUTHOR]

This paper introduces two sets of measures as exploratory tools to study physical activity patterns: active‐to‐sedentary/sedentary‐to‐active rate function (ASRF/SARF) and active/sedentary rate function (ARF/SRF). These two sets of measures are complementary to each other and can be effectively used together to understand physical activity patterns. The specific features are illustrated by an analysis of wearable device data from National Health and Nutrition Examination Survey (NHANES). A two‐level semiparametric regression model for ARF and the associated activity magnitude is developed under a unified framework using the marked point process formulation. The inactive and active states measured by accelerometers are treated as a 0‐1 point process, and the activity magnitude measured at each active state is defined as a marked variable. The commonly encountered missing data problem due to device nonwear is referred to as "window censoring," which is handled by a proper estimation approach that adopts techniques from recurrent event data. Large sample properties of the estimator and comparison between two regression models as measurement frequency increases are studied. Simulation and NHANES data analysis results are presented. The statistical inference and analysis results suggest that ASRF/SARF and ARF/SRF provide useful analytical tools to practitioners for future research on wearable device data. [ABSTRACT FROM AUTHOR]

A time‐dependent measure, termed the rate ratio, was proposed to assess the local dependence between two types of recurrent event processes in one‐sample settings. However, the one‐sample work does not consider modeling the dependence by covariates such as subject characteristics and treatments received. The focus of this paper is to understand how and in what magnitude the covariates influence the dependence strength for bivariate recurrent events. We propose the covariate‐adjusted rate ratio, a measure of covariate‐adjusted dependence. We propose a semiparametric regression model for jointly modeling the frequency and dependence of bivariate recurrent events: the first level is a proportional rates model for the marginal rates and the second level is a proportional rate ratio model for the dependence structure. We develop a pseudo‐partial likelihood to estimate the parameters in the proportional rate ratio model. We establish the asymptotic properties of the estimators and evaluate the finite sample performance via simulation studies. We illustrate the proposed models and methods using a soft tissue sarcoma study that examines the effects of initial treatments on the marginal frequencies of local/distant sarcoma recurrence and the dependence structure between the two types of cancer recurrence. [ABSTRACT FROM AUTHOR]

Tree‐based methods are popular nonparametric tools in studying time‐to‐event outcomes. In this article, we introduce a novel framework for survival trees and ensembles, where the trees partition the dynamic survivor population and can handle time‐dependent covariates. Using the idea of randomized tests, we develop generalized time‐dependent receiver operating characteristic (ROC) curves for evaluating the performance of survival trees. The tree‐building algorithm is guided by decision‐theoretic criteria based on ROC, targeting specifically for prediction accuracy. To address the instability issue of a single tree, we propose a novel ensemble procedure based on averaging martingale estimating equations, which is different from existing methods that average the predicted survival or cumulative hazard functions from individual trees. Extensive simulation studies are conducted to examine the performance of the proposed methods. We apply the methods to a study on AIDS for illustration. [ABSTRACT FROM AUTHOR]

Recent evidence indicates that measures from cerebrospinal fluid, MRI scans and cognitive testing obtained from cognitively normal individuals can be used to predict likelihood of progression to mild cognitive impairment several years later, for groups of individuals. However, it remains unclear whether these measures are useful for predicting likelihood of progression for an individual. The increasing focus on early intervention in clinical trials for Alzheimer's disease emphasizes the importance of improving the ability to identify which cognitively normal individuals are more likely to progress over time, thus allowing researchers to efficiently screen participants, as well as determine the efficacy of any treatment intervention. The goal of this study was to determine which measures, obtained when individuals were cognitively normal, predict on an individual basis, the onset of clinical symptoms associated with a diagnosis of mild cognitive impairment due to Alzheimer's disease. Cognitively normal participants (n = 224, mean baseline age = 57 years) were evaluated with a range of measures, including: cerebrospinal fluid amyloid-β and phosphorylated-tau, hippocampal and entorhinal cortex volume, cognitive tests scores and APOE genotype. They were then followed to determine which individuals developed mild cognitive impairment over time (mean follow-up = 11 years). The primary outcome was progression from normal cognition to the onset of clinical symptoms of mild cognitive impairment due to Alzheimer's disease at 5 years post-baseline. Time-dependent receiver operating characteristic analyses examined the sensitivity and specificity of individual measures, and combinations of measures, as predictors of the outcome. Six measures, in combination, were the most parsimonious predictors of transition to mild cognitive impairment 5 years after baseline (area under the curve = 0.85; sensitivity = 0.80, specificity = 0.75). The addition of variables from each domain significantly improved the accuracy of prediction. The incremental accuracy of prediction achieved by adding individual measures or sets of measures successively to one another was also examined, as might be done when enrolling individuals in a clinical trial. The results indicate that biomarkers obtained when individuals are cognitively normal can be used to predict which individuals are likely to develop clinical symptoms at 5 years post-baseline. As a number of the measures included in the study could also be used as subject selection criteria in a clinical trial, the findings also provide information about measures that would be useful for screening in a clinical trial aimed at individuals with preclinical Alzheimer's disease. [ABSTRACT FROM AUTHOR]

Summary: The second stage of labour begins when the cervix is fully dilated and pushing begins until the fetus is delivered. A Caesarean delivery (CD) or operative vaginal delivery (OVD) is typically encouraged after the recommended time set by 'expert consensus'. This recommended time has been set out of concern for an increased chance of maternal and neonatal morbidities due to a prolonged second stage of labour, but without thorough consideration of heterogeneous risks for spontaneous vaginal delivery (SVD) and morbidities among women. To provide quantitative evidence for the recommendation, the first step is to compare the risks for SVD, CD or OVD, and the risks of maternal or neonatal morbidities simultaneously across the duration of the second stage of labour. To address such risk comparisons statistically, one needs to study the joint distribution for the time to delivery due to each mode and time to maternal or neonatal morbidity given information provided for each individual. We introduce a joint model which combines the competing risks data for delivery time and current status data for any type of maternal or neonatal morbidity given each woman's baseline characteristics. These two processes are assumed dependent through individual‐specific frailty under the joint model. Our numerical studies include a simulation that reflects the structure of observed real data and a detailed real data analysis based on nearly 12000 spontaneous labours. Our finding indicates the necessity to incorporate maternal characteristic such as age or body mass index in assessing the probability for delivery due to SVD, CD or OVD and the onset of morbidities across the second stage of labour. [ABSTRACT FROM AUTHOR]

In biomedical studies involving survival data, the observation of failure times is sometimes accompanied by a variable which describes the type of failure event (Kalbeisch and Prentice, 2002). This paper considers two specific challenges which are encountered in the joint analysis of failure time and failure type. First, because the observation of failure times is subject to left truncation, the sampling bias extends to the failure type which is associated with the failure time. An analytical challenge is to deal with such sampling bias. Second, in case that the joint distribution of failure time and failure type is allowed to have a temporal trend, it is of interest to estimate the joint distribution of failure time and failure type nonparametrically. This paper develops statistical approaches to address these two analytical challenges on the basis of prevalent survival data. The proposed approaches are examined through simulation studies and illustrated by using a real data set. [ABSTRACT FROM AUTHOR]

Summary: Recent advances of wearable computing technology have allowed continuous health monitoring in large observational studies and clinical trials. Examples of data collected by wearable devices include minute‐by‐minute physical activity proxies measured by accelerometers or heart rate. The analysis of data generated by wearable devices has so far been quite limited to crude summaries, for example, the mean activity count over the day. To better utilize the full data and account for the dynamics of activity level in the time domain, we introduce a two‐stage regression model for the minute‐by‐minute physical activity proxy data. The model allows for both time‐varying parameters and time‐invariant parameters, which helps capture both the transition dynamics between active/inactive periods (Stage 1) and the activity intensity dynamics during active periods (Stage 2). The approach extends methods developed for zero‐inflated Poisson data to account for the high‐dimensionality and time‐dependence of the high density data generated by wearable devices. Methods are motivated by and applied to the Baltimore Longitudinal Study of Aging. [ABSTRACT FROM AUTHOR]

Recurrent events together with longitudinal measurements are commonly observed in follow-up studies where the observation is terminated by censoring or a primary failure event. In this article, we developed a joint model where the dependence of longitudinal measurements, recurrent event process and time to failure event is modeled through rescaling the time index. The general idea is that the trajectories of all biology processes of subjects in the survivors' population are elongated or shortened by the rate identified from a model for the failure event. To avoid making disputing assumptions on recurrent events or biomarkers after the failure event (such as death), the model is constructed on the basis of survivors' population. The model also possesses a specific feature that, by aligning failure events as time origins, the backward-in-time model of recurrent events and longitudinal measurements shares the same parameter values with the forward time model. The statistical properties, simulation studies and real data examples are conducted. The proposed method can be generalized to analyze left-truncated data. [ABSTRACT FROM AUTHOR]

This article considers nonparametric methods for studying recurrent disease and death with competing risks. We first point out that comparisons based on the well-known cumulative incidence function can be confounded by different prevalence rates of the competing events, and that comparisons of the conditional distribution of the survival time given the failure event type are more relevant for investigating the prognosis of different patterns of recurrence disease. We then propose nonparametric estimators for the conditional cumulative incidence function as well as the conditional bivariate cumulative incidence function for the bivariate gap times, that is, the time to disease recurrence and the residual lifetime after recurrence. To quantify the association between the two gap times in the competing risks setting, a modified Kendall's tau statistic is proposed. The proposed estimators for the conditional bivariate cumulative incidence distribution and the association measure account for the induced dependent censoring for the second gap time. Uniform consistency and weak convergence of the proposed estimators are established. Hypothesis testing procedures for two-sample comparisons are discussed. Numerical simulation studies with practical sample sizes are conducted to evaluate the performance of the proposed nonparametric estimators and tests. An application to data from a pancreatic cancer study is presented to illustrate the methods developed in this article. [ABSTRACT FROM AUTHOR]

This article presents methods and inference for causal estimation in semiparametric transformation models for the prevalent survival data. Through the estimation of the transformation models and covariate distribution, we propose a few analytical procedures to estimate the causal survival function. As the data are observational, the unobserved potential outcome (survival time) may be associated with the treatment assignment, and therefore there may exist a systematic imbalance between the data observed from each treatment arm. Further, due to prevalent sampling, subjects are observed only if they have not experienced the failure event when data collection began, causing the prevalent sampling bias. We propose a unified approach, which simultaneously corrects the bias from the prevalent sampling and balances the systematic differences from the observational data. We illustrate in the simulation study that standard analysis without proper adjustment would result in biased causal inference. Large sample properties of the proposed estimation procedures are established by techniques of empirical processes and examined by simulation studies. The proposed methods are applied to the Surveillance, Epidemiology, and End Results (SEER) and Medicare-linked data for women diagnosed with breast cancer. [ABSTRACT FROM AUTHOR]

Bivariate or multivariate recurrent event processes are often encountered in longitudinal studies in which more than one type of event is of interest. There has been much research on regression analysis for such data, but little has been done to measure the dependence between recurrent event processes. We propose a time-dependent measure, termed the rate ratio, to assess the local dependence between two types of recurrent event processes. We model the rate ratio as a parametric function of time, and leave unspecified all other aspects of the distribution. We develop a composite likelihood procedure for model fitting and parameter estimation. We show that the proposed estimator is consistent and asymptotically normal. Its finite sample performance is evaluated by simulation and illustrated by an application to a soft tissue sarcoma study. [ABSTRACT FROM AUTHOR]

In many biomedical applications, interest focuses on the occurrence of two or more consecutive failure events and the relationship between event times, such as age of disease onset and residual lifetime. Bivariate survival data with interval sampling arise frequently when disease registries or surveillance systems collect data based on disease incidence occurring within a specific calendar time interval. The initial event is then retrospectively confirmed and the subsequent failure event may be observed during follow-up. In life history studies, the initial and two consecutive failure events could correspond to birth, disease onset and death. The statistical features and bias of observed data in relation to interval sampling were discussed by Zhu & Wang (2012). Here we propose nonparametric estimation of the association between bivariate failure times based on Kendall’s tau for data collected with interval sampling. A nonparametric estimator is given, where the contribution of each comparable and orderable pair is weighted by the inverse of the associated selection probability. Analysis methods for bivariate survival data with interval sampling rely on the assumption of quasi-independence, i.e., that bivariate failure times and the time of the initial event are independent in the observable region. This paper develops a nonparametric test of quasi-independence based on a bivariate conditional Kendall’s tau for such data. Simulation studies demonstrate that the association estimator and testing procedure perform well with moderate sample sizes. Illustrations with two real datasets are provided. [ABSTRACT FROM PUBLISHER]

This paper proposes a unified framework to characterize the rate function of a recurrent event process through shape and size parameters. In contrast to the intensity function, which is the event occurrence rate conditional on the event history, the rate function is the occurrence rate unconditional on the event history, and thus it can be interpreted as a population-averaged count of events in unit time. In this paper, shape and size parameters are introduced and used to characterize the association between the rate function λ(⋅) and a random variable X. Measures of association between X and λ(⋅) are defined via shape- and size-based coefficients. Rate-independence of X and λ(⋅) is studied through tests of shape-independence and size-independence, where the shape- and size-based test statistics can be used separately or in combination. These tests can be applied when X is a covariable possibly correlated with the recurrent event process through λ(⋅) or, in the one-sample setting, when X is the censoring time at which the observation of N(⋅) is terminated. The proposed tests are shape- and size-based, so when a null hypothesis is rejected, the test results can serve to distinguish the source of violation. [ABSTRACT FROM PUBLISHER]

The article presents a quantitative proteomics study depicting the protective results of grape seed procyanidin B2 (GSPB2) on diabetic cardiomyopathy in db/db mice, a model of obesity mice. It states the increased in the number of diabetes mellitus incidence worldwide with common complications such as independent of coronary heart disease and atherosclerosis. It also emphasizes the characterization of diabetic cardiomyopathy and its structural and functional changes in the heart.

This article considers receiver operating characteristic (ROC) analysis for bivariate marker measurements. The research interest is to extend tools and rules from univariate marker to bivariate marker setting for evaluating predictive accuracy of markers using a tree-based classification rule. Using an and-or classifier, an ROC function together with a weighted ROC function (WROC) and their conjugate counterparts are proposed for examining the performance of bivariate markers. The proposed functions evaluate the performance of and-or classifiers among all possible combinations of marker values, and are ideal measures for understanding the predictability of biomarkers in target population. Specific features of ROC and WROC functions and other related statistics are discussed in comparison with those familiar properties for univariate marker. Nonparametric methods are developed for estimating ROC-related functions (partial) area under curve and concordance probability. With emphasis on average performance of markers, the proposed procedures and inferential results are useful for evaluating marker predictability based on a single or bivariate marker (or test) measurements with different choices of markers, and for evaluating different and-or combinations in classifiers. The inferential results developed in this article also extend to multivariate markers with a sequence of arbitrarily combined and-or classifier. [ABSTRACT FROM AUTHOR]

This article develops semiparametric approaches for estimation of propensity scores and causal survival functions from prevalent survival data. The analytical problem arises when the prevalent sampling is adopted for collecting failure times and, as a result, the covariates are incompletely observed due to their association with failure time. The proposed procedure for estimating propensity scores shares interesting features similar to the likelihood formulation in case-control study, but in our case it requires additional consideration in the intercept term. The result shows that the corrected propensity scores in logistic regression setting can be obtained through standard estimation procedure with specific adjustments on the intercept term. For causal estimation, two different types of missing sources are encountered in our model: one can be explained by potential outcome framework; the other is caused by the prevalent sampling scheme. Statistical analysis without adjusting bias from both sources of missingness will lead to biased results in causal inference. The proposed methods were partly motivated by and applied to the Surveillance, Epidemiology, and End Results (SEER)-Medicare linked data for women diagnosed with breast cancer. [ABSTRACT FROM AUTHOR]

Incidence is an important epidemiological concept most suitably studied using an incident cohort study. However, data are often collected from the more feasible prevalent cohort study, whereby diseased individuals are recruited through a cross-sectional survey and followed in time. In the absence of temporal trends in survival, we derive an efficient nonparametric estimator of the cumulative incidence based on such data and study its asymptotic properties. Arbitrary calendar time variations in disease incidence are allowed. Age-specific incidence and adjustments for both stratified sampling and temporal variations in survival are also discussed. Simulation results are presented and data from the Canadian Study of Health and Aging are analysed to infer the incidence of dementia in the Canadian elderly population. [ABSTRACT FROM PUBLISHER]

A prevalent sample consists of individuals who have experienced disease incidence but not failure event at the sampling time. We discuss methods for estimating the distribution function of a random vector defined at baseline for an incident disease population when data are collected by prevalent sampling. Prevalent sampling design is often more focused and economical than incident study design for studying the survival distribution of a diseased population, but prevalent samples are biased by design. Subjects with longer survival time are more likely to be included in a prevalent cohort, and other baseline variables of interests that are correlated with survival time are also subject to sampling bias induced by the prevalent sampling scheme. Without recognition of the bias, applying empirical distribution function to estimate the population distribution of baseline variables can lead to serious bias. In this article, nonparametric and semiparametric methods are developed for distribution estimation of baseline variables using prevalent data. [ABSTRACT FROM AUTHOR]

In biomedical studies, ordered bivariate survival data are frequently encountered when bivariate failure events are used as outcomes to identify the progression of a disease. In cancer studies, interest could be focused on bivariate failure times, for example, time from birth to cancer onset and time from cancer onset to death. This paper considers a sampling scheme, termed interval sampling, in which the first failure event is identified within a calendar time interval, the time of the initiating event can be retrospectively confirmed and the occurrence of the second failure event is observed subject to right censoring. In a cancer data application, the initiating, first and second events could correspond to birth, cancer onset and death. The fact that the data are collected conditional on the first failure event occurring within a time interval induces bias. Interval sampling is widely used for collection of disease registry data by governments and medical institutions, though the interval sampling bias is frequently overlooked by researchers. This paper develops statistical methods for analysing such data. Semiparametric methods are proposed under semi-stationarity and stationarity. Numerical studies demonstrate that the proposed estimation approaches perform well with moderate sample sizes. We apply the proposed methods to ovarian cancer registry data. [ABSTRACT FROM PUBLISHER]

In this paper, we study panel count data with informative observation times. We assume nonparametric and semiparametric proportional rate models for the underlying event process, where the form of the baseline rate function is left unspecified and a subject-specific frailty variable inflates or deflates the rate function multiplicatively. The proposed models allow the event processes and observation times to be correlated through their connections with the unobserved frailty; moreover, the distributions of both the frailty variable and observation times are considered as nuisance parameters. The baseline rate function and the regression parameters are estimated by maximising a conditional likelihood function of observed event counts and solving estimation equations. Large-sample properties of the proposed estimators are studied. Numerical studies demonstrate that the proposed estimation procedures perform well for moderate sample sizes. An application to a bladder tumour study is presented. [ABSTRACT FROM PUBLISHER]

This article considers statistical models in which two different types of events, such as the diagnosis of a disease and the remission of the disease, occur alternately over time and are observed subject to right censoring. We propose nonparametric estimators for the joint distribution of bivariate recurrence times and the marginal distribution of the first recurrence time. In general, the marginal distribution of the second recurrence time cannot be estimated due to an identifiability problem, but a conditional distribution of the second recurrence time can be estimated nonparametrically. In the literature, statistical methods have been developed to estimate the joint distribution of bivariate recurrence times based on data on the first pair of censored bivariate recurrence times. These methods are inefficient in the model considered here because recurrence times of higher orders are not used. Asymptotic properties of the proposed estimators are established. Numerical studies demonstrate the estimators perform well with practical sample sizes. We apply the proposed method to the South Verona, Italy, psychiatric case register (PCR) data set for illustration of the methods and theory. [ABSTRACT FROM AUTHOR]

SUMMARY Length-biased sampling is frequently a convenient technique for the collection of positive-valued or lifetime data. Estimation porocedures based on pseudo-likelihood are developed under the proportional hazards model for length-biased data. Bias-adjusted risk set sampling is used for the construction of the pseudo-likelihood and the risk set sampling is rephcated to improve estimation performance. The average of the resulting likelihood estimators is taken as the estimator for the regression coefficients. Although the replication procedure is expected to improve estimation accuracy when the sample size is small or moderate, it does not increase the asymptotic efficiency for estimating the regression coefficient. An estimator for the baseline survival function is also presented. It reduces to the maximum likelihood estimator when the regression parameter in the proportional hazards model is zero. Statistical properties of the proposed estimation procedures are developed. Examples are presented to illustrate the methods. [ABSTRACT FROM AUTHOR]