Joint regression analysis for survival data in the presence of two sets of semi‐competing risks

In many clinical trials, multiple time‐to‐event endpoints including the primary endpoint (e.g., time to death) and secondary endpoints (e.g., progression‐related endpoints) are commonly used to determine treatment efficacy. These endpoints are often biologically related. This work is motivated by a study of bone marrow transplant (BMT) for leukemia patients, who may experience the acute graft‐versus‐host disease (GVHD), relapse of leukemia, and death after an allogeneic BMT. The acute GVHD is associated with the relapse free survival, and both the acute GVHD and relapse of leukemia are intermediate nonterminal events subject to dependent censoring by the informative terminal event death, but not vice versa, giving rise to survival data that are subject to two sets of semi‐competing risks. It is important to assess the impacts of prognostic factors on these three time‐to‐event endpoints. We propose a novel statistical approach that jointly models such data via a pair of copulas to account for multiple dependence structures, while the marginal distribution of each endpoint is formulated by a Cox proportional hazards model. We develop an estimation procedure based on pseudo‐likelihood and carry out simulation studies to examine the performance of the proposed method in finite samples. The practical utility of the proposed method is further illustrated with data from the motivating example.     

Regulation of the terminal event in cellular differentiation: biological mechanisms of the loss of proliferative potential

Human plasma has been demonstrated to contain factors that induce the sequential expression of nonterminal and terminal adipocyte differentiation in 3T3 T mesenchymal stem cells. We now report the development of methods for the isolation of purified populations of nonterminally differentiated cells and terminally differentiated cells, and we show that it is possible to experimentally induce transition from the nonterminal to the terminal state of differentiation. With this model system it is therefore now possible to examine the biological and molecular processes associated with the terminal event in differentiation, i.e., the irreversible loss of proliferative potential. In this regard, we demonstrate that transition from the nonterminal to terminal state of differentiation is a complex metabolic process that consists of at least two steps and that this process can be triggered by pulse exposure to an inducer for approximately 12 h but that approximately 24-48 h is required for the process to be completed. The data also establish that induction of the terminal event in differentiation requires protein synthesis but not RNA and DNA synthesis. These and additional results suggest that loss of proliferative potential associated with the terminal event in cellular differentiation is a distinct regulatory process, and we suggest that defects in this regulatory process may be of etiological significance in the pathogenesis of specific human diseases, especially cancer.     

Semiparametric analysis of correlated recurrent and terminal events

In clinical and observational studies, recurrent event data (e.g., hospitalization) with a terminal event (e.g., death) are often encountered. In many instances, the terminal event is strongly correlated with the recurrent event process. In this article, we propose a semiparametric method to jointly model the recurrent and terminal event processes. The dependence is modeled by a shared gamma frailty that is included in both the recurrent event rate and terminal event hazard function. Marginal models are used to estimate the regression effects on the terminal and recurrent event processes, and a Poisson model is used to estimate the dispersion of the frailty variable. A sandwich estimator is used to achieve additional robustness. An analysis of hospitalization data for patients in the peritoneal dialysis study is presented to illustrate the proposed method.     

Penalized estimation of frailty-based illness–death models for semi-competing risks

Semi-competing risks refer to the time-to-event analysis setting, where the occurrence of a non-terminal event is subject to whether a terminal event has occurred, but not vice versa. Semi-competing risks arise in a broad range of clinical contexts, including studies of preeclampsia, a condition that may arise during pregnancy and for which delivery is a terminal event. Models that acknowledge semi-competing risks enable investigation of relationships between covariates and the joint timing of the outcomes, but methods for model selection and prediction of semi-competing risks in high dimensions are lacking. Moreover, in such settings researchers commonly analyze only a single or composite outcome, losing valuable information and limiting clinical utility—in the obstetric setting, this means ignoring valuable insight into timing of delivery after preeclampsia has onset. To address this gap, we propose a novel penalized estimation framework for frailty-based illness–death multi-state modeling of semi-competing risks. Our approach combines non-convex and structured fusion penalization, inducing global sparsity as well as parsimony across submodels. We perform estimation and model selection via a pathwise routine for non-convex optimization, and prove statistical error rate results in this setting. We present a simulation study investigating estimation error and model selection performance, and a comprehensive application of the method to joint risk modeling of preeclampsia and timing of delivery using pregnancy data from an electronic health record.     

Estimating survival and association in a semicompeting risks model

Summary .   In many follow-up studies, patients are subject to concurrent events. In this article, we consider semicompeting risks data as defined by Fine, Jiang, and Chappell (2001, Biometrika 88 , 907–919) where one event is censored by the other but not vice versa. The proposed model involves marginal survival functions for the two events and a parametric family of copulas for their dependency. This article suggests a general method for estimating the dependence parameter when the dependency is modeled with an Archimedean copula. It uses the copula-graphic estimator of Zheng and Klein (1995, Biometrika 82 , 127–138) for estimating the survival function of the nonterminal event, subject to dependent censoring. Asymptotic properties of these estimators are derived. Simulations show that the new methods work well with finite samples. The copula-graphic estimator is shown to be more accurate than the estimator proposed by Fine et al. (2001) ; its performances are similar to those of the self-consistent estimator of Jiang, Fine, Kosorok, and Chappell (2005, Scandinavian Journal of Statistics 33, 1–20). The analysis of a data set, emphasizing the estimation of characteristics of the observable region, is presented as an illustration.     

Analysis of longitudinal data in the presence of informative observational times and a dependent terminal event, with application to medical cost data

Summary .   In longitudinal observational studies, repeated measures are often taken at informative observation times. Also, there may exist a dependent terminal event such as death that stops the follow-up. For example, patients in poorer health are more likely to seek medical treatment and their medical cost for each visit tends to be higher. They are also subject to a higher mortality rate. In this article, we propose a random effects model of repeated measures in the presence of both informative observation times and a dependent terminal event. Three submodels are used, respectively, for (1) the intensity of recurrent observation times, (2) the amount of repeated measure at each observation time, and (3) the hazard of death. Correlated random effects are incorporated to join the three submodels. The estimation can be conveniently accomplished by Gaussian quadrature techniques, e.g., SAS Proc NLMIXED . An analysis of the cost-accrual process of chronic heart failure patients from the clinical data repository at the University of Virginia Health System is presented to illustrate the proposed method.     

Flexible Estimation of Differences in Treatment-Specific Recurrent Event Means in the Presence of a Terminating Event

Summary .  In this article, we consider the setting where the event of interest can occur repeatedly for the same subject (i.e., a recurrent event; e.g., hospitalization) and may be stopped permanently by a terminating event (e.g., death). Among the different ways to model recurrent/terminal event data, the marginal mean (i.e., averaging over the survival distribution) is of primary interest from a public health or health economics perspective. Often, the difference between treatment-specific recurrent event means will not be constant over time, particularly when treatment-specific differences in survival exist. In such cases, it makes more sense to quantify treatment effect based on the cumulative difference in the recurrent event means, as opposed to the instantaneous difference in the rates. We propose a method that compares treatments by separately estimating the survival probabilities and recurrent event rates given survival, then integrating to get the mean number of events. The proposed method combines an additive model for the conditional recurrent event rate and a proportional hazards model for the terminating event hazard. The treatment effects on survival and on recurrent event rate among survivors are estimated in constructing our measure and explain the mechanism generating the difference under study. The example that motivates this research is the repeated occurrence of hospitalization among kidney transplant recipients, where the effect of expanded criteria donor (ECD) compared to non-ECD kidney transplantation on the mean number of hospitalizations is of interest.     

Quantile regression for left-truncated semicompeting risks data

Semicompeting risks is often encountered in biomedical studies where a terminating event censors a nonterminating event but not vice versa. In practice, left truncation on the terminating event may arise and can greatly complicate the regression analysis on the nonterminating event. In this work, we propose a quantile regression method for left-truncated semicompeting risks data, which provides meaningful interpretations as well as the flexibility to accommodate varying covariate effects. We develop estimation and inference procedures that can be easily implemented by existing statistical software. Asymptotic properties of the resulting estimators are established including uniform consistency and weak convergence. The finite-sample performance of the proposed method is evaluated via simulation studies. An application to a registry dataset provides an illustration of our proposals.     

Attributable risk estimation for adjusted disability multistate models: Application to nosocomial infections

Attributable risk has become an important concept in clinical epidemiology. In this paper, we suggest to estimate the attributable risk of nosocomial infections using a multistate approach. Recently, a multistate model (called progressive disability model in the literature) has been developed in order to take into consideration both the time‐dependency of the risk factor (e.g., nosocomial infections) and the presence of competing risks (e.g., death and discharge) at each time point. However, this approach does not take into account the possible heterogeneity of the study population. In this paper, we investigate an extension of this model and suggest an adjusted disability multistate model including covariates in each transition. This new multistate model has led us to define the concepts of overall and profiled attributable risk. We use a classical semiparametric approach to estimate the model and the new attributable risk. A simulation study is investigated and we show, in particular, that neglecting the presence of covariates when estimating the model can lead to an important bias. The methodology developed in this paper is applied to data on ventilator‐associated pneumonia in 12 French intensive care units.     

Time‐Dependent Predictive Accuracy in the Presence of Competing Risks

Summary Competing risks arise naturally in time‐to‐event studies. In this article, we propose time‐dependent accuracy measures for a marker when we have censored survival times and competing risks. Time‐dependent versions of sensitivity or true positive (TP) fraction naturally correspond to consideration of either cumulative (or prevalent) cases that accrue over a fixed time period, or alternatively to incident cases that are observed among event‐free subjects at any select time. Time‐dependent (dynamic) specificity (1–false positive (FP)) can be based on the marker distribution among event‐free subjects. We extend these definitions to incorporate cause of failure for competing risks outcomes. The proposed estimation for cause‐specific cumulative TP/dynamic FP is based on the nearest neighbor estimation of bivariate distribution function of the marker and the event time. On the other hand, incident TP/dynamic FP can be estimated using a possibly nonproportional hazards Cox model for the cause‐specific hazards and riskset reweighting of the marker distribution. The proposed methods extend the time‐dependent predictive accuracy measures of Heagerty, Lumley, and Pepe (2000, Biometrics 56, 337–344) and Heagerty and Zheng (2005, Biometrics 61, 92–105).     

Exploring Migration Data Using Interval-Censored Time-to-Event Models

Abstract: Ecologists and wildlife biologists rely on periodic observation of radiocollared animals to study habitat use, survival, movement, and migration, resulting in response times (e.g., mortality and migration) known only to occur within an interval of time. We illustrate methods for analyzing interval-censored data using data on the timing of fall migration (from spring-summer-fall to winter ranges) for white-tailed deer (Odocoileus virginianus) in northern Minnesota, USA, during years 1991–1992 to 2005–2006. We compare both nonparametric and parametric methods for estimating the cumulative distribution function of migration times, and we suggest a parametric (cure rate) model that accounts for conditional (facultative) migrators as a potential alternative to traditional parametric models. Lastly, we illustrate methods for exploring the effect of environmental covariates on migration timing. Models with time-dependent covariates (snow depth, temp) were sensitive to the treatment of the data (as interval-censored or known event times), suggesting the need to account for interval-censoring when modeling the effect of these covariates.     

Tumor necrosis factor inhibits the terminal event in mesenchymal stem cell differentiation

Control of the terminal event in cellular differentiation is an important normal regulatory process, and the expression of defects in the control of this process has been implicated in the pathogenesis of cancer. To determine if tumor necrosis factor (TNF), which is an important biological response modifier, can inhibit terminal differentiation, we have studied 3T3 T mesenchymal stem cells. This experimental cell system was employed because a well-defined series of steps in differentiation has been defined and cells at each stage of differentiation can be isolated. For example, nonterminal differentiated cells can be isolated, and their transition to a terminal differentiation state can be evaluated. The most interesting results in the current studies show that TNF blocks the terminal event in mesenchymal stem cell differentiation. Inhibition of the terminal event of differentiation by TNF is reversible and is not associated with inhibition of selective or general protein synthesis. Evidence is also presented that cell clones that are defective in their ability to undergo the terminal event in differentiation secrete factor(s) that inhibit the terminal event in differentiation. These observations suggest that the inhibition of the terminal event in differentiation may be mediated via autocrine or paracrine regulatory molecules such as tumor necrosis factor.     

Polypeptide changes associated with loss of proliferative potential during the terminal event in differentiation

The differentiation of murine mesenchymal stem cells occurs in nonterminal and terminal phases. In previous reports we established the characteristics of nonterminally differentiated cells and showed that transition from the nonterminal to the terminal state of differentiation can be induced by human plasma. We also showed that this transition is blocked by protein synthesis inhibitors and other pharmacological agents. In this paper, we have employed two-dimensional gel electrophoresis to evaluate changes in specific polypeptides that are induced when cells lose proliferative capacity associated with the terminal event in differentiation. Using silver staining procedures for analysis of electrophoretograms, we detected only seven major polypeptide differences between nonterminally differentiated and terminally differentiated cells. Six polypeptides were expressed only in preparations of terminally differentiated cells; these included two polypeptides identified in cytosolic fractions and four polypeptides identified in nuclear fractions. One polypeptide was also found to be selectively expressed only in nuclear fractions of nonterminally differentiated cells. Based on these observations we conclude that the loss of proliferative potential that occurs during the terminal event in mesenchymal stem cell differentiation is associated with changes in the composition of a limited number of specific polypeptides. We suggest that one or more of these polypeptides may be important in the regulation of cellular proliferation.     

A Bayesian multi-risks survival (MRS) model in the presence of double censorings

Semi-competing risks data include the time to a nonterminating event and the time to a terminating event, while competing risks data include the time to more than one terminating event. Our work is motivated by a prostate cancer study, which has one nonterminating event and two terminating events with both semi-competing risks and competing risks present as well as two censoring times. In this paper, we propose a new multi-risks survival (MRS) model for this type of data. In addition, the proposed MRS model can accommodate noninformative right-censoring times for nonterminating and terminating events. Properties of the proposed MRS model are examined in detail. Theoretical and empirical results show that the estimates of the cumulative incidence function for a nonterminating event may be biased if the information on a terminating event is ignored. A Markov chain Monte Carlo sampling algorithm is also developed. Our methodology is further assessed using simulations and also an analysis of the real data from a prostate cancer study. As a result, a prostate-specific antigen velocity greater than 2.0 ng/mL per year and higher biopsy Gleason scores are positively associated with a shorter time to death due to prostate cancer.     

A Joint Modeling Approach for Longitudinal Data with Informative Observation Times and a Terminal Event

In this article, we propose a new joint modeling approach for the analysis of longitudinal data with informative observation times and a dependent terminal event. We specify a semiparametric mixed effects model for the longitudinal process, a proportional rate frailty model for the observation process, and a proportional hazards frailty model for the terminal event. The association among the three related processes is modeled via two latent variables. Estimating equation approaches are developed for parameter estimation, and the asymptotic properties of the proposed estimators are established. The finite sample performance of the proposed estimators is examined through simulation studies, and an application to a medical cost study of chronic heart failure patients is illustrated.     

Regional and global climate risks for reef corals: Incorporating species-specific vulnerability and exposure to climate hazards

Climate change is driving rapid and widespread erosion of the environmental conditions that formerly supported species persistence. Existing projections of climate change typically focus on forecasts of acute environmental anomalies and global extinction risks. The current projections also frequently consider all species within a broad taxonomic group together without differentiating species-specific patterns. Consequently, we still know little about the explicit dimensions of climate risk (i.e., species-specific vulnerability, exposure and hazard) that are vital for predicting future biodiversity responses (e.g., adaptation, migration) and developing management and conservation strategies. Here, we use reef corals as model organisms (n = 741 species) to project the extent of regional and global climate risks of marine organisms into the future. We characterise species-specific vulnerability based on the global geographic range and historical environmental conditions (1900–1994) of each coral species within their ranges, and quantify the projected exposure to climate hazard beyond the historical conditions as climate risk. We show that many coral species will experience a complete loss of pre-modern climate analogs at the regional scale and across their entire distributional ranges, and such exposure to hazardous conditions are predicted to pose substantial regional and global climate risks to reef corals. Although high-latitude regions may provide climate refugia for some tropical corals until the mid-21st century, they will not become a universal haven for all corals. Notably, high-latitude specialists and species with small geographic ranges remain particularly vulnerable as they tend to possess limited capacities to avoid climate risks (e.g., via adaptive and migratory responses). Predicted climate risks are amplified substantially under the SSP5-8.5 compared with the SSP1-2.6 scenario, highlighting the need for stringent emission controls. Our projections of both regional and global climate risks offer unique opportunities to facilitate climate action at spatial scales relevant to conservation and management.     

The Mitochondrial Permeability Transition as a Target for Neuroprotection

Mitochondria serve as checkpoints and amplifiers on cell death pathways. In the central nervous system, mitochondrial involvement seems essential for normal expression of cell death phenotypes, and interference with these pathways thus seems a reasonable approach to neuroprotection. We have been involved in examining the potential involvement of the mitochondrial permeability transition (mPT) as one of several possible mechanisms by which mitochondria may be drawn into these death cascades. This possibility, though still controversial, is supported by evidence that factors that may stimulate mPT induction are associated with some forms of cell death (e.g., in stroke) and are modulated by diseases of the central nervous system (e.g., Huntington's). Evidence of neuroprotection seen with compounds such as N-Met-Val cyclosporine also support this possibility.     

Joint Models of Longitudinal Data and Recurrent Events with Informative Terminal Event

This article presents semiparametric joint models to analyze longitudinal data with recurrent events (e.g. multiple tumors, repeated hospital admissions) and a terminal event such as death. A broad class of transformation models for the cumulative intensity of the recurrent events and the cumulative hazard of the terminal event is considered, which includes the proportional hazards model and the proportional odds model as special cases. We propose to estimate all the parameters using the nonparametric maximum likelihood estimators (NPMLE). We provide the simple and efficient EM algorithms to implement the proposed inference procedure. Asymptotic properties of the estimators are shown to be asymptotically normal and semiparametrically efficient. Finally, we evaluate the performance of the method through extensive simulation studies and a real-data application.     

Unimodal productivity–diversity relationships among bacterial communities in a simple polar soil ecosystem

Unlike other macroecological principles, relationships between productivity and diversity have not been effectively tested for microbial communities. Here we describe an experiment in which the availability of resources to soil bacterial communities was manipulated in a model system, the McMurdo Dry Valleys of Antarctica. Mannitol additions were used to simulate a productivity gradient such that a response in bacterial biomass production, taxonomic diversity and functioning (e.g., enzyme activity) were induced. Resource amendment induced a positive linear response in microbial productivity (P < 0.001) but a unimodal (hump-shaped) response in microbial diversity at multiple taxonomic scales (P = 0.035). Putative oligotrophic (e.g., phyla Nitrospirae and Cyanobacteria) and copiotrophic (e.g., phylum Proteobacteria) taxa were apparent through substantial community turnover along the resource gradient. Soil enzyme activity was inversely related to bacterial biomass but positively related to diversity, suggesting the latter may be a stronger control over enzyme-mediated decomposition. The mechanisms behind this pattern are consistent with macroecological theory of a shift from environmental (e.g., stress tolerance) to biotic (e.g., competition) drivers with increasing resource availability. This evidence is among the first of its kind to document a significant unimodal productivity–diversity relationship for soil bacteria.     

Meta-analysis for surrogacy: accelerated failure time models and semicompeting risks modeling

There has been great recent interest in the medical and statistical literature in the assessment and validation of surrogate endpoints as proxies for clinical endpoints in medical studies. More recently, authors have focused on using metaanalytical methods for quantification of surrogacy. In this article, we extend existing procedures for analysis based on the accelerated failure time model to this setting. An advantage of this approach relative to proportional hazards model is that it allows for analysis in the semicompeting risks setting, where we model the region where the surrogate endpoint occurs before the true endpoint. Several estimation methods and attendant inferential procedures are presented. In addition, between- and within-trial methods for evaluating surrogacy are developed; a novel principal components procedure is developed for quantifying trial-level surrogacy. The methods are illustrated by application to data from several studies in colorectal cancer.