Weighted NPMLE for the Subdistribution of a Competing Risk

Changes in tuberculosis risk after transplantation in the setting of decreased community tuberculosis incidence: a national population-based study, 2008-2020

BACKGROUND

Transplant recipients are immunocompromised and vulnerable to developing tuberculosis. However, active tuberculosis incidence is rapidly declining in South Korea, but the trend of tuberculosis infection among transplant recipients has not been elucidated. This study aimed to evaluate the risk of active tuberculosis after transplantation, including risk factors for tuberculosis and standardized incidence ratios, compared with that in the general population.

METHODS

This retrospective study was conducted based on the South Korean health insurance review and assessment database among those who underwent transplantation (62,484 recipients) between 2008 and 2020. Tuberculosis incidence was compared in recipients treated during higher- (2010-2012) and lower-disease burden (2016-2018) periods. Standardized incidence ratios were analyzed using the Korean Tuberculosis Surveillance System. The primary outcome was the number of new tuberculosis cases after transplantation.

RESULTS

Of 57,103 recipients analyzed, the overall cumulative incidence rate 1 year after transplantation was 0.8% (95% confidence interval [CI]: 0.7-0.8), significantly higher in the higher-burden period than in the lower-burden period (1.7% vs. 1.0% 3 years after transplantation, P < 0.001). Individuals who underwent allogeneic hematopoietic stem cell transplantation had the highest tuberculosis incidence, followed by those who underwent solid organ transplantation and autologous hematopoietic stem cell transplantation (P < 0.001). The overall standardized incidence ratio was 3.9 (95% CI 3.7-4.2) and was the highest in children aged 0-19 years, at 9.0 (95% CI 5.7-13.5). Male sex, older age, tuberculosis history, liver transplantation, and allogeneic hematopoietic stem cell transplantation were risk factors for tuberculosis.

CONCLUSIONS

Transplant recipients are vulnerable to developing tuberculosis, possibly influenced by their immunocompromised status, solid organ transplant type, age, and community prevalence of tuberculosis. Tuberculosis prevalence by country, transplant type, and age should be considered to establish an appropriate tuberculosis prevention strategy for high-risk groups.

Gene Screening for Prognosis of Non-Muscle-Invasive Bladder Carcinoma under Competing Risks Endpoints

Background: Discovering clinically useful molecular markers for predicting the survival of patients diagnosed with non−muscle-invasive bladder cancer can provide insights into cancer dynamics and improve treatment outcomes. However, the presence of competing risks (CR) endpoints complicates the estimation and inferential framework. There is also a lack of statistical analysis tools and software for coping with the high-throughput nature of these data, in terms of marker screening and selection. Aims: To propose a gene screening procedure for proportional subdistribution hazards regression under a CR framework, and illustrate its application in using molecular profiling to predict survival for non-muscle invasive bladder carcinoma. Methods: Tumors from 300 patients diagnosed with bladder cancer were analyzed for genomic abnormalities while controlling for clinically important covariates. Genes with expression patterns that were associated with survival were identified through a screening procedure based on proportional subdistribution hazards regression. A molecular predictor of risk was constructed and examined for prediction accuracy. Results: A six-gene signature was found to be a significant predictor associated with survival of non−muscle-invasive bladder cancer, subject to competing risks after adjusting for age, gender, reevaluated WHO grade, stage and BCG/MMC treatment (p-value < 0.001). Conclusion: The proposed gene screening procedure can be used to discover molecular determinants of survival for non−muscle-invasive bladder cancer and in general facilitate high-throughput competing risks data analysis with easy implementation.

Marginal semiparametric transformation models for clustered multivariate competing risks data

Multivariate survival models are often used in studying multiple outcomes for right-censored data. However, the outcomes of interest often have competing risks, where standard multivariate survival models may lead to invalid inferences. For example, patients who had stem cell transplantation may experience multiple types of infections after transplant while reconstituting their immune system, where death without experiencing infections is a competing risk for infections. Such competing risks data often suffer from cluster effects due to a matched pair design or correlation within study centers. The cumulative incidence function (CIF) is widely used to summarize competing risks outcomes. Thus, it is often of interest to study direct covariate effects on the CIF. Most literature on clustered competing risks data analyses is limited to the univariate proportional subdistribution hazards model with inverse probability censoring weighting which requires correctly specifying the censoring distribution. We propose a marginal semiparametric transformation model for multivariate competing risks outcomes. The proposed model does not require modeling the censoring distribution, accommodates nonproportional subdistribution hazards structure, and provides a platform for joint inference of all causes and outcomes.

Trends in COVID-19 hospital outcomes in England before and after vaccine introduction, a cohort study

Widespread vaccination campaigns have changed the landscape for COVID-19, vastly altering symptoms and reducing morbidity and mortality. We estimate trends in mortality by month of admission and vaccination status among those hospitalised with COVID-19 in England between March 2020 to September 2021, controlling for demographic factors and hospital load. Among 259,727 hospitalised COVID-19 cases, 51,948 (20.0%) experienced mortality in hospital. Hospitalised fatality risk ranged from 40.3% (95% confidence interval 39.4–41.3%) in March 2020 to 8.1% (7.2–9.0%) in June 2021. Older individuals and those with multiple co-morbidities were more likely to die or else experienced longer stays prior to discharge. Compared to unvaccinated people, the hazard of hospitalised mortality was 0.71 (0.67–0.77) with a first vaccine dose, and 0.56 (0.52–0.61) with a second vaccine dose. Compared to hospital load at 0–20% of the busiest week, the hazard of hospitalised mortality during periods of peak load (90–100%), was 1.23 (1.12–1.34). The prognosis for people hospitalised with COVID-19 in England has varied substantially throughout the pandemic and according to case-mix, vaccination, and hospital load. Our estimates provide an indication for demands on hospital resources, and the relationship between hospital burden and outcomes.

This study investigates trends in mortality and length of stay for people hospitalised with COVID-19 in England until September 2021. It shows that risks were higher for unvaccinated people and those with multiple comorbidities, and that busier hospitals had higher mortality rates at the start of the pandemic but this effect lessened over time.

Kidney Graft Failure and Patient Survival Modelling Based on Competing Risks Under Nonproportional Hazards

We analyze data on Silesian patients after kidney transplantation under competing events scenarios where time to death and time to graft failure are considered as absorbing competing events. Our objectives are to use model diagnostics in identifying violations of proportionality assumption under the framework of subdistribution and cause-specific hazards. We use the Fine-Gray proportional hazards model for the subdistribution. Under the cause-specific hazards (CSH) scenario we use the Cox proportional hazards model and Gray's time-varying coefficients model and available model diagnostics. We show that violation of proportional subdistribution hazards assumption may be conveniently identified using residual diagnostics and properly accounted for by involving time interactions with appropriate model predictors. We also show that although the nonproportional effects on cumulative incidence do not necessarily translate in those on cause-specific hazards, they often take place simultaneously, and a violation of the proportionality assumption needs to be checked rigorously. Time-varying effects have a profound impact on clinical inference under competing risks. They do not translate directly between the frameworks of subdistribution and cause-specific hazards because the cumulative incidence is obtained via integrating the cause-specific hazard weighted by the overall survival function. Also, a different definition of the risk set is in place under the cumulative incidence and CSH framework, respectively. However, a simultaneous violation of the proportionality assumption under both frameworks is still possible. Clinical inference may change considerably when such a violation occurs. Nonproportional effects may be properly identified under each framework using available model diagnostics.

Evaluation of competing risks prediction models using polytomous discrimination index

For competing risks data, it is often important to predict a patient's outcome status at a clinically meaningful time point after incorporating the informative censoring due to competing risks. This can be done by adopting a regression model that relates the cumulative incidence probabilities to a set of covariates. To assess the performance of the resulting prediction tool, we propose an estimator of the polytomous discrimination index applicable to competing risks data, which can quantify a prognostic model's ability to discriminate among subjects from different outcome groups. The proposed estimator allows the prediction model to be subject to model misspecification and enjoys desirable asymptotic properties. We also develop an efficient computation algorithm that features a computational complexity of O(n log n). A perturbation resampling scheme is developed to achieve consistent variance estimation. Numerical results suggest that the estimator performs well under realistic sample sizes. We apply the proposed methods to a study of monoclonal gammopathy of undetermined significance.

Regularized Weighted Nonparametric Likelihood Approach for High-Dimension Sparse Subdistribution Hazards Model for Competing Risk Data

Variable selection and penalized regression models in high-dimension settings have become an increasingly important topic in many disciplines. For instance, omics data are generated in biomedical researches that may be associated with survival of patients and suggest insights into disease dynamics to identify patients with worse prognosis and to improve the therapy. Analysis of high-dimensional time-to-event data in the presence of competing risks requires special modeling techniques. So far, some attempts have been made to variable selection in low- and high-dimension competing risk setting using partial likelihood-based procedures. In this paper, a weighted likelihood-based penalized approach is extended for direct variable selection under the subdistribution hazards model for high-dimensional competing risk data. The proposed method which considers a larger class of semiparametric regression models for the subdistribution allows for taking into account time-varying effects and is of particular importance, because the proportional hazards assumption may not be valid in general, especially in the high-dimension setting. Also, this model relaxes from the constraint of the ability to simultaneously model multiple cumulative incidence functions using the Fine and Gray approach. The performance/effectiveness of several penalties including minimax concave penalty (MCP); adaptive LASSO and smoothly clipped absolute deviation (SCAD) as well as their L₂ counterparts were investigated through simulation studies in terms of sensitivity/specificity. The results revealed that sensitivity of all penalties were comparable, but the MCP and MCP-L₂ penalties outperformed the other methods in term of selecting less noninformative variables. The practical use of the model was investigated through the analysis of genomic competing risk data obtained from patients with bladder cancer and six genes of CDC20, NCF2, SMARCAD1, RTN4, ETFDH, and SON were identified using all the methods and were significantly correlated with the subdistribution.

General regression model for the subdistribution of a competing risk under left-truncation and right-censoring

Left-truncation poses extra challenges for the analysis of complex time-to-event data. We propose a general semiparametric regression model for left-truncated and right-censored competing risks data that is based on a novel weighted conditional likelihood function. Targeting the subdistribution hazard, our parameter estimates are directly interpretable with regard to the cumulative incidence function. We compare different weights from recent literature and develop a heuristic interpretation from a cure model perspective that is based on pseudo risk sets. Our approach accommodates external time-dependent covariate effects on the subdistribution hazard. We establish consistency and asymptotic normality of the estimators and propose a sandwich estimator of the variance. In comprehensive simulation studies we demonstrate solid performance of the proposed method. Comparing the sandwich estimator with the inverse Fisher information matrix, we observe a bias for the inverse Fisher information matrix and diminished coverage probabilities in settings with a higher percentage of left-truncation. To illustrate the practical utility of the proposed method, we study its application to a large HIV vaccine efficacy trial dataset.

Quantifying time-varying cause-specific hazard and subdistribution hazard ratios with competing risks data

Various non-proportional hazard models have been developed in the literature for competing risks data. The regression coefficients under these models, however, typically cannot be compared directly. We propose new methods to quantify the average of the time-varying cause-specific hazard ratios and subdistribution hazard ratios through two general classes of transformations and weight functions that are chosen to reflect the relative importance of the hazard ratios in different time periods. We further propose an L∞ -norm type of test statistic that incorporates the test statistics for all possible pairs of the transformation function and weight function under consideration. Extensive simulations are conducted under various settings of the hazards and demonstrate that the proposed test performs well under all settings. An application to a clinical trial in follicular lymphoma is examined in detail.

Subdistribution hazard models for competing risks in discrete time

A popular modeling approach for competing risks analysis in longitudinal studies is the proportional subdistribution hazards model by Fine and Gray (1999. A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association94, 496–509). This model is widely used for the analysis of continuous event times in clinical and epidemiological studies. However, it does not apply when event times are measured on a discrete time scale, which is a likely scenario when events occur between pairs of consecutive points in time (e.g., between two follow-up visits of an epidemiological study) and when the exact lengths of the continuous time spans are not known. To adapt the Fine and Gray approach to this situation, we propose a technique for modeling subdistribution hazards in discrete time. Our method, which results in consistent and asymptotically normal estimators of the model parameters, is based on a weighted ML estimation scheme for binary regression. We illustrate the modeling approach by an analysis of nosocomial pneumonia in patients treated in hospitals.

Prospects and challenges for clinical decision support in the era of big data

Recently, there has been burgeoning interest in developing more effective and robust clinical decision support systems (CDSSs) for oncology. This has been primarily driven by the demands for more personalized and precise medical practice in oncology in the era of so-called Big Data (BD); an era that promises to harness the power of large-scale data flow to revolutionize cancer treatment. This interest in BD analytics has created new opportunities as well as new unmet challenges. These include: routine aggregation and standardization of clinical data; patient privacy; transformation of current analytical approaches to handle such noisy and heterogeneous data; and expanded use of advanced statistical learning methods based on confluence of modern statistical methods and machine learning algorithms. In this review, we present the current status of CDSSs in oncology, the prospects and current challenges of BD analytics, and the promising role of integrated modern statistics and machine learning algorithms in predicting complex clinical endpoints, individualizing treatment rules, and optimizing dynamic personalized treatment regimens. We discuss issues pertaining to these topics and present application examples from an aggregate of experiences. We also discuss the role of human factors in improving the utilization and acceptance of such enhanced CDSSs and how to mitigate possible sources of human error to achieve optimal performance and wider acceptance.