A transformer model for cause-specific hazard prediction.

BACKGROUD: Modelling discrete-time cause-specific hazards in the presence of competing events and non-proportional hazards is a challenging task in many domains. Survival analysis in longitudinal cohorts often requires such models; notably when the data is gathered at discrete points in time and the predicted events display complex dynamics. Current models often rely on strong assumptions of proportional hazards, that is rarely verified in practice; or do not handle sequential data in a meaningful way. This study proposes a Transformer architecture for the prediction of cause-specific hazards in discrete-time competing risks. Contrary to Multilayer perceptrons that were already used for this task (DeepHit), the Transformer architecture is especially suited for handling complex relationships in sequential data, having displayed state-of-the-art performance in numerous tasks with few underlying assumptions on the task at hand. RESULTS: Using synthetic datasets of 2000-50,000 patients, we showed that our Transformer model surpassed the CoxPH, PyDTS, and DeepHit models for the prediction of cause-specific hazard, especially when the proportional assumption did not hold. The error along simulated time outlined the ability of our model to anticipate the evolution of cause-specific hazards at later time steps where few events are observed. It was also superior to current models for prediction of dementia and other psychiatric conditions in the English longitudinal study of ageing cohort using the integrated brier score and the time-dependent concordance index. We also displayed the explainability of our model's prediction using the integrated gradients method. CONCLUSIONS: Our model provided state-of-the-art prediction of cause-specific hazards, without adopting prior parametric assumptions on the hazard rates. It outperformed other models in non-proportional hazards settings for both the synthetic dataset and the longitudinal cohort study. We also observed that basic models such as CoxPH were more suited to extremely simple settings than deep learning models. Our model is therefore especially suited for survival analysis on longitudinal cohorts with complex dynamics of the covariate-to-outcome relationship, which are common in clinical practice. The integrated gradients provided the importance scores of input variables, which indicated variables guiding the model in its prediction. This model is ready to be utilized for time-to-event prediction in longitudinal cohorts.

Conditional score approaches to errors-in-variables competing risks data in discrete time.

Analysis of competing risks data has been an important topic in survival analysis due to the need to account for the dependence among the competing events. Also, event times are often recorded on discrete time scales, rendering the models tailored for discrete-time nature useful in the practice of survival analysis. In this work, we focus on regression analysis with discrete-time competing risks data, and consider the errors-in-variables issue where the covariates are prone to measurement errors. Viewing the true covariate value as a parameter, we develop the conditional score methods for various discrete-time competing risks models, including the cause-specific and subdistribution hazards models that have been popular in competing risks data analysis. The proposed estimators can be implemented by efficient computation algorithms, and the associated large sample theories can be simply obtained. Simulation results show satisfactory finite sample performances, and the application with the competing risks data from the scleroderma lung study reveals the utility of the proposed methods.

The incidence and risk factors of unplanned removal of peripherally inserted central catheters among adult patients: A multi-centre cohort study.

AIMS AND OBJECTIVES: (i) To estimate the national incidence of unplanned removal of peripherally inserted central catheters (PICCs) in China. (ii) To explore the associated risk factors to provide evidence for the prevention. DESIGN: A multi-centre prospective cohort study. METHODS: A representative sample of 3222 Chinese adult patients with successful PICC insertion was recruited for the PICC Safety Management Research (PATH) using a two-stage cluster sampling method from December 2020 to June 2022. Sixty hospitals from seven Chinese provinces representing all geographical regions were selected. Demographic information and PICC characteristics were collected using a standard online case report form. Risk factors for the unplanned removal of PICCs were assessed using a cause-specific hazard model and verified using a sub-distribution hazard model. STROBE guidelines were followed in reporting this study. RESULTS: Three thousand one hundred and sixty-six patients were included in the final analysis with a mean age of 59 years and a total of 344,247 catheter days. The incidence of unplanned removal was 10.04%. Female, with thrombosis history, PICC insertion due to infusion failure, valved catheter and double-lumen catheter were risk factors, whereas longer insertion and exposure length were protective factors in the cause-specific hazard model. Higher BMI became an independent risk factor in the sub-distribution hazard model. CONCLUSIONS: Unplanned removal of PICCs is a serious clinical challenge in China. Our findings call for prevention strategies targeting the identified risk factors. RELEVANCE TO CLINICAL PRACTICE: Our study characterised the epidemiology of unplanned removal of PICCs among Chinese adult inpatients, highlighting the need for prevention among this population and providing a basis for the formulation of relevant prevention strategies. PATIENT OR PUBLIC CONTRIBUTION: Patients contributed through sharing their information required for the case report form. Healthcare professionals who provide direct care to the patient at each medical centre contributed by completing the online case report form.

Competing risks analysis for neutrophil to lymphocyte ratio as a predictor of diabetic retinopathy incidence in the Scottish population.

BACKGROUND: Diabetic retinopathy (DR) is a major sight-threatening microvascular complication in individuals with diabetes. Systemic inflammation combined with oxidative stress is thought to capture most of the complexities involved in the pathology of diabetic retinopathy. A high level of neutrophil-lymphocyte ratio (NLR) is an indicator of abnormal immune system activity. Current estimates of the association of NLR with diabetes and its complications are almost entirely derived from cross-sectional studies, suggesting that the nature of the reported association may be more diagnostic than prognostic. Therefore, in the present study, we examined the utility of NLR as a biomarker to predict the incidence of DR in the Scottish population. METHODS: The incidence of DR was defined as the time to the first diagnosis of R1 or above grade in the Scottish retinopathy grading scheme from type 2 diabetes diagnosis. The effect of NLR and its interactions were explored using a competing risks survival model adjusting for other risk factors and accounting for deaths. The Fine and Gray subdistribution hazard model (FGR) was used to predict the effect of NLR on the incidence of DR. RESULTS: We analysed data from 23,531 individuals with complete covariate information. At 10 years, 8416 (35.8%) had developed DR and 2989 (12.7%) were lost to competing events (death) without developing DR and 12,126 individuals did not have DR. The median (interquartile range) level of NLR was 2.04 (1.5 to 2.7). The optimal NLR cut-off value to predict retinopathy incidence was 3.04. After accounting for competing risks at 10 years, the cumulative incidence of DR and deaths without DR were 50.7% and 21.9%, respectively. NLR was associated with incident DR in both Cause-specific hazard (CSH = 1.63; 95% CI: 1.28-2.07) and FGR models the subdistribution hazard (sHR = 2.24; 95% CI: 1.70-2.94). Both age and HbA1c were found to modulate the association between NLR and the risk of DR. CONCLUSIONS: The current study suggests that NLR has a promising potential to predict DR incidence in the Scottish population, especially in individuals less than 65 years and in those with well-controlled glycaemic status.

Estimating disease incidence rates and transition probabilities in elderly patients using multi-state models: a case study in fragility fracture using a Bayesian approach.

BACKGROUND: Multi-state models are complex stochastic models which focus on pathways defined by the temporal and sequential occurrence of numerous events of interest. In particular, the so-called illness-death models are especially useful for studying probabilities associated to diseases whose occurrence competes with other possible diseases, health conditions or death. They can be seen as a generalization of the competing risks models, which are widely used to estimate disease-incidences among populations with a high risk of death, such as elderly or cancer patients. The main advantage of the aforementioned illness-death models is that they allow the treatment of scenarios with non-terminal competing events that may occur sequentially, which competing risks models fail to do. METHODS: We propose an illness-death model using Cox proportional hazards models with Weibull baseline hazard functions, and applied the model to a study of recurrent hip fracture. Data came from the PREV2FO cohort and included 34491 patients aged 65 years and older who were discharged alive after a hospitalization due to an osteoporotic hip fracture between 2008-2015. We used a Bayesian approach to approximate the posterior distribution of each parameter of the model, and thus cumulative incidences and transition probabilities. We also compared these results with a competing risks specification. RESULTS: Posterior transition probabilities showed higher probabilities of death for men and increasing with age. Women were more likely to refracture as well as less likely to die after it. Free-event time was shown to reduce the probability of death. Estimations from the illness-death and the competing risks models were identical for those common transitions although the illness-death model provided additional information from the transition from refracture to death. CONCLUSIONS: We illustrated how multi-state models, in particular illness-death models, may be especially useful when dealing with survival scenarios which include multiple events, with competing diseases or when death is an unavoidable event to consider. Illness-death models via transition probabilities provide additional information of transitions from non-terminal health conditions to absorbing states such as death, what implies a deeper understanding of the real-world problem involved compared to competing risks models.

Competing risks predictions with different time scales under the additive risk model.

In the analysis for competing risks data, regression modeling of the cause-specific hazard functions has been usually conducted using the same time scale for all event types. However, when the true time scale is different for each event type, it would be appropriate to specify regression models for the cause-specific hazards on different time scales for different event types. Often, the proportional hazards model has been used for regression modeling of the cause-specific hazard functions. However, the proportionality assumption may not be appropriate in practice. In this article, we consider the additive risk model as an alternative to the proportional hazards model. We propose predictions of the cumulative incidence functions under the cause-specific additive risk models employing different time scales for different event types. We establish the consistency and asymptotic normality of the predicted cumulative incidence functions under the cause-specific additive risk models specified on different time scales using empirical processes and derive consistent variance estimators of the predicted cumulative incidence functions. Through simulation studies, we show that the proposed prediction methods perform well. We illustrate the methods using stage III breast cancer data obtained from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute.

Fine-Gray subdistribution hazard models to simultaneously estimate the absolute risk of different event types: Cumulative total failure probability may exceed 1.

The Fine-Gray subdistribution hazard model has become the default method to estimate the incidence of outcomes over time in the presence of competing risks. This model is attractive because it directly relates covariates to the cumulative incidence function (CIF) of the event of interest. An alternative is to combine the different cause-specific hazard functions to obtain the different CIFs. A limitation of the subdistribution hazard approach is that the sum of the cause-specific CIFs can exceed 1 (100%) for some covariate patterns. Using data on 9479 patients hospitalized with acute myocardial infarction, we estimated the cumulative incidence of both cardiovascular death and non-cardiovascular death for each patient. We found that when using subdistribution hazard models, approximately 5% of subjects had an estimated risk of 5-year all-cause death (obtained by combining the two cause-specific CIFs obtained from subdistribution hazard models) that exceeded 1. This phenomenon was avoided by using the two cause-specific hazard models. We provide a proof that the sum of predictions exceeds 1 is a fundamental problem with the Fine-Gray subdistribution hazard model. We further explored this issue using simulations based on two different types of data-generating process, one based on subdistribution hazard models and other based on cause-specific hazard models. We conclude that care should be taken when using the Fine-Gray subdistribution hazard model in situations with wide risk distributions or a high cumulative incidence, and if one is interested in the risk of failure from each of the different event types.

Absolute mortality risk assessment of COVID-19 patients: the Khorshid COVID Cohort (KCC) study.

BACKGROUND: Already at hospital admission, clinicians require simple tools to identify hospitalized COVID-19 patients at high risk of mortality. Such tools can significantly improve resource allocation and patient management within hospitals. From the statistical point of view, extended time-to-event models are required to account for competing risks (discharge from hospital) and censoring so that active cases can also contribute to the analysis. METHODS: We used the hospital-based open Khorshid COVID Cohort (KCC) study with 630 COVID-19 patients from Isfahan, Iran. Competing risk methods are used to develop a death risk chart based on the following variables, which can simply be measured at hospital admission: sex, age, hypertension, oxygen saturation, and Charlson Comorbidity Index. The area under the receiver operator curve was used to assess accuracy concerning discrimination between patients discharged alive and dead. RESULTS: Cause-specific hazard regression models show that these baseline variables are associated with both death, and discharge hazards. The risk chart reflects the combined results of the two cause-specific hazard regression models. The proposed risk assessment method had a very good accuracy (AUC = 0.872 [CI 95%: 0.835-0.910]). CONCLUSIONS: This study aims to improve and validate a personalized mortality risk calculator based on hospitalized COVID-19 patients. The risk assessment of patient mortality provides physicians with additional guidance for making tough decisions.

Specific causes of recurrence after surgery and mortality in patients with colorectal cancer: A competing risks survival analysis.

BACKGROUND: In situation where there are more than one cause of occurring the outcome such as recurrence after surgery and death, the assumption of classical survival analyses are not satisfied. To cover this issue, this study aimed at utilizing competing risks survival analysis to assess the specific risk factors of local-distance recurrence and mortality in patients with colorectal cancer (CRC) undergoing surgery. MATERIALS AND METHODS: In this retrospective cohort study, 254 patients with CRC undergoing resection surgery were studied. Data of the outcome from the available documents in the hospital were gathered. Furthermore, based on pathological report, the diagnosis of CRC was considered. We model the risk factors on the hazard of recurrence and death using competing risk survival in R3.6.1 software. RESULTS: A total of 114 patients had local or distant recurrence (21 local recurrences, 72 distant recurrences, and 21 local and distant recurrence). Pathological stage (adjusted hazard ratio [AHR] = 4.28 and 5.37 for stage 3 and 4, respectively), tumor site (AHR = 2.45), recurrence (AHR = 3.92) and age (AHR = 3.15 for age >70) was related to hazard of death. Also based on cause-specific hazard model, pathological stage (AHR = 7.62 for stage 4), age (AHR = 1.46 for age >70), T stage (AHR = 1.8 and 2.7 for T3 and T4, respectively), N stage (AHR = 2.59 for N2), and white blood cells (AHR = 1.95) increased the hazard of recurrence in patients with CRC. CONCLUSION: This study showed that older age, higher pathological, rectum tumor site and presence of recurrence were independent risk factors for mortality among CRC patients. Also age, higher T/N stage, higher pathological stage and higher values of WBC were significantly related to higher hazard of local/distance recurrence of patients with CRC.

Association measures for clustered competing risks.

We propose a semiparameteric model for multivariate clustered competing risks data when the cause-specific failure times and the occurrence of competing risk events among subjects within the same cluster are of interest. The cause-specific hazard functions are assumed to follow Cox proportional hazard models, and the associations between failure times given the same or different cause events and the associations between occurrences of competing risk events within the same cluster are investigated through copula models. A cross-odds ratio measure is explored under our proposed models. Two-stage estimation procedure is proposed in which the marginal models are estimated in the first stage, and the dependence parameters are estimated via an expectation-maximization algorithm in the second stage. The proposed estimators are shown to yield consistent and asymptotically normal under mild regularity conditions. Simulation studies are conducted to assess finite sample performance of the proposed method. The proposed technique is demonstrated through an application to a multicenter Bone Marrow transplantation dataset.

On the relation between the cause-specific hazard and the subdistribution rate for competing risks data: The Fine-Gray model revisited.

The Fine-Gray proportional subdistribution hazards model has been puzzling many people since its introduction. The main reason for the uneasy feeling is that the approach considers individuals still at risk for an event of cause 1 after they fell victim to the competing risk of cause 2. The subdistribution hazard and the extended risk sets, where subjects who failed of the competing risk remain in the risk set, are generally perceived as unnatural . One could say it is somewhat of a riddle why the Fine-Gray approach yields valid inference. To take away these uneasy feelings, we explore the link between the Fine-Gray and cause-specific approaches in more detail. We introduce the reduction factor as representing the proportion of subjects in the Fine-Gray risk set that has not yet experienced a competing event. In the presence of covariates, the dependence of the reduction factor on a covariate gives information on how the effect of the covariate on the cause-specific hazard and the subdistribution hazard relate. We discuss estimation and modeling of the reduction factor, and show how they can be used in various ways to estimate cumulative incidences, given the covariates. Methods are illustrated on data of the European Society for Blood and Marrow Transplantation.

Semiparametric regression and risk prediction with competing risks data under missing cause of failure.

The cause of failure in cohort studies that involve competing risks is frequently incompletely observed. To address this, several methods have been proposed for the semiparametric proportional cause-specific hazards model under a missing at random assumption. However, these proposals provide inference for the regression coefficients only, and do not consider the infinite dimensional parameters, such as the covariate-specific cumulative incidence function. Nevertheless, the latter quantity is essential for risk prediction in modern medicine. In this paper we propose a unified framework for inference about both the regression coefficients of the proportional cause-specific hazards model and the covariate-specific cumulative incidence functions under missing at random cause of failure. Our approach is based on a novel computationally efficient maximum pseudo-partial-likelihood estimation method for the semiparametric proportional cause-specific hazards model. Using modern empirical process theory we derive the asymptotic properties of the proposed estimators for the regression coefficients and the covariate-specific cumulative incidence functions, and provide methodology for constructing simultaneous confidence bands for the latter. Simulation studies show that our estimators perform well even in the presence of a large fraction of missing cause of failures, and that the regression coefficient estimator can be substantially more efficient compared to the previously proposed augmented inverse probability weighting estimator. The method is applied using data from an HIV cohort study and a bladder cancer clinical trial.

Analysis of the time-varying Cox model for the cause-specific hazard functions with missing causes.

This paper studies the Cox model with time-varying coefficients for cause-specific hazard functions when the causes of failure are subject to missingness. Inverse probability weighted and augmented inverse probability weighted estimators are investigated. The latter is considered as a two-stage estimator by directly utilizing the inverse probability weighted estimator and through modeling available auxiliary variables to improve efficiency. The asymptotic properties of the two estimators are investigated. Hypothesis testing procedures are developed to test the null hypotheses that the covariate effects are zero and that the covariate effects are constant. We conduct simulation studies to examine the finite sample properties of the proposed estimation and hypothesis testing procedures under various settings of the auxiliary variables and the percentages of the failure causes that are missing. These simulation results demonstrate that the augmented inverse probability weighted estimators are more efficient than the inverse probability weighted estimators and that the proposed testing procedures have the expected satisfactory results in sizes and powers. The proposed methods are illustrated using the Mashi clinical trial data for investigating the effect of randomization to formula-feeding versus breastfeeding plus extended infant zidovudine prophylaxis on death due to mother-to-child HIV transmission in Botswana.

Analyzing discrete competing risks data with partially overlapping or independent data sources and nonstandard sampling schemes, with application to cancer registries.

This paper demonstrates the flexibility of a general approach for the analysis of discrete time competing risks data that can accommodate complex data structures, different time scales for different causes, and nonstandard sampling schemes. The data may involve a single data source where all individuals contribute to analyses of both cause-specific hazard functions, overlapping datasets where some individuals contribute to the analysis of the cause-specific hazard function of only one cause while other individuals contribute to analyses of both cause-specific hazard functions, or separate data sources where each individual contributes to the analysis of the cause-specific hazard function of only a single cause. The approach is modularized into estimation and prediction. For the estimation step, the parameters and the variance-covariance matrix can be estimated using widely available software. The prediction step utilizes a generic program with plug-in estimates from the estimation step. The approach is illustrated with three prognostic models for stage IV male oral cancer using different data structures. The first model uses only men with stage IV oral cancer from population-based registry data. The second model strategically extends the cohort to improve the efficiency of the estimates. The third model improves the accuracy for those with a lower risk of other causes of death, by bringing in an independent data source collected under a complex sampling design with additional other-cause covariates. These analyses represent novel extensions of existing methodology, broadly applicable for the development of prognostic models capturing both the cancer and noncancer aspects of a patient's health.

Parametric estimation of association in bivariate failure-time data subject to competing risks: sensitivity to underlying assumptions.

There has arisen a considerable body of research addressing the estimation of association between paired failure times in the presence of competing risks. In a 2002 paper, Bandeen-Roche and Liang proposed the conditional cause-specific hazard ratio (CCSHR) as a measure of this association and a parametric method by which to estimate it. The method features an interpretable decomposition of the CCSHR into factors describing the association between a pair's times to first failure among multiple failure causes and the association in pair members' propensities to fail due to a common cause. There were indications of sensitivity to model assumptions, however, in the 2002 work. Here we report a detailed study of the method's sensitivity to its parametric assumptions. We conclude that the method's performance is most sensitive to mis-specification of temporality in the association between pair members' first-failure times and of correlation between propensity to fail early or late and the propensity to fail of a specific cause. Implications for methods development are highlighted.

On the analysis of discrete time competing risks data.

Regression methodology has been well developed for competing risks data with continuous event times, both for the cause-specific hazard and cumulative incidence functions. However, in many applications, including those from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute, the event times may be observed discretely. Naive application of continuous time regression methods to such data is not appropriate. We propose maximum likelihood inferences for estimation of model parameters for the discrete time cause-specific hazard functions, develop predictions for the associated cumulative incidence functions, and derive consistent variance estimators for the predicted cumulative incidence functions. The methods are readily implemented using standard software for generalized estimating equations, where models for different causes may be fitted separately. For the SEER data, it may be desirable to model different event types on different time scales and the methods are generalized to accommodate such scenarios, extending earlier work on continuous time data. Simulation studies demonstrate that the methods perform well in realistic set-ups. The methodology is illustrated with stage III colon cancer data from SEER.

Hierarchical likelihood inference on clustered competing risks data.

The frailty model, an extension of the proportional hazards model, is often used to model clustered survival data. However, some extension of the ordinary frailty model is required when there exist competing risks within a cluster. Under competing risks, the underlying processes affecting the events of interest and competing events could be different but correlated. In this paper, the hierarchical likelihood method is proposed to infer the cause-specific hazard frailty model for clustered competing risks data. The hierarchical likelihood incorporates fixed effects as well as random effects into an extended likelihood function, so that the method does not require intensive numerical methods to find the marginal distribution. Simulation studies are performed to assess the behavior of the estimators for the regression coefficients and the correlation structure among the bivariate frailty distribution for competing events. The proposed method is illustrated with a breast cancer dataset.

Cause-Specific Hazard Regression for Competing Risks Data Under Interval Censoring and Left Truncation.

Inference for cause-specific hazards from competing risks data under interval censoring and possible left truncation has been understudied. Aiming at this target, a penalized likelihood approach for a Cox-type proportional cause-specific hazards model is developed, and the associated asymptotic theory is discussed. Monte Carlo simulations show that the approach performs very well for moderate sample sizes. An application to a longitudinal study of dementia illustrates the practical utility of the method. In the application, the age-specific hazards of AD, other dementia and death without dementia are estimated, and risk factors of all competing risks are studied.

Nonparametric association analysis of bivariate left-truncated competing risks data.

We develop time-varying association analyses for onset ages of two lung infections to address the statistical challenges in utilizing registry data where onset ages are left-truncated by ages of entry and competing-risk censored by deaths. Two types of association estimators are proposed based on conditional cause-specific hazard function and cumulative incidence function that are adapted from unconditional quantities to handle left truncation. Asymptotic properties of the estimators are established by using the empirical process techniques. Our simulation study shows that the estimators perform well with moderate sample sizes. We apply our methods to the Cystic Fibrosis Foundation Registry data to study the relationship between onset ages of Pseudomonas aeruginosa and Staphylococcus aureus infections.

Additive gamma frailty models with applications to competing risks in related individuals.

Epidemiological studies of related individuals are often complicated by the fact that follow-up on the event type of interest is incomplete due to the occurrence of other events. We suggest a class of frailty models with cause-specific hazards for correlated competing events in related individuals. The frailties are based on sums of gamma distributed variables and offer closed form expressions for the observed intensities. An inference procedure with a recursive baseline estimator is proposed, and its large sample properties are established. The estimator readily handles cluster left-truncation as occurring in the Nordic twin registers. The performance in finite samples is investigated by simulations and an example on prostate cancer in twins is provided for illustration.