The standard approach to regression modeling for cause-specific hazards with prospective competing risks data specifies separate models for each failure type. An alternative proposed by Lunn and McNeil (1995) assumes the cause-specific hazards are proportional across causes. This may be more efficient than the standard approach, and allows the comparison of covariate effects across causes. In this paper, we extend Lunn and McNeil (1995) to nested case-control studies, accommodating scenarios with additional matching and non-proportionality. We also consider the case where data for different causes are obtained from different studies conducted in the same cohort. It is demonstrated that while only modest gains in efficiency are possible in full cohort analyses, substantial gains may be attained in nested case-control analyses for failure types that are relatively rare. Extensive simulation studies are conducted and real data analyses are provided using the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial (PLCO) study.

During patient follow-up in a randomized trial, some deaths may occur. Where death (or noncardiovascular death) is not part of an outcome of interest it is termed a competing risk. Conventional analyses (eg, Cox proportional hazards model) handle death similarly to other censored follow-up. Patients still alive are unrealistically assumed to be representative of those who died. The Fine and Gray model has been used to handle competing risks, but is often used inappropriately and can be misleading. We propose an alternative multiple imputation approach that plausibly accounts for the fact that patients who die tend also to be at high risk for the (unobserved) outcome of interest. This provides a logical framework for exploring the impact of a competing risk, recognizing that there is no unique solution. We illustrate these issues in 3 cardiovascular trials and in simulation studies. We conclude with practical recommendations for handling competing risks in future trials.

BACKGROUND: Comprehensive investigations of the prognosis factors and treatment strategies with adjustment of competing causes of death for patients with malignant meningioma (MM) is still lacking.
METHODS: The surveillance, Epidemiology, and End Results (SEER) database were used to include adult patients with this rare disease between 2004 and 2018. The probability of MM-caused mortality (MMCM) and non-MM-caused mortality (non-MMCM) were presented by cumulative incidence function curves. Then, the association between variates with non-MMCM was evaluated by the cox proportional hazard model, and the prognostic factors of MMCM were identified by Fine-Gray competing risk regression model. Furthermore, a nomogram was developed to predict the 1-year, 2-year, and 5-year MMCM and the performance was tested by a time-dependent area under the receiver operating characteristic (ROC) curve and calibration.
RESULTS: 577 patients were included, with a median age of 62 (18-100) years old and a median overall survival time of 36 (0-176) months. The percentage of non-MMCM was 15.4% (n = 89) in the entire population and 21.7% (n = 54) in elderly patients. The multivariable Cox proportional hazard regression model revealed that older age and other tumor(s) before or after MM had an independently significant association with higher non-MMCM. After adjustment of competing causes of death, the multivariable Fine-gray regression model identified age group ≥ 65 year, tumor size > 5.3 cm, recurrent MM, and histologic type 9530/3 (Meningioma, malignant) had an independently significant association with higher MMCM. Compared with gross total (GTR) of tumor, subtotal resection of tumor (HR 1.66, 95%CI 1.08-2.56, P = 0.02), partial resection of lobe (HR 2.26, 95%CI 1.32-3.87, P = 0.003), and gross total resection of lobe (HR 1.69, 95%CI 1.12-2.51, P = 0.01) had an independently significant association with higher MMCM.
CONCLUSIONS: The competing risk nomogram including age group, tumor size, initial status, histologic type, and extent of resection is discriminative and clinically useful. This study emphasized the importance of the GTR of tumor in the treatment of MM patients, which had a significantly lower incidence of MMCM compared with biopsy, STR of tumor, partial resection of lobe, and GTR of lobe.

OBJECTIVE: To study the relationships of cardiovascular risk factors with cancer and cardiovascular mortality in a cohort of middle-aged men followed-up for 61 years.
METHODS: A rural cohort of 1611 cancer- and cardiovascular disease-free men aged 40-59 years was examined in 1960 within the Italian Section of the Seven Countries Study, and 28 risk factors measured at baseline were used to predict cancer (n = 459) and cardiovascular deaths (n = 678) that occurred during 61 years of follow-up until the extinction of the cohort with Cox proportional hazard models.
RESULTS: A model with 28 risk factors and cancer deaths as the end-point produced eight statistically significant coefficients for age, smoking habits, mother early death, corneal arcus, xanthelasma and diabetes directly related to events, and arm circumference and healthy diet inversely related. In the corresponding models for major cardiovascular diseases and their subgroups, only the coefficients of age and smoking habits were significant among those found for cancer deaths, to which healthy diet can be added if considering coronary heart disease alone. Following a competing risks analysis by the Fine-Gray method, risk factors significantly common to both conditions were only age, smoking, and xanthelasma.
CONCLUSIONS: A sizeable number of traditional cardiovascular risk factors were not predictors of cancer death in a middle-aged male cohort followed-up until extinction.

BACKGROUND: According to long-term follow-up data of malignant tumor patients, assessing treatment effects requires careful consideration of competing risks. The commonly used cause-specific hazard ratio (CHR) and sub-distribution hazard ratio (SHR) are relative indicators and may present challenges in terms of proportional hazards assumption and clinical interpretation. Recently, the restricted mean time lost (RMTL) has been recommended as a supplementary measure for better clinical interpretation. Moreover, for observational study data in epidemiological and clinical settings, due to the influence of confounding factors, covariate adjustment is crucial for determining the causal effect of treatment.
METHODS: We construct an RMTL estimator after adjusting for covariates based on the inverse probability weighting method, and derive the variance to construct interval estimates based on the large sample properties. We use simulation studies to study the statistical performance of this estimator in various scenarios. In addition, we further consider the changes in treatment effects over time, constructing a dynamic RMTL difference curve and corresponding confidence bands for the curve.
RESULTS: The simulation results demonstrate that the adjusted RMTL estimator exhibits smaller biases compared with unadjusted RMTL and provides robust interval estimates in all scenarios. This method was applied to a real-world cervical cancer patient data, revealing improvements in the prognosis of patients with small cell carcinoma of the cervix. The results showed that the protective effect of surgery was significant only in the first 20 months, but the long-term effect was not obvious. Radiotherapy significantly improved patient outcomes during the follow-up period from 17 to 57 months, while radiotherapy combined with chemotherapy significantly improved patient outcomes throughout the entire period.
CONCLUSIONS: We propose the approach that is easy to interpret and implement for assessing treatment effects in observational competing risk data.

OBJECTIVE: Rheumatoid arthritis (RA) patients have an increased risk for cardiovascular diseases, including atrial fibrillation (AF), but the impact of RA on ischemic stroke risk in the context of AF remains unknown. We explored whether the risk of ischemic stroke after diagnosis of AF is further increased among patients with RA compared with non-RA patients.
METHODS: In the nationwide Norwegian Cardio-Rheuma Register, we evaluated cumulative incidence and hazard rate of ischemic stroke after the first AF diagnosis (2,750 individuals with RA and 158 879 without RA between 2010 and 2017) by using a competing risk model with a 3-month delayed entry.
RESULTS: The 5-year unadjusted cumulative incidence of ischemic stroke was 7.3% (95% CI: 5.9%-8.7%) for patients with RA and 5.0% (95% CI 4.9%-5.2%) for patients without RA. Unadjusted univariate analyses indicated that AF patients with RA had a HR of 1.36 (95% CI: 1.13, 1.62) for ischemic stroke compared with those without RA. Sex- and age-adjusted HR for ischemic stroke in RA patients with AF was 1.25 (95% CI: 1.05, 1.50), and the effect size remained unchanged after adjustment for diabetes, hypertension, atherosclerotic cardiovascular disease, and oral anticoagulant (OAC) treatment. RA patients were less likely to receive OAC treatment than non-RA patients (adjusted odds ratio 0.88, 95% CI 0.80, 0.97).
CONCLUSIONS: RA patients diagnosed with AF are at a further increased risk for stroke compared with non-RA patients with AF, and less likely to receive OAC treatment, emphasizing the need to improve stroke prevention in AF patients with RA.

Time-to-event data are often recorded on a discrete scale with multiple, competing risks as potential causes for the event. In this context, application of continuous survival analysis methods with a single risk suffers from biased estimation. Therefore, we propose the multivariate Bernoulli detector for competing risks with discrete times involving a multivariate change point model on the cause-specific baseline hazards. Through the prior on the number of change points and their location, we impose dependence between change points across risks, as well as allowing for data-driven learning of their number. Then, conditionally on these change points, a multivariate Bernoulli prior is used to infer which risks are involved. Focus of posterior inference is cause-specific hazard rates and dependence across risks. Such dependence is often present due to subject-specific changes across time that affect all risks. Full posterior inference is performed through a tailored local-global Markov chain Monte Carlo (MCMC) algorithm, which exploits a data augmentation trick and MCMC updates from nonconjugate Bayesian nonparametric methods. We illustrate our model in simulations and on ICU data, comparing its performance with existing approaches.

UNASSIGNED: Existing models predicting hepatocellular carcinoma (HCC) occurrence do not account for competing risk events and, thus, may overestimate the probability of HCC. Our goal was to quantify this bias for patients with cirrhosis and cured hepatitis C.
UNASSIGNED: We analyzed a nationwide cohort of patients with cirrhosis and cured hepatitis C infection from Scotland. Two HCC prognostic models were developed: (1) a Cox regression model ignoring competing risk events and (2) a Fine-Gray regression model accounting for non-HCC mortality as a competing risk. Both models included the same set of prognostic factors used by previously developed HCC prognostic models. Two predictions were calculated for each patient: first, the 3-year probability of HCC predicted by model 1 and second, the 3-year probability of HCC predicted by model 2.
UNASSIGNED: The study population comprised 1629 patients with cirrhosis and cured HCV, followed for 3.8 years on average. A total of 82 incident HCC events and 159 competing risk events (ie, non-HCC deaths) were observed. The mean predicted 3-year probability of HCC was 3.37% for model 1 (Cox) and 3.24% for model 2 (Fine-Gray). For most patients (76%), the difference in the 3-year probability of HCC predicted by model 1 and model 2 was minimal (ie, within 0 to ±0.3%). A total of 2.6% of patients had a large discrepancy exceeding 2%; however, these were all patients with a 3-year probability exceeding >5% in both models.
UNASSIGNED: Prognostic models that ignore competing risks do overestimate the future probability of developing HCC. However, the degree of overestimation-and the way it is patterned-means that the impact on HCC screening decisions is likely to be modest.

Placental abruption, the premature placental separation, confers increased perinatal mortality risk with preterm delivery as an important pathway through which the risk appears mediated. While pregnancies complicated by abruption are often delivered through an obstetrical intervention, many deliver spontaneously. We examined the contributions of clinician-initiated (PTDIND) and spontaneous (PTDSPT) preterm delivery at <37 weeks as competing causal mediators of the abruption-perinatal mortality association. Using the Consortium for Safe Labor (2002-2008) data (n = 203,990; 1.6% with abruption), we applied a potential outcomes-based mediation analysis to decompose the total effect into direct and mediator-specific indirect effects through PTDIND and PTDSPT. Each mediated effect describes the reduction in the counterfactual mortality risk if that preterm delivery subtype was shifted from its distribution under abruption to without abruption. The total effect risk ratio (RR) of abruption on perinatal mortality was 5.4 (95% confidence interval [CI] 4.6, 6.3). The indirect effect RRs for PTDIND and PTDSPT were 1.5 (95% CI: 1.4, 1.6) and 1.5 (95% CI: 1.5, 1.6), respectively; these corresponded to mediated proportions of 25% each. These findings underscore that spontaneous and clinician-initiated preterm deliveries each play essential roles in shaping perinatal mortality risks associated with placental abruption.

Graft failure and recipient death with functioning graft are important competing outcomes after kidney transplantation. Risk prediction models typically censor for the competing outcome thereby overestimating the cumulative incidence. The magnitude of this overestimation is not well described in real-world transplant data. This retrospective cohort study analyzed data from the European Collaborative Transplant Study (n = 125 250) and from the American Scientific Registry of Transplant Recipients (n = 190 258). Separate cause-specific hazard models using donor and recipient age as continuous predictors were developed for graft failure and recipient death. The hazard of graft failure increased quadratically with increasing donor age and decreased decaying with increasing recipient age. The hazard of recipient death increased linearly with increasing donor and recipient age. The cumulative incidence overestimation due to competing risk-censoring was largest in high-risk populations for both outcomes (old donors/recipients), sometimes amounting to 8.4 and 18.8 percentage points for graft failure and recipient death, respectively. In our illustrative model for posttransplant risk prediction, the absolute risk of graft failure and death is overestimated when censoring for the competing event, mainly in older donors and recipients. Prediction models for absolute risks should treat graft failure and death as competing events.