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Competing risks occur frequently in the analysis of survival data. A competing risk is an event whose occurrence precludes the occurrence of the primary event of interest. In a study examining time to death attributable to cardiovascular causes, death attributable to noncardiovascular causes is a competing risk. When estimating the crude incidence...
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Context 1
... incidences of cardiovascular and noncardiovascu- lar death in the overall sample are described in Figure 1, along with the incidence of the composite outcome of all-cause mor- tality. The cumulative incidence of all-cause mortality is equal to the sum of the cumulative incidences of the 2 cause-specific mortalities. Although the cumulative incidence of cardiovas- cular death exceeded that of noncardiovascular death at each point in time, the incidence of noncardiovascular death was not negligible in this population. A figure similar to Figure 1 should be presented to estimate cumulative incidence in the presence of competing risk. 13 In Figure 2, 3 additional curves have been added to the cumulative incidence functions described in Figure 1: esti- mates of the incidence of each of the 2 outcomes derived from the complement of the Kaplan-Meier estimate of the survival function, along with the sum of the incidence of each outcome derived from the 2 Kaplan-Meier survival functions. Two observations warrant merit. First, as antici- pated, the Kaplan-Meier estimate of incidence of each of the 2 outcomes is larger than the corresponding estimate derived from the CIF. The overestimates of incidence when using the Kaplan-Meier estimates are moderately large for both cardiovascular death and noncardiovascular death. Second, the sum of the 2 Kaplan-Meier estimates of incidence is greater than the estimate of incidence of the composite outcome of all-cause mortality. The estimates described in Figure 2 illustrate the incorrect estimates of cumulative incidence that can arise when an analyst naïvely uses the Kaplan-Meier survival function to estimate cumu- lative ...
Context 2
... incidences of cardiovascular and noncardiovascu- lar death in the overall sample are described in Figure 1, along with the incidence of the composite outcome of all-cause mor- tality. The cumulative incidence of all-cause mortality is equal to the sum of the cumulative incidences of the 2 cause-specific mortalities. Although the cumulative incidence of cardiovas- cular death exceeded that of noncardiovascular death at each point in time, the incidence of noncardiovascular death was not negligible in this population. A figure similar to Figure 1 should be presented to estimate cumulative incidence in the presence of competing risk. 13 In Figure 2, 3 additional curves have been added to the cumulative incidence functions described in Figure 1: esti- mates of the incidence of each of the 2 outcomes derived from the complement of the Kaplan-Meier estimate of the survival function, along with the sum of the incidence of each outcome derived from the 2 Kaplan-Meier survival functions. Two observations warrant merit. First, as antici- pated, the Kaplan-Meier estimate of incidence of each of the 2 outcomes is larger than the corresponding estimate derived from the CIF. The overestimates of incidence when using the Kaplan-Meier estimates are moderately large for both cardiovascular death and noncardiovascular death. Second, the sum of the 2 Kaplan-Meier estimates of incidence is greater than the estimate of incidence of the composite outcome of all-cause mortality. The estimates described in Figure 2 illustrate the incorrect estimates of cumulative incidence that can arise when an analyst naïvely uses the Kaplan-Meier survival function to estimate cumu- lative ...
Context 3
... incidences of cardiovascular and noncardiovascu- lar death in the overall sample are described in Figure 1, along with the incidence of the composite outcome of all-cause mor- tality. The cumulative incidence of all-cause mortality is equal to the sum of the cumulative incidences of the 2 cause-specific mortalities. Although the cumulative incidence of cardiovas- cular death exceeded that of noncardiovascular death at each point in time, the incidence of noncardiovascular death was not negligible in this population. A figure similar to Figure 1 should be presented to estimate cumulative incidence in the presence of competing risk. 13 In Figure 2, 3 additional curves have been added to the cumulative incidence functions described in Figure 1: esti- mates of the incidence of each of the 2 outcomes derived from the complement of the Kaplan-Meier estimate of the survival function, along with the sum of the incidence of each outcome derived from the 2 Kaplan-Meier survival functions. Two observations warrant merit. First, as antici- pated, the Kaplan-Meier estimate of incidence of each of the 2 outcomes is larger than the corresponding estimate derived from the CIF. The overestimates of incidence when using the Kaplan-Meier estimates are moderately large for both cardiovascular death and noncardiovascular death. Second, the sum of the 2 Kaplan-Meier estimates of incidence is greater than the estimate of incidence of the composite outcome of all-cause mortality. The estimates described in Figure 2 illustrate the incorrect estimates of cumulative incidence that can arise when an analyst naïvely uses the Kaplan-Meier survival function to estimate cumu- lative ...
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Objective
To examine whether reduced handgrip strength, as a marker of muscle weakness, is linked with the risk of cardiovascular, cancer and all-cause mortality among older adults.
Design
We used data from the 2006 to 2014 Korean longitudinal study of ageing study. Estimates of handgrip strength were collected using a handheld dynamometer. Cox pr...
Citations
... In this case consideration may have to be given to non-standard ways of analyzing the data. There are a number of statistical methods to assess effects of two or more competing risks [126]. One of the most popular is the so-called subdistribution hazard of Fine and Gray [127]. ...
Background
Cardiovascular disease (CVD) is the leading cause of death worldwide. It has been known for some considerable time that radiation is associated with excess risk of CVD. A recent systematic review of radiation and CVD highlighted substantial inter-study heterogeneity in effect, possibly a result of confounding or modifications of radiation effect by non-radiation factors, in particular by the major lifestyle/environmental/medical risk factors and latent period.
Methods
We assessed effects of confounding by lifestyle/environmental/medical risk factors on radiation-associated CVD and investigated evidence for modifying effects of these variables on CVD radiation dose–response, using data assembled for a recent systematic review.
Results
There are 43 epidemiologic studies which are informative on effects of adjustment for confounding or risk modifying factors on radiation-associated CVD. Of these 22 were studies of groups exposed to substantial doses of medical radiation for therapy or diagnosis. The remaining 21 studies were of groups exposed at much lower levels of dose and/or dose rate. Only four studies suggest substantial effects of adjustment for lifestyle/environmental/medical risk factors on radiation risk of CVD; however, there were also substantial uncertainties in the estimates in all of these studies. There are fewer suggestions of effects that modify the radiation dose response; only two studies, both at lower levels of dose, report the most serious level of modifying effect.
Conclusions
There are still large uncertainties about confounding factors or lifestyle/environmental/medical variables that may influence radiation-associated CVD, although indications are that there are not many studies in which there are substantial confounding effects of these risk factors.
... Thus, the molecular mechanisms behind these associations remain to be clarified. Since mortality due to other causes is a competing event for dementia, we demonstrated here, in parallel, two survival models accounting for competing risk of death, Poisson and Fine-Gray, as recommended in 31 . Sometimes differences can be detected between aetiological risk factors, emphasised by the cause-specific hazard model, and factors that affect real cumulative incidence in the presence of competing events, emphasised by the Fine-Gray sub-distribution hazard model. ...
... We considered death and incidence of dementia as competing risks and fitted two alternative models: Poisson Cause-specific hazard model and Fine-Gray sub-distribution hazard model 31 . In multiplicative Poisson models, death or incidence of disease was modelled using the log-link function and log length of follow-up time as an offset. ...
Previous genome-wide association and replication study for job-related exhaustion indicated a risk variant, rs13219957 in the UST gene. Epidemiological studies suggest connection of stress-related conditions and dementia risk. Therefore, we first studied association of rs13219957 and register-based incident dementia using survival models in the Finnish National FINRISK study surveys (N = 26,693). The AA genotype of rs13219957 was significantly associated with 40% increased risk of all-cause dementia. Then we analysed the UST locus association with brain pathology in the Vantaa 85+ cohort and found association with tau pathology (Braak stage) but not with amyloid pathology. Finally, in the functional analyses, rs13219957 showed a highly significant association with two DNA methylation sites of UST, and UST expression. Thus, the results suggest a common risk variant for a stress-related condition and dementia. Mechanisms to mediate the connection may include differential DNA methylation and transcriptional regulation of UST.
... The aforementioned methodology typically relies on the assumption of non-informative censoring, which asserts that censoring occurs independently of the risk for the outcome of interest. The violation of this assumption introduces bias in the analysis [43]. ...
... Competing risks occur frequently in the survival analysis. A competing risk is an event whose occurrence prohibits the occurrence of clinical outcome of interest [43]. In a study focusing on the time to CVD and stroke mortality, the risk of death attributable to non-CVD and non-stroke causes is called a competing risk. ...
Stroke patients rarely have satisfactory survival, which worsens further if comorbidities develop in such patients. Limited data availability from Southeast Asian countries, especially Indonesia, has impeded the disentanglement of post-stroke mortality determinants. This study aimed to investigate predictors of in-hospital mortality in patients with ischemic stroke (IS). This retrospective observational study used IS medical records from the National Brain Centre Hospital, Jakarta, Indonesia. A theoretically driven Cox’s regression and Fine-Gray models were established by controlling for age and sex to calculate the hazard ratio of each plausible risk factor for predicting in-hospital stroke mortality and addressing competing risks if they existed. This study finally included 3,278 patients with IS, 917 (28%) of whom had cardiovascular disease and 376 (11.5%) suffered renal disease. Bivariate exploratory analysis revealed lower blood levels of triglycerides, low density lipoprotein, and total cholesterol associated with in-hospital-stroke mortality. The average age of patients with post-stroke mortality was 64.06 ± 11.32 years, with a mean body mass index (BMI) of 23.77 kg/m² and a median Glasgow Coma Scale (GCS) score of 12 and an IQR of 5. Cardiovascular disease was significantly associated with IS mortality risk. NIHSS score at admission (hazard ratio [HR] = 1.04; 95% confidence interval [CI]: 1.00–1.07), male sex (HR = 1.51[1.01–2.26] and uric acid level (HR = 1.02 [1.00–1.03]) predicted survivability. Comorbidities, such as cardiovascular disease (HR = 2.16 [1.37–3.40], pneumonia (HR = 2.43 [1.42–4.15] and sepsis (HR = 2.07 [1.09–3.94, had higher hazards for post-stroke mortality. Contrarily, the factors contributing to a lower hazard of mortality were BMI (HR = 0.94 [0.89–0.99]) and GCS (HReye = 0.66 [0.48–0.89]. In summary, our study reported that male sex, NIHSS, uric acid level, cardiovascular diseases, pneumonia, sepsis. BMI, and GCS on admission were strong determinants of in-hospital mortality in patients with IS.
... An appropriate alternative is subdistribution hazard modeling proposed by [26], which accounts for competing risks. The subdistribution hazard model is similar to the Cox proportional hazard model except that it models a hazard function that is derived from cumulative incidence function [27]. We estimated subdistribution hazard ratios (sHRs) and 95% confidence intervals (CIs) for all covariates, which were added to the model sequentially in sets of predisposing, need, and enabling factors. ...
Simple Summary
A new class of therapy named cyclin-dependent kinase 4/6 inhibitors (CDK4/6is) is the recommended preferred treatment for patients with metastatic breast cancer (MBC) who have the HR+/HER2− subtype; however, several barriers may still exist that prevent or delay the initiation of this treatment. In this observational study, we examined how the social determinants of health (SDOH) (e.g., income status, insurance coverage) and other patient characteristics are associated with the initiation of CDK4/6i for HR+/HER2− MBC in a Medicare population of patients aged 65 years or older. Our analysis showed that Medicare patients residing in areas with high vs. low median household income and those living in areas with a high vs. low proportion of Medicare-only coverage had higher rates of initiating treatment with CDK4/6i. Our study findings highlight the influence of SDOH on access to novel and effective cancer therapies and a need for strategies to improve equity in cancer care.
Abstract
In hormone receptor-positive/human epidermal growth factor receptor 2-negative (HR+/HER2−) metastatic breast cancer (MBC), cyclin-dependent kinase 4/6 inhibitors (CDK4/6is) have replaced endocrine therapy alone as the standard of care; however, several barriers to treatment initiation still exist. We assessed social determinants of health (SDOH) and other factors associated with the initiation of CDK4/6i for HR+/HER2− MBC in the Medicare population. Using a retrospective cohort design, patients aged ≥65 years and diagnosed during 2015–2017 were selected from the SEER-Medicare database. Time from MBC diagnosis to first CDK4/6i initiation was the study outcome. The effect of SDOH measures and other predictors on the outcome was assessed using the multivariable Fine and Gray hazard modeling. Of 752 eligible women, 352 (46.8%) initiated CDK4/6i after MBC diagnosis (median time to initiation: 27.9 months). In adjusted analysis, SDOH factors significantly associated with CDK4/6i initiation included high versus low median household income (HHI) (hazard ratio [HR] = 1.70; 95% CI = 1.03–2.81) and the percentage of population with high versus low Medicare-only coverage (HR = 1.54; 95% CI = 1.04–2.27). In summary, older Medicare patients with HR+/HER2− MBC residing in areas with high median HHI and a high proportion of Medicare-only coverage had higher rates of initiating CDK4/6i, suggesting inequitable access to these novel, effective treatments and a need for policy intervention.
... It is noteworthy that the risk set in a cause-specific hazards CRA includes only subjects who have not yet experienced any event. The estimated regression parameters thus directly quantify the cause-specific hazard ratios among those individuals who are at risk of developing the event of interest [13]. This is distinct from the Fine and Gray sub-distribution hazards CRA model, which includes subjects who are currently event free and those who have experienced the competing event [9]. ...
Background
The influence of center volume on kidney transplant outcomes is a topic of ongoing debate. In this study, we employed competing risk analyses to accurately estimate the marginal probability of graft failure in the presence of competing events, such as mortality from other causes with long-term outcomes. The incorporation of immunosuppression protocols and extended follow-up offers additional insights. Our emphasis on long-term follow-up aligns with biological considerations where competing risks play a significant role.
Methods
We examined data from 219,878 adult kidney-only transplantations across 256 U.S. transplant centers (January 2001-December 2015) sourced from the Organ Procurement and Transplantation Network registry. Centers were classified into quartiles by annual volume: low (Q1 = 28), medium (Q2 = 75), medium-high (Q3 = 121), and high (Q4 = 195). Our study investigated the relationship between center volume and 5-year outcomes, focusing on graft failure and mortality. Sub-population analyses included deceased donors, living donors, diabetic recipients, those with kidney donor profile index >85%, and re-transplants from deceased donors.
Results
Adjusted cause-specific hazard ratios (aCHR) for Five-Year Graft Failure and Patient Death were examined by center volume, with low-volume centers as the reference standard (aCHR: 1.0). In deceased donors, medium-high and high-volume centers showed significantly lower cause-specific hazard ratios for graft failure (medium-high aCHR = 0.892, p<0.001; high aCHR = 0.953, p = 0.149) and patient death (medium-high aCHR = 0.828, p<0.001; high aCHR = 0.898, p = 0.003). Among living donors, no significant differences were found for graft failure, while a trend towards lower cause-specific hazard ratios for patient death was observed in medium-high (aCHR = 0.895, p = 0.107) and high-volume centers (aCHR = 0.88, p = 0.061).
Conclusion
Higher center volume is associated with significantly lower cause-specific hazard ratios for graft failure and patient death in deceased donors, while a trend towards reduced cause-specific hazard ratios for patient death is observed in living donors.
... However, T1DM patients admitted to the CDiC program are followed to achieve the desired result and death appears as a competing risk event when dropout is the primary event. In this situation, standard survival methods such as KM method or Cox model are inadequate to analyze survival data in the presence of competing risk [12,13]. Death from any cause in T1DM patients precludes observation of dropout from treatment and thus a competing of dropout. ...
... It indicates the instantaneous rate at which the event of interest occurs in individuals who remain at risk of the event. While the regression coefficient of the Cox model explains the proportional impact of covariates on the event's hazard, this relationship also holds in the absence of competing risks [13]: ...
... where S(t) represents the survival function for an individual with a given set of covariates, X, and S₀(t) signifies the baseline survival function (i.e., the survival function for individuals with covariates equal to zero). Consequently, the impact of a covariate on the event's hazard is equivalent to its impact on the natural logarithm of the survival function [13,15]. In scenarios where competing risks are present, two distinct types of hazard functions emerge: the cause-specific hazard function and the subdistribution hazard function. ...
Understanding the survival dynamics of registered patients on a disease control program is a vital issue for the success of program objectives. Dropout of registered patients from such a program is a critical issue, hindering the effectiveness of the program. This study aimed to identify the risk factors of dropout of patients who were registered on the Changing Diabetes in Children (CDiC) program, taking a case of Uganda. Survival analysis was done by integrating competing risk of factors associated with attrition from the CDiC program. The data for the study was obtained from patients with type 1 diabetes mellitus (T1DM) registered during 2009-2018 at health units with specialized pediatric diabetes clinics from various regions in Uganda. The study considered follow-up data of 1132 children with T1DM. Our analysis revealed that the Body Mass Index (BMI) significantly influences dropout time, with patients classified as underweight showing higher hazards than those with normal BMI. Moreover, when considering competing risks, dropout hazards increased. Comparing the Cox model with the Fine and Gray model shows the latter exhibiting a smaller AIC value, which indicates its superiority in the time-to-dropout analysis. Thus, utilizing methods that integrate competing risks for CDiC dropout analysis is preferable and recommended for related studies. These findings provide actionable insights for enhancing CDiC program efficacy.
... The outcome of interest is typically a specific event (e.g., sepsis), but competing events may preclude the occurrence of the event of interest (e.g.: being discharged in good health conditions or dying of other causes). Competing events are regularly ignored during model building, which may be detrimental to the models' predictive performance according to statistical literature (Austin et al, 2016). ...
... The calibration was similar for RF and regression models: median E:O ratio at LM5 between 0.95 and 0.97 for RF models and between 0.940 and 0.977 for regression models. Lower performance for survival models that censor the competing risks at their time of occurrence was also observed in the companion study, and this finding is in line with the extensive research done on statistical survival models (Austin et al, 2016). ...
Objective: Prognostic outcomes related to hospital admissions typically do not suffer from censoring, and can be modeled either categorically or as time-to-event. Competing events are common but often ignored. We compared the performance of random forest (RF) models to predict the risk of central line-associated bloodstream infections (CLABSI) using different outcome operationalizations.
Methods: We included data from 27478 admissions to the University Hospitals Leuven, covering 30862 catheter episodes (970 CLABSI, 1466 deaths and 28426 discharges) to build static and dynamic RF models for binary (CLABSI vs no CLABSI), multinomial (CLABSI, discharge, death or no event), survival (time to CLABSI) and competing risks (time to CLABSI, discharge or death) outcomes to predict the 7-day CLABSI risk. We evaluated model performance across 100 train/test splits.
Results: Performance of binary, multinomial and competing risks models was similar: AUROC was 0.74 for baseline predictions, rose to 0.78 for predictions at day 5 in the catheter episode, and decreased thereafter. Survival models overestimated the risk of CLABSI (E:O ratios between 1.2 and 1.6), and had AUROCs about 0.01 lower than other models. Binary and multinomial models had lowest computation times. Models including multiple outcome events (multinomial and competing risks) display a different internal structure compared to binary and survival models.
Discussion and Conclusion: In the absence of censoring, complex modelling choices do not considerably improve the predictive performance compared to a binary model for CLABSI prediction in our studied settings. Survival models censoring the competing events at their time of occurrence should be avoided.
... Clinical check-ups were done for each patient 1, 3,5,7,10,12,15,17,20,22 and 24 years after enrolment. At each recruitment hospital, two cardiologists were responsible for monitoring the cohort of patients throughout the follow-up. ...
... Survival curves were constructed using cumulative incidence as a function of incident stroke [15]. ...
Background: Previous studies link myocardial infarction to increased stroke risk. This long-term prospective study examines stroke incidence and outcomes in acute coronary syndrome (ACS) patients, identifying risk factors and geographic disparities.
Methods: We enrolled 535 ACS patients admitted to hospitals across three provinces in the Veneto region of Italy. Patients' residences were classified into three urban and three rural areas in each province. Patients were followed prospectively for 24 years or until death.
Results: All patients, except for three, completed the follow-up, totaling 6151 person-years. During follow-up, 84 patients experienced a stroke, with 85% being ischemic and 15% hemorrhagic, proving fatal in 43 cases. The stroke incidence rate was 14/1000 person-years. Multivariable Cox regression analysis identified older age (HR 1.84; 95% CI 1.30-2.60), atrial fibrillation (AF) (HR 2.64; 95% CI 1.49-4.67), and a higher albumin-to-creatinine ratio (HR 1.38; 95% CI 1.04-1.83) as independent predictors of overall stroke risk, while higher eGFR (HR 0.71; 95% CI 0.53-0.95) was independently associated with a lower risk.
A sub-analysis revealed older age (HR 2.67; 95% CI 1.60-4.45) and AF (HR 2.95; 95% CI 1.38-6.32) as independent predictors of fatal stroke. Unexpectedly, we observed a higher fatal stroke risk in urban areas (HR 1.89; 95% CI 1.03-3.48) and southern provinces (HR 1.71; 95% CI 1.15-2.53).
Conclusion: The ABC study identified several baseline clinical predictors associated with higher stroke risk long after ACS. A geographical association with the risk of fatal stroke was also observed, underscoring the importance of considering both individual clinical predictors and broader geographic factors in stroke prevention policies.
... For a brief overview of the role of the GP in Dutch Healthcare, please refer to Supplementary Methods 2. All-cause mortality was collected as secondary outcome. 21 Participants leaving the participating GPRNs (e.g., moving from the region) were censored at the deregistration date. ...
Background Hypertension is a modifiable risk factor for dementia affecting over 70% of individuals older than 60. Lowering dementia risk through preferential treatment with antihypertensive medication (AHM) classes that are otherwise equivalent in indication could offer a cost-effective, safe, and accessible approach to reducing dementia incidence globally. Certain AHM-classes have been associated with lower dementia risk, potentially attributable to angiotensin-II-receptor (Ang-II) stimulating properties. Previous study results have been inconclusive, possibly due to heterogeneous methodology and limited power. We aimed to comprehensively investigate associations between AHM (sub-)classes and dementia risk using large-scale continuous, real-world prescription and outcome data from primary care.
... Competing risk analysis is based on the CIF to predict the probability of any event occurring first, resulting in a desirable total probability from zero to one (or the sum of probabilities for each event) (16). Meantime, because of the occurrence of competing events precluding the occurrence of event of interest, its probability does not necessarily approach unity in the end (34). ...
Objective
The study aimed to build and validate a competitive risk nomogram to predict the cumulative incidence of hepatocellular carcinoma (HCC) for patients with hepatitis B virus (HBV)-related cirrhosis.
Methods
A total of 1401 HBV-related cirrhosis patients were retrospectively enrolled from January 1, 2011 to December 31, 2014. Application of 20 times imputation dealt with missing data using multiple imputation by chained equations (MICE). The patients were randomly divided into a training set (n = 1017) and a validation set (n = 384) at a ratio of 3:1. A prediction study was carried out using a competing risk model, where the event of interest was HCC and the competing events were death and liver transplantation, and subdistribution hazard ratios (sHRs) with 95% CIs were reported. The multivariate competing risk model was constructed and validated.
Results
There was a negligible difference between the original database and the 20 imputed datasets. At the end of follow-up, the median follow-up time was 69.9 months (interquartile range: 43.8–86.6). There were 31.5% (442/1401) of the patients who developed HCC, with a 5-year cumulative incidence of 22.9 (95%CI, 20.8%–25.2%). The univariate and multivariate competing risk regression and construction of the nomogram were performed in 20 imputed training datasets. Age, sex, antiviral therapy history, hepatitis B e antigen, alcohol drinking history, and alpha-fetoprotein levels were included in the nomogram. The area under receiver operating characteristic curve values at 12, 24, 36, 60, and 96 months were 0.68, 0.69, 0.70, 0.68, and 0.80, and the Brier scores were 0.30, 0.25, 0.23, 0.21, and 0.20 in the validation set. According to the cumulative incidence function, the nomogram effectively screened out high-risk HCC patients from low-risk patients in the presence of competing events (Fine–Gray test p < 0.001).
Conclusion
The competitive risk nomogram was allowed to be used for predicting HCC risk in individual patients with liver cirrhosis, taking into account both the association between risk factors and HCC and the modifying effect of competition events on this association.
