Study of n-fold Weibull competing risk model

This paper deals with an n-fold Weibull competing risk model. A characterisation of the WPP plot is given along with estimation of model parameters when modelling a given data set. These are illustrated through two examples. A study of the different possible shapes for the density and failure rate functions is also presented. (C) 2003 Elsevier Ltd. All rights reserved.

Nonparametric Estimation of Survivor Function in Bivariate Competing Risk Models’

So far, in the bivariate set up, the analysis of lifetime (failure time) data with multiple causes of failure is done by treating each cause of failure separately. with failures from other causes considered as independent censoring. This approach is unrealistic in many situations. For example, in the analysis of mortality data on married couples one would be interested to compare the hazards for the same cause of death as well as to check whether death due to one cause is more important for the partners’ risk of death from other causes. In reliability analysis. one often has systems with more than one component and many systems. subsystems and components have more than one cause of failure. Design of high-reliability systems generally requires that the individual system components have extremely high reliability even after long periods of time. Knowledge of the failure behaviour of a component can lead to savings in its cost of production and maintenance and. in some cases, to the preservation of human life. For the purpose of improving reliability. it is necessary to identify the cause of failure down to the component level. By treating each cause of failure separately with failures from other causes considered as independent censoring, the analysis of lifetime data would be incomplete. Motivated by this. we introduce a new approach for the analysis of bivariate competing risk data using the bivariate vector hazard rate of Johnson and Kotz (1975).

Estimating loss to follow-up in HIV-infected patients on antiretroviral therapy: the effect of the competing risk of death in Zambia and Switzerland

Background Loss to follow-up (LTFU) is common in antiretroviral therapy (ART) programmes. Mortality is a competing risk (CR) for LTFU; however, it is often overlooked in cohort analyses. We examined how the CR of death affected LTFU estimates in Zambia and Switzerland. Methods and Findings HIV-infected patients aged ≥18 years who started ART 2004–2008 in observational cohorts in Zambia and Switzerland were included. We compared standard Kaplan-Meier curves with CR cumulative incidence. We calculated hazard ratios for LTFU across CD4 cell count strata using cause-specific Cox models, or Fine and Gray subdistribution models, adjusting for age, gender, body mass index and clinical stage. 89,339 patients from Zambia and 1,860 patients from Switzerland were included. 12,237 patients (13.7%) in Zambia and 129 patients (6.9%) in Switzerland were LTFU and 8,498 (9.5%) and 29 patients (1.6%), respectively, died. In Zambia, the probability of LTFU was overestimated in Kaplan-Meier curves: estimates at 3.5 years were 29.3% for patients starting ART with CD4 cells <100 cells/µl and 15.4% among patients starting with ≥350 cells/µL. The estimates from CR cumulative incidence were 22.9% and 13.6%, respectively. Little difference was found between naïve and CR analyses in Switzerland since only few patients died. The results from Cox and Fine and Gray models were similar: in Zambia the risk of loss to follow-up and death increased with decreasing CD4 counts at the start of ART, whereas in Switzerland there was a trend in the opposite direction, with patients with higher CD4 cell counts more likely to be lost to follow-up. Conclusions In ART programmes in low-income settings the competing risk of death can substantially bias standard analyses of LTFU. The CD4 cell count and other prognostic factors may be differentially associated with LTFU in low-income and high-income settings.

Impact of age and comorbidities on long-term survival of patients with high-risk prostate cancer treated with radical prostatectomy: a multi-institutional competing-risks analysis

Survival after surgical treatment using competing-risk analysis has been previously examined in patients with prostate cancer (PCa). However, the combined effect of age and comorbidities has not been assessed in patients with high-risk PCa who might have heterogeneous rates of competing mortality despite the presence of aggressive disease.

Polypharmacy is Associated with an Increased Risk of Bleeding in Elderly Patients with Venous Thromboembolism.

BACKGROUND: Polypharmacy, defined as the concomitant use of multiple medications, is very common in the elderly and may trigger drug-drug interactions and increase the risk of falls in patients receiving vitamin K antagonists. OBJECTIVE: To examine whether polypharmacy increases the risk of bleeding in elderly patients who receive vitamin K antagonists for acute venous thromboembolism (VTE). DESIGN: We used a prospective cohort study. PARTICIPANTS: In a multicenter Swiss cohort, we studied 830 patients aged ≥ 65 years with VTE. MAIN MEASURES: We defined polypharmacy as the prescription of more than four different drugs. We assessed the association between polypharmacy and the time to a first major and clinically relevant non-major bleeding, accounting for the competing risk of death. We adjusted for known bleeding risk factors (age, gender, pulmonary embolism, active cancer, arterial hypertension, cardiac disease, cerebrovascular disease, chronic liver and renal disease, diabetes mellitus, history of major bleeding, recent surgery, anemia, thrombocytopenia) and periods of vitamin K antagonist treatment as a time-varying covariate. KEY RESULTS: Overall, 413 (49.8 %) patients had polypharmacy. The mean follow-up duration was 17.8 months. Patients with polypharmacy had a significantly higher incidence of major (9.0 vs. 4.1 events/100 patient-years; incidence rate ratio [IRR] 2.18, 95 % confidence interval [CI] 1.32-3.68) and clinically relevant non-major bleeding (14.8 vs. 8.0 events/100 patient-years; IRR 1.85, 95 % CI 1.27-2.71) than patients without polypharmacy. After adjustment, polypharmacy was significantly associated with major (sub-hazard ratio [SHR] 1.83, 95 % CI 1.03-3.25) and clinically relevant non-major bleeding (SHR 1.60, 95 % CI 1.06-2.42). CONCLUSIONS: Polypharmacy is associated with an increased risk of both major and clinically relevant non-major bleeding in elderly patients receiving vitamin K antagonists for VTE.

Risk of falls and bleeding in elderly patients with acute venous thromboembolism.

OBJECTIVE: Whether or not a high risk of falls increases the risk of bleeding in patients receiving anticoagulants remains a matter of debate. METHODS: We conducted a prospective cohort study involving 991 patients ≥65 years of age who received anticoagulants for acute venous thromboembolism (VTE) at nine Swiss hospitals between September 2009 and September 2012. The study outcomes were as follows: the time to a first major episode of bleeding; and clinically relevant nonmajor bleeding. We determined the associations between the risk of falls and the time to a first episode of bleeding using competing risk regression, accounting for death as a competing event. We adjusted for known bleeding risk factors and anticoagulation as a time-varying covariate. RESULTS: Four hundred fifty-eight of 991 patients (46%) were at high risk of falls. The mean duration of follow-up was 16.7 months. Patients at high risk of falls had a higher incidence of major bleeding (9.6 vs. 6.6 events/100 patient-years; P = 0.05) and a significantly higher incidence of clinically relevant nonmajor bleeding (16.7 vs. 8.3 events/100 patient-years; P < 0.001) than patients at low risk of falls. After adjustment, a high risk of falls was associated with clinically relevant nonmajor bleeding [subhazard ratio (SHR) = 1.74, 95% confidence interval (CI) = 1.23-2.46], but not with major bleeding (SHR = 1.24, 95% CI = 0.83-1.86). CONCLUSION: In elderly patients who receive anticoagulants because of VTE, a high risk of falls is significantly associated with clinically relevant nonmajor bleeding, but not with major bleeding. Whether or not a high risk of falls is a reason against providing anticoagulation beyond 3 months should be based on patient preferences and the risk of VTE recurrence.

Low income, community poverty and risk of end stage renal disease

BACKGROUND: The risk of end stage renal disease (ESRD) is increased among individuals with low income and in low income communities. However, few studies have examined the relation of both individual and community socioeconomic status (SES) with incident ESRD. METHODS: Among 23,314 U.S. adults in the population-based Reasons for Geographic and Racial Differences in Stroke study, we assessed participant differences across geospatially-linked categories of county poverty [outlier poverty, extremely high poverty, very high poverty, high poverty, neither (reference), high affluence and outlier affluence]. Multivariable Cox proportional hazards models were used to examine associations of annual household income and geospatially-linked county poverty measures with incident ESRD, while accounting for death as a competing event using the Fine and Gray method. RESULTS: There were 158 ESRD cases during follow-up. Incident ESRD rates were 178.8 per 100,000 person-years (105 py) in high poverty outlier counties and were 76.3 /105 py in affluent outlier counties, p trend = 0.06. In unadjusted competing risk models, persons residing in high poverty outlier counties had higher incidence of ESRD (which was not statistically significant) when compared to those persons residing in counties with neither high poverty nor affluence [hazard ratio (HR) 1.54, 95% Confidence Interval (CI) 0.75-3.20]. This association was markedly attenuated following adjustment for socio-demographic factors (age, sex, race, education, and income); HR 0.96, 95% CI 0.46-2.00. However, in the same adjusted model, income was independently associated with risk of ESRD [HR 3.75, 95% CI 1.62-8.64, comparing the < $20,000 income group to the > $75,000 group]. There were no statistically significant associations of county measures of poverty with incident ESRD, and no evidence of effect modification. CONCLUSIONS: In contrast to annual family income, geospatially-linked measures of county poverty have little relation with risk of ESRD. Efforts to mitigate socioeconomic disparities in kidney disease may be best appropriated at the individual level.

Frailty and risk for heart failure in older adults: The health, aging, and body composition study.

OBJECTIVE: The aim of this study was to assess the association between frailty and risk for heart failure (HF) in older adults. BACKGROUND: Frailty is common in the elderly and is associated with adverse health outcomes. Impact of frailty on HF risk is not known. METHODS: We assessed the association between frailty, using the Health ABC Short Physical Performance Battery (HABC Battery) and the Gill index, and incident HF in 2825 participants aged 70 to 79 years. RESULTS: Mean age of participants was 74 ± 3 years; 48% were men and 59% were white. During a median follow up of 11.4 (7.1-11.7) years, 466 participants developed HF. Compared to non-frail participants, moderate (HR 1.36, 95% CI 1.08-1.71) and severe frailty (HR 1.88, 95% CI 1.02-3.47) by Gill index was associated with a higher risk for HF. HABC Battery score was linearly associated with HF risk after adjusting for the Health ABC HF Model (HR 1.24, 95% CI 1.13-1.36 per SD decrease in score) and remained significant when controlled for death as a competing risk (HR 1.30; 95% CI 1.00-1.55). Results were comparable across age, sex, and race, and in sub-groups based on diabetes mellitus or cardiovascular disease at baseline. Addition of HABC Battery scores to the Health ABC HF Risk Model improved discrimination (change in C-index, 0.014; 95% CI 0.018-0.010) and appropriately reclassified 13.4% (net-reclassification-improvement 0.073, 95% CI 0.021-0.125; P = .006) of participants (8.3% who developed HF and 5.1% who did not). CONCLUSIONS: Frailty is independently associated with risk of HF in older adults.

A new long-term lifetime distribution induced by a latent complementary risk framework

In this paper, we proposed a new three-parameter long-term lifetime distribution induced by a latent complementary risk framework with decreasing, increasing and unimodal hazard function, the long-term complementary exponential geometric distribution. The new distribution arises from latent competing risk scenarios, where the lifetime associated scenario, with a particular risk, is not observable, rather we observe only the maximum lifetime value among all risks, and the presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its reliability, hazard and quantile functions and order statistics. The parameter estimation is based on the usual maximum-likelihood approach. A simulation study assesses the performance of the estimation procedure. We compare the new distribution with its particular cases, as well as with the long-term Weibull distribution on three real data sets, observing its potential and competitiveness in comparison with some usual long-term lifetime distributions.

Frailty and risk for heart failure in older adults: the health, aging, and body composition study

OBJECTIVE The aim of this study was to assess the association between frailty and risk for heart failure (HF) in older adults. BACKGROUND Frailty is common in the elderly and is associated with adverse health outcomes. Impact of frailty on HF risk is not known. METHODS We assessed the association between frailty, using the Health ABC Short Physical Performance Battery (HABC Battery) and the Gill index, and incident HF in 2825 participants aged 70 to 79 years. RESULTS Mean age of participants was 74 ± 3 years; 48% were men and 59% were white. During a median follow up of 11.4 (7.1-11.7) years, 466 participants developed HF. Compared to non-frail participants, moderate (HR 1.36, 95% CI 1.08-1.71) and severe frailty (HR 1.88, 95% CI 1.02-3.47) by Gill index was associated with a higher risk for HF. HABC Battery score was linearly associated with HF risk after adjusting for the Health ABC HF Model (HR 1.24, 95% CI 1.13-1.36 per SD decrease in score) and remained significant when controlled for death as a competing risk (HR 1.30; 95% CI 1.00-1.55). Results were comparable across age, sex, and race, and in sub-groups based on diabetes mellitus or cardiovascular disease at baseline. Addition of HABC Battery scores to the Health ABC HF Risk Model improved discrimination (change in C-index, 0.014; 95% CI 0.018-0.010) and appropriately reclassified 13.4% (net-reclassification-improvement 0.073, 95% CI 0.021-0.125; P = .006) of participants (8.3% who developed HF and 5.1% who did not). CONCLUSIONS Frailty is independently associated with risk of HF in older adults.

Polypharmacy is Associated with an Increased Risk of Bleeding in Elderly Patients with Venous Thromboembolism.

BACKGROUND Polypharmacy, defined as the concomitant use of multiple medications, is very common in the elderly and may trigger drug-drug interactions and increase the risk of falls in patients receiving vitamin K antagonists. OBJECTIVE To examine whether polypharmacy increases the risk of bleeding in elderly patients who receive vitamin K antagonists for acute venous thromboembolism (VTE). DESIGN We used a prospective cohort study. PARTICIPANTS In a multicenter Swiss cohort, we studied 830 patients aged ≥ 65 years with VTE. MAIN MEASURES We defined polypharmacy as the prescription of more than four different drugs. We assessed the association between polypharmacy and the time to a first major and clinically relevant non-major bleeding, accounting for the competing risk of death. We adjusted for known bleeding risk factors (age, gender, pulmonary embolism, active cancer, arterial hypertension, cardiac disease, cerebrovascular disease, chronic liver and renal disease, diabetes mellitus, history of major bleeding, recent surgery, anemia, thrombocytopenia) and periods of vitamin K antagonist treatment as a time-varying covariate. KEY RESULTS Overall, 413 (49.8 %) patients had polypharmacy. The mean follow-up duration was 17.8 months. Patients with polypharmacy had a significantly higher incidence of major (9.0 vs. 4.1 events/100 patient-years; incidence rate ratio [IRR] 2.18, 95 % confidence interval [CI] 1.32-3.68) and clinically relevant non-major bleeding (14.8 vs. 8.0 events/100 patient-years; IRR 1.85, 95 % CI 1.27-2.71) than patients without polypharmacy. After adjustment, polypharmacy was significantly associated with major (sub-hazard ratio [SHR] 1.83, 95 % CI 1.03-3.25) and clinically relevant non-major bleeding (SHR 1.60, 95 % CI 1.06-2.42). CONCLUSIONS Polypharmacy is associated with an increased risk of both major and clinically relevant non-major bleeding in elderly patients receiving vitamin K antagonists for VTE.

Risk of falls and bleeding in elderly patients with acute venous thromboembolism.

OBJECTIVE Whether or not a high risk of falls increases the risk of bleeding in patients receiving anticoagulants remains a matter of debate. METHODS We conducted a prospective cohort study involving 991 patients ≥ 65 years of age who received anticoagulants for acute venous thromboembolism (VTE) at nine Swiss hospitals between September 2009 and September 2012. The study outcomes were as follows: the time to a first major episode of bleeding; and clinically relevant nonmajor bleeding. We determined the associations between the risk of falls and the time to a first episode of bleeding using competing risk regression, accounting for death as a competing event. We adjusted for known bleeding risk factors and anticoagulation as a time-varying covariate. RESULTS Four hundred fifty-eight of 991 patients (46%) were at high risk of falls. The mean duration of follow-up was 16.7 months. Patients at high risk of falls had a higher incidence of major bleeding (9.6 vs. 6.6 events/100 patient-years; P = 0.05) and a significantly higher incidence of clinically relevant nonmajor bleeding (16.7 vs. 8.3 events/100 patient-years; P < 0.001) than patients at low risk of falls. After adjustment, a high risk of falls was associated with clinically relevant nonmajor bleeding [subhazard ratio (SHR) = 1.74, 95% confidence interval (CI) = 1.23-2.46], but not with major bleeding (SHR = 1.24, 95% CI = 0.83-1.86). CONCLUSION In elderly patients who receive anticoagulants because of VTE, a high risk of falls is significantly associated with clinically relevant nonmajor bleeding, but not with major bleeding. Whether or not a high risk of falls is a reason against providing anticoagulation beyond 3 months should be based on patient preferences and the risk of VTE recurrence.

Physical Activity and Risk of Bleeding in Elderly Patients Taking Anticoagulants.

BACKGROUND Although the possibility of bleeding during anticoagulant treatment may limit patients from taking part in physical activity, the association between physical activity and anticoagulation-related bleeding is uncertain. OBJECTIVES To determine whether physical activity is associated with bleeding in elderly patients taking anticoagulants. PATIENTS/METHODS In a prospective multicenter cohort study of 988 patients aged ≥65 years receiving anticoagulants for venous thromboembolism, we assessed patients' self-reported physical activity level. The primary outcome was the time to a first major bleeding, defined as fatal bleeding, symptomatic bleeding in a critical site, or bleeding causing a fall in hemoglobin or leading to transfusions. The secondary outcome was the time to a first clinically-relevant non-major bleeding. We examined the association between physical activity level and time to a first bleeding using competing risk regression, accounting for death as a competing event. We adjusted for known bleeding risk factors and anticoagulation as a time-varying covariate. RESULTS During a mean follow-up of 22 months, patients with a low, moderate, and high physical activity level had an incidence of major bleeding of 11.6, 6.3, and 3.1 events per 100 patient-years, and an incidence of clinically relevant non-major bleeding of 14.0, 10.3, and 7.7 events per 100 patient-years, respectively. A high physical activity level was significantly associated with a lower risk of major bleeding (adjusted sub-hazard ratio 0.40, 95%-CI 0.22-0.72). There was no association between physical activity and non-major bleeding. CONCLUSIONS A high level of physical activity is associated with a decreased risk of major bleeding in elderly patients receiving anticoagulant therapy. This article is protected by copyright. All rights reserved.