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Background
Competing risks are a common occurrence in survival analysis. They arise when a patient is at risk of more than one mutually exclusive event, such as death from different causes, and the occurrence of one of these may prevent any other event from ever happening.
Methods
There are two main approaches to modelling competing risks: the fir...
Context in source publication
Context 1
... example, reading from Figure 3 the probability of death from breast cancer for those aged 60-69 with distant stage cancer at 10 years post diagnosis is approximately 0.75 in the proportional hazards model but approximately 0.7 in the non-proportional hazards model -a difference of 0.05. Figure 4 shows the cumulative incidence functions for each cause stacked on top of each other for the age groups 60 to 69 and 80+. This allows us to visualise the total probability of death and see how it is broken down by the different causes. ...
Similar publications
Background: Breast cancer (BC) is the second most commonly diagnosed cancer after lung cancer. Survival of BC patients is affected by intermediate events. This study was aimed to investigate the disease course of primary nonmetastatic BC patients with first recurrence of the tumor (FRT) as the intermediate event using the illness- death model.
Meth...
Citations
... We used flexible parametric models by following the method of Hinchliffe and Lambert 19 ...
Objective
To explore how the number and type of breast cancers developed after screen detected atypia compare with the anticipated 11.3 cancers detected per 1000 women screened within one three year screening round in the United Kingdom.
Design
Observational analysis of the Sloane atypia prospective cohort in England.
Setting
Atypia diagnoses through the English NHS breast screening programme reported to the Sloane cohort study. This cohort is linked to the English Cancer Registry and the Mortality and Birth Information System for information on subsequent breast cancer and mortality.
Participants
3238 women diagnosed as having epithelial atypia between 1 April 2003 and 30 June 2018.
Main outcome measures
Number and type of invasive breast cancers detected at one, three, and six years after atypia diagnosis by atypia type, age, and year of diagnosis.
Results
There was a fourfold increase in detection of atypia after the introduction of digital mammography between 2010 (n=119) and 2015 (n=502). During 19 088 person years of follow-up after atypia diagnosis (until December 2018), 141 women developed breast cancer. Cumulative incidence of cancer per 1000 women with atypia was 0.95 (95% confidence interval 0.28 to 2.69), 14.2 (10.3 to 19.1), and 45.0 (36.3 to 55.1) at one, three, and six years after atypia diagnosis, respectively. Women with atypia detected more recently have lower rates of subsequent cancers detected within three years (6.0 invasive cancers per 1000 women (95% confidence interval 3.1 to 10.9) in 2013-18 v 24.3 (13.7 to 40.1) in 2003-07, and 24.6 (14.9 to 38.3) in 2008-12). Grade, size, and nodal involvement of subsequent invasive cancers were similar to those of cancers detected in the general screening population, with equal numbers of ipsilateral and contralateral cancers.
Conclusions
Many atypia could represent risk factors rather than precursors of invasive cancer requiring surgery in the short term. Women with atypia detected more recently have lower rates of subsequent cancers detected, which might be associated with changes to mammography and biopsy techniques identifying forms of atypia that are more likely to represent overdiagnosis. Annual mammography in the short term after atypia diagnosis might not be beneficial. More evidence is needed about longer term risks.
... framework, while it is also known as cumulative incidence function in competing risk terminology [18]. Crude probability of death due to cancer and crude probability of death due to other causes can be estimated as: ...
Purpose
This study introduces a novel method for estimating the variance of life expectancy since diagnosis (LEC) and loss in life expectancy (LLE) for cancer patients within a relative survival framework in situations where life tables based on the entire general population are not accessible. LEC and LLE are useful summary measures of survival in population-based cancer studies, but require information on the mortality in the general population. Our method addresses the challenge of incorporating the uncertainty of expected mortality rates when using a sample from the general population.
Methods
To illustrate the approach, we estimated LEC and LLE for patients diagnosed with colon and breast cancer in Sweden. General population mortality rates were based on a random sample drawn from comparators of a matched cohort. Flexible parametric survival models were used to model the mortality among cancer patients and the mortality in the random sample from the general population. Based on the models, LEC and LLE together with their variances were estimated. The results were compared with those obtained using fixed expected mortality rates.
Results
By accounting for the uncertainty of expected mortality rates, the proposed method ensures more accurate estimates of variances and, therefore, confidence intervals of LEC and LLE for cancer patients. This is particularly valuable for older patients and some cancer types, where underestimation of the variance can be substantial when the entire general population data are not accessible.
Conclusion
The method can be implemented using existing software, making it accessible for use in various cancer studies. The provided example of Stata code further facilitates its adoption.
... Censoring events included end of study follow-up, attrition, a competing menopause type, or age 65 years, whichever came first. First, we estimated crude cumulative incidence functions with 95% CI (Hinchliffe and Lambert, 2013). We then estimated hazard ratios (HR) and 95% CIs for earlier menopause, unadjusted and adjusted for Asian ancestry, Indigenous ancestry, education, parity, pregnancy loss, and smoking. ...
(Abstracted from Hum Reprod 2023;38(9):1843–1852)
Up to 25% of women experience infertility in their lifetime, with a variety of possible causes including dysfunction in the endocrine system, immune system, or reproductive anatomic structures. Research has found that infertility is associated with propensity for poor health outcomes later in life, including reproductive cancer, cardiovascular disease, stroke, and diabetes mellitus.
... Time since index date was used as the underlying time scale. Standardized cumulative incidence and its differences of arrhythmia were also estimated using this approach [37]. We presented the cumulative incidence difference at 1 year, 5 years, 10 years, and 25 years after index date. ...
Background
Although previous evidence has suggested an increased risk of cardiovascular disease (CVD) in patients with inflammatory bowel disease (IBD), its association with arrhythmias is inconclusive. In this study, we aimed to explore the long-term risk of arrhythmias in patients with IBD.
Methods and findings
Through a nationwide histopathology cohort, we identified patients with biopsy-confirmed IBD in Sweden during 1969 to 2017, including Crohn’s disease (CD: n = 24,954; median age at diagnosis: 38.4 years; female: 52.2%), ulcerative colitis (UC: n = 46,856; 42.1 years; 46.3%), and IBD-unclassified (IBD-U: n = 12,067; 43.8 years; 49.6%), as well as their matched reference individuals and IBD-free full siblings. Outcomes included overall and specific arrhythmias (e.g., atrial fibrillation/flutter, bradyarrhythmias, other supraventricular arrhythmias, and ventricular arrhythmias/cardiac arrest). Flexible parametric survival models estimated hazard ratios (aHR) with 95% confidence intervals (95% CIs), after adjustment for birth year, sex, county of residence, calendar year, country of birth, educational attainment, number of healthcare visits, and cardiovascular-related comorbidities. Over a median of approximately 10 years of follow-up, 1,904 (7.6%) patients with CD, 4,154 (8.9%) patients with UC, and 990 (8.2%) patients with IBD-U developed arrhythmias, compared with 6.7%, 7.5%, and 6.0% in reference individuals, respectively. Compared with reference individuals, overall arrhythmias were increased in patients with CD [54.6 versus 46.1 per 10,000 person-years; aHR = 1.15 (95% CI [1.09, 1.21], P < 0.001)], patients with UC [64.7 versus 53.3 per 10,000 person-years; aHR = 1.14 (95% CI [1.10, 1.18], P < 0.001)], and patients with IBD-U [78.1 versus 53.5 per 10,000 person-years; aHR = 1.30 (95% CI [1.20, 1.41], P < 0.001)]. The increased risk persisted 25 years after diagnosis, corresponding to 1 extra arrhythmia case per 80 CD, 58 UC, and 29 IBD-U cases over the same period. Patients with IBD also had a significantly increased risk of specific arrhythmias, except for bradyarrhythmias. Sibling comparison analyses confirmed the main findings. Study limitations include lack of clinical data to define IBD activity, not considering the potential role of IBD medications and disease activity, and the potential residual confounding from unmeasured factors for arrhythmias.
Conclusions
In this study, we observed that patients with IBD were at an increased risk of developing arrhythmias. The excess risk persisted even 25 years after IBD diagnosis. Our findings indicate a need for awareness of this excess risk among healthcare professionals.
... Censoring events included end of study follow-up, attrition, a competing menopause type, or age 65 years, whichever came first. First, we estimated crude cumulative incidence functions with 95% CI (Hinchliffe and Lambert, 2013). We then estimated hazard ratios (HR) and 95% CIs for earlier menopause, unadjusted and adjusted for Asian ancestry, Indigenous ancestry, education, parity, pregnancy loss, and smoking. ...
Study question:
What is the association between past infertility and the type and timing of menopause in midlife women?
Summary answer:
Women with a history of infertility were more likely to experience surgical menopause overall and had elevated risk of earlier surgical menopause until age 43 years but experienced no differences in the timing of natural menopause.
What is known already:
Infertility is experienced by 12-25% of women and is thought to reveal a propensity for poor health outcomes, such as chronic illness, later in life. However, little is known about whether infertility is linked with characteristics of the menopausal transition as women age, despite possible shared underlying pathways involving ovarian function and gynecologic disease.
Study design, size, duration:
Secondary analysis of a prospective cohort study of 13 243 midlife females recruited in Phase 1 of the Alberta's Tomorrow Project (Alberta, Canada) and followed approximately every 4 years (2000-2022).
Participants/materials, setting, methods:
Data were collected through standardized self-report questionnaires. History of infertility, defined as ever trying to become pregnant for more than 1 year without conceiving, was measured at baseline. Menopause characteristics were measured at each study follow-up. Menopause type was defined as premenopause, natural menopause, surgical menopause (bilateral oophorectomy), or indeterminate menopause (premenopausal hysterectomy with ovarian conservation). Timing of natural menopause was defined as the age at 1 full year after the final menstrual period, and timing of surgical and indeterminate menopause was defined as the age at the time of surgery. We used flexible parametric survival analysis for the outcome of menopause timing with age as the underlying time scale and multinomial logistic regression for the outcome of menopause type. Multivariable models controlled for race/ethnicity, education, parity, previous pregnancy loss, and smoking. Sensitivity analyses additionally accounted for birth history, menopausal hormone therapy, body mass index, chronic medical conditions, and age at baseline.
Main results and the role of chance:
Overall, 18.2% of women reported a history of infertility. Past infertility was associated with earlier timing of surgical menopause exclusively before age 43 years (age 35: adjusted hazard ratio 3.13, 95% CI 1.95-5.02; age 40: adjusted hazard ratio 1.83, 95% CI 1.40-2.40; age 45: adjusted hazard ratio 1.13, 95% CI 0.87-1.46) as well as greater odds of experiencing surgical menopause compared to natural menopause (adjusted odds ratio 1.40, 95% CI 1.18-1.66). Infertility was not associated with the timing of natural or indeterminate menopause.
Limitations, reasons for caution:
Information on the underlying cause of infertility and related interventions was not collected, which precluded us from disentangling whether associations differed by infertility cause and treatment. Residual confounding is possible given that some covariates were measured at baseline and may not have temporally preceded infertility.
Wider implications of the findings:
Women with a history of infertility were more likely to experience early surgical menopause and may therefore benefit from preemptive screening and treatment for gynecologic diseases to reduce bilateral oophorectomy, where clinically appropriate, and its associated health risks in midlife. Moreover, the lack of association between infertility and timing of natural menopause adds to the emerging knowledge that diminishing ovarian reserve does not appear to be a primary biological mechanism of infertility nor its downstream implications for women's health.
Study funding/competing interest(s):
Alberta's Tomorrow Project is only possible due to the commitment of its research participants, its staff and its funders: Alberta Health, Alberta Cancer Foundation, Canadian Partnership Against Cancer and Health Canada, and substantial in-kind funding from Alberta Health Services. The views expressed herein represent the views of the author(s) and not of Alberta's Tomorrow Project or any of its funders. This secondary analysis is funded by Project Grant Priority Funding in Women's Health Research from the Canadian Institutes of Health Research (Grant no. 491439). N.V.S. is supported by a Banting Postdoctoral Fellowship from the Canadian Institutes of Health Research. H.K.B. is supported by the Canada Research Chairs Program. E.A.B. is supported by an Early Career Investigator Award in Maternal, Reproductive, Child and Youth Health from the Canadian Institutes of Health Research. A.K.S. has received honoraria from Pfizer, Lupin, Bio-Syent, and Eisai and has received grant funding from Pfizer. N.V.S., H.K.B., and E.A.B. have no conflicts of interest to report.
Trial registration number:
N/A.
... Flexible parametric competing-risks survival analysis was carried out to identify factors associated with the time to ipsilateral major amputation and survival 21 . The flexible parametric model uses restricted cubic splines to model the underlying shape of the hazard function and time-dependent effects on the log-cumulative hazard scale 22,23 . The competingrisks framework was chosen because patients were simultaneously at risk of major amputation and death, and death precluded the occurrence of major amputation. ...
Background
Patients with diabetes and peripheral arterial disease are at increased risk of minor amputation. The aim of study was to assess the rate of re-amputations and death after an initial minor amputation, and to identify associated risk factors.
Methods
Data on all patients aged 40 years and over with diabetes and/or peripheral arterial disease, who underwent minor amputation between January 2014 and December 2018, were extracted from Hospital Episode Statistics. Patients who had bilateral index procedures or an amputation in the 3 years before the study were excluded. Primary outcomes were ipsilateral major amputation and death after the index minor amputation. Secondary outcomes were ipsilateral minor re-amputations, and contralateral minor and major amputations.
Results
In this study of 22 118 patients, 16 808 (76.0 per cent) were men and 18 473 (83.5 per cent) had diabetes. At 1 year after minor amputation, the estimated ipsilateral major amputation rate was 10.7 (95 per cent c.i. 10.3 to 11.1) per cent. Factors associated with a higher risk of ipsilateral major amputation included male sex, severe frailty, diagnosis of gangrene, emergency admission, foot amputation (compared with toe amputation), and previous or concurrent revascularization. The estimated mortality rate was 17.2 (16.7 to 17.7) per cent at 1 year and 49.4 (48.6 to 50.1) per cent at 5 years after minor amputation. Older age, severe frailty, comorbidity, gangrene, and emergency admission were associated with a significantly higher mortality risk.
Conclusion
Minor amputations were associated with a high risk of major amputation and death. One in 10 patients had an ipsilateral major amputation within the first year after minor amputation and half had died by 5 years.
... Despite the fact that methods to "address" competing events have been discussed and developed over several decades (2,(6)(7)(8)(9), much of the methodologic and applied discussion has been on estimation (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) with little emphasis on the estimands. More recent work by Young et al. placed historical estimands from the survival analysis literature in competing events settings within a formal counterfactual framework for causal inference (21). ...
Studying causal exposure effects on dementia is challenging when death is a competing event. Researchers often interpret death as a potential source of bias, though bias cannot be defined or assessed if the causal question is not explicitly specified. Here we discuss two possible notions of a causal effect on dementia risk: the "controlled direct effect" and the "total effect." We provide definitions, discuss the "censoring" assumptions needed for identification in either case and their link to familiar statistical methods. We illustrate concepts in a hypothetical randomized trial on smoking cessation in late-midlife, and emulate such trial using observational data from the Rotterdam Study, the Netherlands, 1990-2015. We estimated a total effect of smoking cessation (compared to continued smoking) on 20-year dementia risk of 2.1(95%CI: -0.1, 4.2) percentage points and a controlled direct effect of smoking cessation on 20-year dementia risk had death been prevented of -2.75(-6.1, 0.8) percentage points. Our study highlights how analyses corresponding to different causal questions can have different results, here with point estimates on opposite sides of the null. Having a clear causal question in view of the competing event and transparent and explicit assumptions are essential to interpreting results and potential bias.
... Following second interim analysis (IA2) of the KEYNOTE-054 trial, patient-level time-toevent data were used to estimate exponential rates and standard errors for transitions starting from the LR state to DM or death, and exponential models were fitted for each treatment arm [18,29]. The analytical sample was restricted to patients who experienced LR as their first RFS failure event. ...
Introduction:
The KEYNOTE-054 trial found that adjuvant treatment with pembrolizumab improved recurrence-free survival versus placebo in completely resected high-risk stage III melanoma patients. We assessed the cost-effectiveness of adjuvant pembrolizumab in Colombia compared with watchful waiting, a widely used strategy despite the high risk of recurrence with surgery alone.
Methods:
A four-health state [recurrence-free (RF), locoregional recurrence (LR), distant metastases (DM), and death) Markov model was developed to assess the lifetime medical costs and outcomes (3% annual discount), along with cost-effectiveness ratios (ICERs). The transitions from the RF and LR states were modeled using KEYNOTE-054 data, and those from the DM state were modeled using data from the KEYNOTE-006 trial and a network meta-analysis of advanced treatments received after adjuvant pembrolizumab and watchful waiting. The health state utilities were derived from KEYNOTE-054 Euro-QoL data and literature. Costs are expressed in 2021 Colombian pesos (COP).
Results:
Over a 46-year time horizon, patients on adjuvant pembrolizumab and watchful waiting were estimated to gain 9.69 and 7.56 quality-adjusted life-years (QALYs), 10.83 and 8.65 life-years (LYs), and incur costs of COP 663,595,726 and COP 563,237,206, respectively. The proportion of LYs spent in RF state was 84.63% for pembrolizumab and 72.13% for watchful waiting, yielding lower subsequent treatment, disease management, and terminal care costs for pembrolizumab. Adjuvant pembrolizumab improved survival by 2.18 LYs and 2.13 QALYs versus watchful waiting. The ICER per QALY was COP 47,081,917, primarily driven by recurrence rates and advanced melanoma treatments. The deterministic sensitivity analysis results were robust and consistent across various reasonable inputs and alternative scenarios. At a willingness-to-pay threshold of COP 69,150,201 per QALY, the probability of pembrolizumab being cost-effective was 65.70%.
Conclusion:
Pembrolizumab is cost-effective as an adjuvant treatment compared to watchful waiting among patients with high-risk stage III melanoma after complete resection in Colombia.
... The gender gap in these reproductive indicators is assessed using the cumulative incidence functions (CIFs) of these reproductive events over the age of youths. Rather than an instantaneous measure of the risk of reproductive transition, CIF gives the proportion of youths that have ever experienced an event at any given time (Hinchliffe & Lambert, 2013;Latouche et al., 2013). This property of CIF makes it desirable for the gender gap analysis over the instantaneous measure. ...
The achievement of gender equality and ending all forms of disparity in the spheres of sexual and reproductive health are critical components of sustainable development goals. We endeavor to investigate the characteristics and/or structural sources of the gender gap in the reproductive transition among Ethiopian youths. The analysis was carried out using parts of data drawn from the 2011 and 2016 Ethiopian Demographic and Health Survey. The decomposition of the gender gap in the reproductive transition of youths into components was made using the Blinder-Oaxaca decomposition analysis for non-linear models. The results demonstrate that the delay in the age at first marriage among the youth was accompanied by an increase in the prevalence of premarital sex. Furthermore, the findings show that the gender gap in reproductive transition is triggered by both compositional and structural effects of covariates such as education, modern contraceptive use, and media exposure. Thus, in addition to reducing inequalities in education, media exposure, and deprivation between male and female youths, working on the structural components is recommended to close the gender gap in the reproductive transition of youths.
... To estimate the average and temporal pattern of hazard ratio (HR), with 95% confidence interval (CI), comparing the exposed individuals to the matched population references and unexposed full siblings, flexible parametric survival model using the stpm2 command in Stata was applied to allow normal mucosa to vary over time (a time-varying effect) [40]. Standardized cumulative incidence of IBD was also estimated using such approach [41]. Time since date of cohort entry was used as the underlying time scale. ...
Background
Although evidence suggests a persistently decreased risk of colorectal cancer for up to 10 years among individuals with a negative endoscopic biopsy result (i.e., normal mucosa), concerns have been raised about other long-term health outcomes among these individuals. In this study, we aimed to explore the long-term risk of inflammatory bowel disease (IBD) after an endoscopic biopsy with normal mucosa.
Methods and findings
In the present nationwide cohort study, we identified all individuals in Sweden with a lower or upper gastrointestinal (GI) biopsy of normal mucosa during 1965-2016 (exposed, n=200,495 and 257,192 for lower and upper GI biopsy, respectively), their individually matched population references (n=989,484 and 1,268,897), and unexposed full siblings (n=221,179 and 274,529). Flexible parametric model estimated hazard ratio (HR) as an estimate of the association between a GI biopsy of normal mucosa and IBD as well as cumulative incidence of IBD, with 95% confidence interval (CI). The first 6 months after GI biopsy were excluded to avoid detection bias, surveillance bias or reverse causation. During a median follow-up time of ~10 years, 4,853 individuals with a lower GI biopsy of normal mucosa developed IBD (2.4%) compared to 0.4% of the population references. This corresponded to an incidence rate (IR) of 20.39 and 3.39 per 10,000 person-years in the respective groups or one extra estimated IBD case among 37 exposed individuals during the 30 years after normal GI biopsy. The exposed individuals had a persistently higher risk of overall IBD (average HR=5.56; 95%CI: 5.28-5.85), ulcerative colitis (UC, average HR=5.20; 95%CI: 4.85-5.59) and Crohn’s disease (CD, average HR=6.99; 95%CI: 6.38-7.66) than their matched population references. In the sibling comparison, average HRs were 3.27 (3.05-3.51) for overall IBD, 3.27 (2.96-3.61) for UC, and 3.77 (3.34-4.26) for CD. For individuals with an upper GI biopsy of normal mucosa, the average HR of CD was 2.93 (2.68-3.21) and 2.39 (2.10-2.73), compared with population references and unexposed full siblings, respectively. The increased risk of IBD persisted at least 30 years after cohort entry. Study limitations include lack of data on indications for biopsy and potential residual confounding from unmeasured risk or protective factors for IBD.
Conclusions
Endoscopic biopsy with normal mucosa was associated with an elevated IBD incidence for at least 30 years. This may suggest a substantial symptomatic period of IBD and incomplete diagnostic examinations in patients with early IBD.
