Jul 2026· Journal of the Royal Statistical Society, Series C: Applied Statistics· 0 citations
Medicine
TL;DR
A novel unified competing risks cure model, based on the cause-specific hazard approach, that satisfies the aforementioned desired properties is proposed and an application is illustrated using breast cancer data from the SEER cancer database.
Abstract
Cancer remains the second most prevalent cause of death in the United States, claiming 605,213 lives in 2021, surpassing COVID-19 deaths. The cancer mortality rate continued to decline between 2019 and 2020, dropping by 1.5%, marking a significant 33% decrease since 1991. This ongoing improvement primarily mirrors advances in treatment, allowing patients to achieve clinical remission and recovery. Now, a cancer patient is simultaneously exposed to the risk of primary cancer as well as other risks, such as other cancer(s) or other diseases, leading to a competing risks scenario. Analysis of survival data under competing risks and the presence of cured patients have been extensively studied individually, but there is limited work in the current literature that models the possibility of cure from one risk in the presence of competing risks. Moreover, such a model should allow for the possibility of cure from the cause-specific risk of the primary cancer; however, the overall survival probability should eventually approach zero, thereby incorporating the prevalent belief of eventual failure with certainty. We propose a novel unified competing risks cure model, based on the cause-specific hazard approach, that satisfies the aforementioned desired properties. The conditions required to establish model identifiability are studied in detail. To find the maximum likelihood estimates of the model parameters, a computationally efficient expectation maximization algorithm is developed. An extensive simulation study is carried out to demonstrate the performance of the proposed model and estimation method under different parameter settings and in the presence of multiple competing risks. Finally, an application is illustrated using breast cancer data from the SEER cancer database.
Cure models have become increasingly popular over the last couple of decades. An appealing element of cure models is the idea that part of the population is immune to the event of interest. We argue that, in medical applications, the use of cure models is limited. Thus, true cure cannot exist if the event of interest includes death, as death is inevitable, and if death is excluded then competing risks must be accounted for. In this case, we find it more natural to model the cumulative incidence of both the event of interest and competing events over time, avoiding unreliable estimates at infinity and using observed data. Further, we point out two more technical difficulties with cure models arising, first, from the fact that cure models rely on identifying plateaus in survival curves at the tail, where data may be sparse and unreliable and, second, the mixture cure model faces issues with practical identifiability of covariate effects in the incidence model (probability of cure), especially alongside proportional hazards assumptions in the latency model (survival model, conditionally on not being cured). We also comment on hybrid extensions of the classical single event cure model that allow for both competing risks and a cured fraction. We support our arguments with real and simulated data. Full data and code are available online.
Hein Putter, P. K. Andersen· Lifetime Data Analysis· 0 citations
Leukemia is a hematological malignancy with high mortality, where deaths may arise from leukemia or other causes, leading to competing risks. This study aims to model event-specific mortality by integrating the Extended Cox model with time-dependent covariates into the Cause-Specific Hazard (CSH) framework. Secondary data from 130 leukemia patients at RSUD dr. H. Koesnadi Bondowoso (2022–2024) were analyzed, with survival time as the response and two competing events. Parameter estimation was conducted using maximum partial likelihood within a competing risks structure, optimized via Newton–Raphson iteration. The results show that chronic disease significantly increases the hazard of leukemia-related death (HR = 4.60; 95% CI: 1,46-14,44), while sex (HR = 0.30; 95% CI: 0,12-0,73) and body mass index (HR = 0.82; 95% CI: 0,73-0,91) significantly influence mortality due to other causes. These findings demonstrate that the CSH framework provides more accurate and clinically interpretable estimates by distinguishing event-specific risks. This approach supports improved risk stratification and evidence-based clinical decision-making in leukemia management.
Mohamad Fatekurohman, Ilma Safitri· ZERO Jurnal Sains Matematika...· 0 citations
Background As CRC survival improves, the shifting contributions of metastatic and non-cancer causes to mortality remain poorly characterized, with implications for survivorship care and public health policy. This study aimed to examine temporal trends in CRC mortality with selected contributing conditions from 1999 to 2023 and project rates through 2040 across demographic and geographic subgroups in the United States. Methods This population-based cohort study utilized mortality data from the Centers for Disease Control and Prevention Wide-ranging Online Data for Epidemiologic Research (CDC WONDER) database. The study included 1,323,609 US residents aged 25 years or older who died from 1999 through 2023 with colorectal cancer listed as the underlying cause of death. We analyzed selected contributing conditions recorded in the multiple cause-of-death field, including heart failure, ischemic heart disease, liver metastasis, lung metastasis, pulmonary embolism, and sepsis. Age-adjusted mortality rates (AAMRs) were calculated per 100,000 persons. Temporal trends were analyzed using Joinpoint regression to estimate annual percent change (APC) and average annual percent change (AAPC). Future mortality rates were projected to 2040 using autoregressive integrated moving average (ARIMA) modeling. Results Overall CRC AAMR declined from 32.06 in 1999 to 19.57 in 2023 (AAPC,−2.08%). Recent significant increases were observed in liver metastasis mortality from 2016 to 2023 (APC: 2.89%), lung metastasis mortality from 2017 to 2023 (APC: 2.08%), pulmonary embolism mortality from 2012 to 2023 (APC: 3.59%), and heart failure mortality from 2013 to 2023 (APC: 3.16%). These trends were most pronounced among adults aged 35–64 years, non-Hispanic Black individuals, and residents of the Southern US. Model-based projections indicate that overall lung metastasis mortality will continue to increase through 2040, whereas liver metastasis mortality will peak in 2028 and subsequently decline. In pre-pandemic sensitivity analyses, the post-2012 increase in PE mortality persisted, whereas recent increases in IHD, HF, liver metastasis, and sepsis mortality were attenuated or no longer statistically significant. Conclusions Despite declining overall CRC mortality, recent increases were observed in several metastatic and noncancer contributing conditions. However, pre-pandemic sensitivity analyses suggested that some late-period changes may have been amplified during the COVID-19 era, whereas the increase in PE mortality clearly preceded the pandemic.
Zi-Chen He, Ya-Dong Chen, Yu-Xing Hu et al.· Frontiers in Public Health· 0 citations
OBJECTIVE
Major successes in improving health in the United States during the past century have occurred as our nation moved through the epidemiologic transition from high infectious disease mortality to predominantly chronic disease mortality. The objective of this study was to identify successes in improving America's health in the first 2 decades of the 21st century.
METHODS
We identified leading causes of death among US adults with age-adjusted mortality rates that declined by ≥20% from 2000 to 2019.
RESULTS
Eleven disease categories achieved a ≥20% mortality reduction, including the leading causes of death in the United States (heart disease, stroke, cancer) and 2 infectious diseases. Seven of the 11 "success" conditions were forms of cancer, showing progress in screening, early diagnosis, treatment, and cure. A cautionary note is warranted for conditions with increasing cause-specific mortality, such as brain diseases, suicide, drug overdose, accidental deaths, and liver disease.
CONCLUSIONS
The impact of research innovation translated into prevention and medical care is clearer with each passing decade. Similar strategies that prioritize behavioral health will be needed to reverse conditions with worsening mortality. Successful public health strategies have continued to reduce mortality from somatic "below-the-neck" causes, but parallel strategies are needed to address mental health, substance use, health behaviors, and healthy aging.
George Rust, Tyra Dark, R. Eke et al.· Public health reports (1974)· 0 citations
This research demonstrates the feasibility of using big data to conduct case-control analyses to identify associations between possible risk factors and cancers and demonstrates the limitations of the traditional epidemiological approach by requiring less effort, time, and cost.
Summary Background Cancer prevalence is the number of people alive with a past cancer diagnosis in a specified number of previous years (e.g., last 5 or 30 years). This study estimates 1- to 30-year cancer prevalence in Australia for each year in 2025–2050, for 24 cancer types, the group of remaining cancers, and for all cancers combined. Methods We used validated methods to estimate prevalence as a function of incidence and survival, using tabulated data from the Australian Institute of Health and Welfare and incorporating the effect of influential cancer-specific factors. The number of people living with cancer (cancers not yet cured) is estimated using the time-to-cure method. Findings The 30-year prevalence is projected to increase by 57.1% from 1,666,020 (95% uncertainty interval [UI]: 1,553,825–1,784,900) in 2025 to 2,617,016 (95% UI: 2,333,949–2,947,174) in 2050. For people aged 80+ years, 30-year prevalence is projected to increase by 111.0% from 481,079 (95% UI: 448,799–515,286) in 2025 to 1,015,061 (95% UI: 917,670–1,125,036) in 2050. Breast cancer is projected to be the most prevalent cancer in Australia in 2050, followed by prostate, melanoma and colorectal cancer. For 30-year prevalence in 2050, 43.9% of people (1,149,364; 95% UI: 1,103,165–1,238,377) are estimated to be living with cancer (cancers not yet cured) and requiring initial treatment or ongoing care. Interpretation A substantial increase in the number of people with a past cancer diagnosis in Australia is expected in 2025–2050. Expansion of appropriate services to meet the demand will be a key challenge for the health system in Australia. Funding This work was not supported by a dedicated research grant. This work and open access publishing were supported by the 10.13039/501100001102Cancer Council NSW, through funding to the Daffodil Centre. KC is a recipient of a Fellowship from the 10.13039/501100000925National Health and Medical Research Council of Australia (APP1194679). JS is a recipient of a Cancer Institute NSW Career Development Fellowship (2022/CDF1154).
Q. Luo, David P. Smith, Michael David et al.· The Lancet Regional Health -...· 0 citations
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