Comparison of two treatments in the presence of competing risks.

Competing risks data arise frequently in clinical trials, and a common problem encountered is the overall homogeneity between two groups. In competing risks analysis, when the proportional subdistribution hazard assumption is violated or two cumulative incidence function (CIF) curves cross; currently, the most commonly used testing methods, for example, the Gray test and the Pepe and Mori test, may lead to a significant loss of statistical testing power. In this article, we propose a testing method based on the area between the CIF curves (ABC). The ABC test captures the difference over the whole time interval for which survival information is available for both groups and is not based on any special assumptions regarding the underlying distributions. The ABC test was also extended to test short-term and long-term effects. We also consider a combined test and a two-stage procedure based on this new method, and a bootstrap resampling procedure is suggested in practice to approximate the limiting distribution of the combined test and two-stage test. An extensive series of Monte Carlo simulations is conducted to investigate the power and the type I error rate of the methods. In addition, based on our simulations, our proposed TS, Comb, and ABC tests have a relatively high power in most situations. In addition, the methods are illustrated using two different datasets with different CIF situations.

Assessing treatment benefit with competing risks not affected by the randomized treatment.

The comparison of overall survival curves between treatment arms will always be of interest in a randomized clinical trial involving a life-shortening disease. In some settings, the experimental treatment is only expected to affect the deaths caused by the disease, and the proportion of deaths caused by the disease is relatively low. In these settings, the ability to assess treatment-effect differences between Kaplan-Meier survival curves can be hampered by the large proportion of deaths in both arms that are unrelated to the disease. To address this problem, frequently displayed are cause-specific survival curves or cumulative incidence curves, which respectively censor and immortalize events (deaths) not caused by the disease. However, the differences between the experimental and control treatment arms for these curves overestimate the difference between the overall survival curves for the treatment arms and thus could result in overestimation of the benefit of the experimental treatment for the patients. To address this issue, we propose new estimators of overall survival for the treatment arms that are appropriate when the treatment does not affect the non-disease-related deaths. These new estimators give a more precise estimate of the treatment benefit, potentially enabling future patients to make a more informed decision concerning treatment choice. We also consider the case where an exponential assumption allows the simple presentation of mortality rates as the outcome measures. Applications are given for estimating overall survival in a prostate-cancer treatment randomized clinical trial, and for estimating the overall mortality rates in a prostate-cancer screening trial.

Establishment and validation of a competitive risk model for predicting cancer-specific survival in patients with osteosarcoma: a population-based study.

BACKGROUND: Osteosarcoma is the most common primary bone tumor with a poor prognosis. The aim of this study was to establish a competitive risk model nomogram to predict cancer-specific survival in patients with osteosarcoma. METHODS: Patient data was obtained from the Surveillance, Epidemiology, and End Results database in the United States. A sub-distribution proportional hazards model was used to analyze independent risk factors affecting cancer-specific mortality (CSM) in osteosarcoma patients. Based on these risk factors, a competitive risk model was constructed to predict 1-year, 3-year, and 5-year cancer-specific survival (CSS) in osteosarcoma patients. The reliability and accuracy of the nomogram were evaluated using the concordance index (C-index), the area under the receiver operating characteristic curve (AUC), and calibration curves. RESULTS: A total of 2900 osteosarcoma patients were included. The analysis showed that age, primary tumor site, M stage, surgery, chemotherapy, and median household income were independent risk factors influencing CSM in patients. The competitive risk model was constructed to predict CSS in osteosarcoma patients. In the training and validation sets, the C-index of the model was 0.756 (95% CI 0.725-0.787) and 0.737 (95% CI 0.717-0.757), respectively, and the AUC was greater than 0.7 for both. The calibration curves also demonstrated a high consistency between the predicted survival rates and the actual survival rates, confirming the accuracy and reliability of the model. CONCLUSION: We established a competitive risk model to predict 1-year, 3-year, and 5-year CSS in osteosarcoma patients. The model demonstrated good predictive performance and can assist clinicians and patients in making clinical decisions and formulating follow-up strategies.

Lifespans of Twins: Does Zygosity Matter?

Studies with twins provide fundamental insights to lifespans of humans. We aim to clarify if monozygotic and dizygotic twin individuals differ in lifespan, that is, if zygosity matters. We investigate whether a possible difference in mortality after infancy between zygosities is stable in different age cohorts, and whether the difference remains when twins with unknown zygosity are taken into account. Further, we compare the distribution of long-livers, that is, the upper-tail of the lifespan distribution, between monozygotic and same-sex dizygotic twin individuals. The Danish Twin Registry provides a nationwide cohort of 109,303 twins born during 1870 to 1990 with valid vital status. Standard survival analysis is used to compare mortality in monozygotic and dizygotic twin individuals and twin individuals with unknown zygosity. The mortality of monozygotic and dizygotic twin individuals differs slightly after taking into consideration effects of birth- and age-cohorts, gender differences, and that twins are paired. However, no substantial nor systematic differences remain when taking twins with unknown zygosity into account. Further, the distribution of long-livers is very similar by zygosity, suggesting the same mortality process. The population-based and oldest twin cohort ever studied suggests that monozygotic and dizygotic twins have similar lifespans.