In oncology, \"survival curves\" frequently appear in journal articles and meeting presentations. The most common labels on survival curves are: Overall Survival, Relapse Free Survival, Progression Free Survival, Distant Metastasis Free Survival and Local and/or Regional Control. Unfortunately, consistency in the definition of an event differs between authors for the same prescribed survival analyses. Furthermore, the quality of a survival curves can be greatly impacted by the methodology used for endpoint selection. This paper will briefly explain widely used names and event endpoints for survival analyses in a way that will help radiation oncologists consistently present and interpret experimental findings that influence clinical practice decisions.

Clinical trials with random assignment of treatment provide evidence about causal effects of an experimental treatment compared to standard care. However, when disease processes involve multiple types of possibly semi-competing events, specification of target estimands and causal inferences can be challenging. Intercurrent events such as study withdrawal, the introduction of rescue medication, and death further complicate matters. There has been much discussion about these issues in recent years, but guidance remains ambiguous. Some recommended approaches are formulated in terms of hypothetical settings that have little bearing in the real world. We discuss issues in formulating estimands, beginning with intercurrent events in the context of a linear model and then move on to more complex disease history processes amenable to multistate modeling. We elucidate the meaning of estimands implicit in some recommended approaches for dealing with intercurrent events and highlight the disconnect between estimands formulated in terms of potential outcomes and the real world.

The conditional survival function of a time-to-event outcome subject to censoring and truncation is a common target of estimation in survival analysis. This parameter may be of scientific interest and also often appears as a nuisance in nonparametric and semiparametric problems. In addition to classical parametric and semiparametric methods (e.g., based on the Cox proportional hazards model), flexible machine learning approaches have been developed to estimate the conditional survival function. However, many of these methods are either implicitly or explicitly targeted toward risk stratification rather than overall survival function estimation. Others apply only to discrete-time settings or require inverse probability of censoring weights, which can be as difficult to estimate as the outcome survival function itself. Here, we employ a decomposition of the conditional survival function in terms of observable regression models in which censoring and truncation play no role. This allows application of an array of flexible regression and classification methods rather than only approaches that explicitly handle the complexities inherent to survival data. We outline estimation procedures based on this decomposition, empirically assess their performance, and demonstrate their use on data from an HIV vaccine trial. Supplementary materials for this article are available online.

Composite endpoints defined as the time to the earliest of two or more events are often used as primary endpoints in clinical trials. Component-wise censoring arises when different components of the composite endpoint are censored differently. We focus on a composite of death and a non-fatal event where death time is right censored and the non-fatal event time is interval censored because the event can only be detected during study visits. Such data are most often analysed using methods for right censored data, treating the time the non-fatal event was first detected as the time it occurred. This can lead to bias, particularly when the time between assessments is long. We describe several approaches for estimating the event-free survival curve and the effect of treatment on event-free survival via the hazard ratio that are specifically designed to handle component-wise censoring. We apply the methods to a randomized study of breastfeeding versus formula feeding for infants of mothers infected with human immunodeficiency virus.

Graft failure and recipient death with functioning graft are important competing outcomes after kidney transplantation. Risk prediction models typically censor for the competing outcome thereby overestimating the cumulative incidence. The magnitude of this overestimation is not well described in real-world transplant data. This retrospective cohort study analyzed data from the European Collaborative Transplant Study (n = 125 250) and from the American Scientific Registry of Transplant Recipients (n = 190 258). Separate cause-specific hazard models using donor and recipient age as continuous predictors were developed for graft failure and recipient death. The hazard of graft failure increased quadratically with increasing donor age and decreased decaying with increasing recipient age. The hazard of recipient death increased linearly with increasing donor and recipient age. The cumulative incidence overestimation due to competing risk-censoring was largest in high-risk populations for both outcomes (old donors/recipients), sometimes amounting to 8.4 and 18.8 percentage points for graft failure and recipient death, respectively. In our illustrative model for posttransplant risk prediction, the absolute risk of graft failure and death is overestimated when censoring for the competing event, mainly in older donors and recipients. Prediction models for absolute risks should treat graft failure and death as competing events.

The win ratio has been increasingly used in trials with hierarchical composite endpoints. While the outcomes involved and the rule for their comparisons vary with the application, there is invariably little attention to the estimand of the resulting statistic, causing difficulties in interpretation and cross-trial comparison. We make the case for articulating the estimand as a first step to win ratio analysis and establish that the root cause for its elusiveness is its intrinsic dependency on the time frame of comparison, which, if left unspecified, is set haphazardly by trial-specific censoring. From the statistical literature, we summarize two general approaches to overcome this uncertainty-a nonparametric one that pre-specifies the time frame for all comparisons, and a semiparametric one that posits a constant win ratio across all times-each with publicly available software and real examples. Finally, we discuss unsolved challenges, such as estimand construction and inference in the presence of intercurrent events.

Latent classification model is a class of statistical methods for identifying unobserved class membership among the study samples using some observed data. In this study, we proposed a latent classification model that takes a censored longitudinal binary outcome variable and uses its changing pattern over time to predict individuals\' latent class membership. Assuming the time-dependent outcome variables follow a continuous-time Markov chain, the proposed method has two primary goals: (1) estimate the distribution of the latent classes and predict individuals\' class membership, and (2) estimate the class-specific transition rates and rate ratios. To assess the model\'s performance, we conducted a simulation study and verified that our algorithm produces accurate model estimates (ie, small bias) with reasonable confidence intervals (ie, achieving approximately 95% coverage probability). Furthermore, we compared our model to four other existing latent class models and demonstrated that our approach yields higher prediction accuracies for latent classes. We applied our proposed method to analyze the COVID-19 data in Houston, Texas, US collected between January first 2021 and December 31st 2021. Early reports on the COVID-19 pandemic showed that the severity of a SARS-CoV-2 infection tends to vary greatly by cases. We found that while demographic characteristics explain some of the differences in individuals\' experience with COVID-19, some unaccounted-for latent variables were associated with the disease.

Methods for designing and analyzing multiple arms survival trials that incorporate patient\'s treatment choice are needed. In these trials, patients are randomized into two groups, random and choice. Participants in the choice group choose their treatment, which is not a current standard practice in randomized clinical trials. In this paper, we propose a new method based on the likelihood function to design and analyze these trials with time to event outcomes in the presence of non-informative right censoring. We use simulations to evaluate the methods for Weibull outcomes, complete and censored. Finally, we provide an illustration for designing a study in which we discuss some design considerations and demonstrate the methods.

Data analysis methods for the study of treatments or exposures in relation to a clinical outcome in the presence of competing risks have a long history, often with inference targets that are hypothetical, thereby requiring strong assumptions for identifiability with available data. Here data analysis methods are considered that are based on single and higher dimensional marginal hazard rates, quantities that are identifiable under standard independent censoring assumptions. These lead naturally to joint survival function estimators for outcomes of interest, including competing risk outcomes, and provide the basis for addressing a variety of data analysis questions. These methods will be illustrated using simulations and Women\'s Health Initiative cohort and clinical trial data sets, and additional research needs will be described.

Chronic progressive lymphedema (CPL) is a prevalent and progressive disease in Rhenish German draught horses. The objective of our follow-up study was to evaluate the heritability of this disease in Rhenish German draught horses using pedigree-based and genomic relationship matrices. We employed linear and threshold animal models. Models included the random animal effect and effects of breeding association, coat colour, sex, and age within sex, and farm-related factors, on CPL scores. In addition, we estimated heritabilities in models assuming censoring for data when horses were below an age of 1-15 years. The heritabilities of CPL scores across all ages were 0.595 ± 0.131 and 0.482 ± 0.105 in the threshold and linear animal model with pedigree-based relationship matrices, respectively. The restriction of data to horses with a minimum age at examination or accounting for censored data in younger animals showed an increase in heritabilities of CPL scores up to 0.788 ± 0.168 (threshold model) and 0.752 ± 0.153 (linear model) at an age of 7-8 years. Analyses including genomic relationship matrices yielded very similar estimates, but with smaller standard errors than pedigree-based analyses. Heritabilities in threshold models for CPL prevalence (CPL-bin-score) and the number of affected limbs (CPL-bin-sum) were 0.176-0.189 ± 0.061-0.064 and 0.375-0.433 ± 0.164-0.170, respectively. We were able to show moderately to highly positive genetic correlations between the CPL score and cannon bone circumference (0.529-0.825), height at withers (0.338-0.555), and skinfold thickness (0.241-0.517). Using the dichotomous trait for the CPL score and the genomic relationship matrix resulted in corresponding estimates of 0.868, 0.793, and 0.784, respectively. This study showed the great importance of additive genetic variation influencing the expression of chronic progressive lymphedema in Rhenish German draught horses. Therefore, further research is warranted to implement breeding programmes in a small breeding population that exploit the potential of additive genetic differences among animals for reducing the prevalence and severity of lesions of this incurable disease.