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The log-rank test and the Cox proportional hazards model are commonly used to compare time-to-event data in clinical trials, as they are most powerful under proportional hazards. But there is a loss of power if this assumption is violated,…
Harrel's concordance index is a commonly used discrimination metric for survival models, particularly for models where the relative ordering of the risk of individuals is time-independent, such as the proportional hazards model. There are…
Survival models are a popular tool for the analysis of time to event data with applications in medicine, engineering, economics, and many more. Advances like the Cox proportional hazard model have enabled researchers to better describe…
Identifying causal relationships for a treatment intervention is a fundamental problem in health sciences. Randomized controlled trials (RCTs) are considered the gold standard for identifying causal relationships. However, recent…
Survival analysis, or time-to-event analysis, is an important and widespread problem in healthcare research. Medical research has traditionally relied on Cox models for survival analysis, due to their simplicity and interpretability. Cox…
In studies of time-to-event outcomes with unmeasured heterogeneity, the hazard ratio for treatment is known to have a complex causal interpretation. Accelerated failure time (AFT) models, which assess the effect on the survival time ratio…
The hazard ratio is routinely used as a summary measure to assess the treatment effect in clinical trials with time-to-event endpoints. It is frequently assumed as constant over time although this assumption often does not hold. When the…
The proportional hazards assumption in the commonly used Cox model for censored failure time data is often violated in scientific studies. Yang and Prentice (2005) proposed a novel semiparametric two-sample model that includes the…
One of the most common ways researchers compare survival outcomes across treatments when confounding is present is using Cox regression. This model is limited by its underlying assumption of proportional hazards; in some cases, substantial…
Time-to-event analysis often relies on prior parametric assumptions, or, if a non-parametric approach is chosen, Cox's model. This is inherently tied to the assumption of proportional hazards, with the analysis potentially invalidated if…
We consider a class of semiparametric regression models which are one-parameter extensions of the Cox [J. Roy. Statist. Soc. Ser. B 34 (1972) 187-220] model for right-censored univariate failure times. These models assume that the hazard…
The problem of how to best select variables for confounding adjustment forms one of the key challenges in the evaluation of exposure effects in observational studies, and has been the subject of vigorous recent activity in causal inference.…
Tests for proportional hazards assumption concerning specified covariates or groups of covariates are proposed. The class of alternatives is wide: log-hazard rates under different values of covariates may cross, approach, go away. The data…
For the analysis of time-to-event data, frequently used methods such as the log-rank test or the Cox proportional hazards model are based on the proportional hazards assumption, which is often debatable. Although a wide range of parametric…
The Risk Ratio (RR) is the ratio of the outcome among the exposed to risk of the outcome among the unexposed. This is a simple concept, which makes one wonder why it has not gained the same popularity as the odds ratio. Using logistic…
Frailty models are often the model of choice for heterogeneous survival data. A frailty model contains both random effects and fixed effects, with the random effects accommodating for the correlation in the data. Different estimation…
The Cox regression, a semi-parametric method of survival analysis, is extremely popular in biomedical applications. The proportional hazards assumption is a key requirement in the Cox model. To accommodate non-proportional hazards, we…
While well-established methods for time-to-event data are available when the proportional hazards assumption holds, there is no consensus on the best inferential approach under non-proportional hazards (NPH). However, a wide range of…
Survivorship analysis allows to statistically analyze situations that can be modeled as waiting times to an event. These waiting times are characterized by the cumulative hazard rate, which can be estimated by the Nelson-Aalen estimator or…
Survival analysis provides a well-established framework for modeling time-to-event data, with hazard and survival functions formally defined as population-level quantities. In applied work, however, these quantities are often interpreted as…