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The Cox regression model and its associated hazard ratio (HR) are frequently used for summarizing the effect of treatments on time to event outcomes. However, the HR's interpretation strongly depends on the assumed underlying survival…
Cox's proportional hazards model is one of the most popular statistical models to evaluate associations of exposure with a censored failure time outcome. When confounding factors are not fully observed, the exposure hazard ratio estimated…
The ratio of the hazard functions of two populations or two strata of a single population plays an important role in time-to-event analysis. Cox regression is commonly used to estimate the hazard ratio under the assumption that it is…
Aalen's linear hazard rate regression model is a useful and increasingly popular alternative to Cox' multiplicative hazard rate model. It postulates that an individual has hazard rate function $h(s)=z_1\alpha_1(s)+\cdots+z_r\alpha_r(s)$ in…
Given the limitations of using the Cox hazard ratio to summarize the magnitude of the treatment effect, alternative measures that do not have these limitations are gaining attention. One of the recently proposed alternative methods uses the…
The average hazard (AH), recently introduced by Uno and Horiguchi, represents a novel summary metric of event time distributions, conceptualized as the general censoring-free average person-time incidence rate on a given time window,…
The hazard ratio, typically estimated using Cox's famous proportional hazards model, is the most common effect measure used to describe the association or effect of a covariate on a time-to-event outcome. In recent years the hazard ratio…
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…
In observational studies, unmeasured confounders present a crucial challenge in accurately estimating desired causal effects. To calculate the hazard ratio (HR) in Cox proportional hazard models for time-to-event outcomes, two-stage…
Interval-censoring frequently occurs in studies of chronic diseases where disease status is inferred from intermittently collected biomarkers. Although many methods have been developed to analyze such data, they typically assume perfect…
Previous studies have shown that hazard ratios between treatment groups estimated with the Cox model are uninterpretable because the unspecified baseline hazard of the model fails to identify temporal change in the risk set composition due…
Prognostic models in survival analysis are aimed at understanding the relationship between patients' covariates and the distribution of survival time. Traditionally, semi-parametric models, such as the Cox model, have been assumed. These…
The Hazard Ratio (HR) is often reported as the main causal effect when studying survival data. Despite its popularity, the HR suffers from an unclear causal interpretation. As already pointed out in the literature, there is a built-in…
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…
Hazard ratios are often used to evaluate time to event outcomes, but they may be hard to interpret. A particular issue arise because hazards are typically estimated conditional on survival, i.e.\ on left truncated samples. Then, hazard…
Prevalent cohort sampling is commonly used to study the natural history of a disease when the disease is rare or it usually takes a long time to observe the failure event. It is known, however, that the collected sample in this situation is…
A class of estimating functions is introduced for the regression parameter of the Cox proportional hazards model to allow unknown failure statuses on some study subjects. The consistency and asymptotic normality of the resulting estimators…
Semi-parametric survival analysis methods like the Cox Proportional Hazards (CPH) regression (Cox, 1972) are a popular approach for survival analysis. These methods involve fitting of the log-proportional hazard as a function of the…
There remain theoretical gaps in deep neural network estimators for the nonparametric Cox proportional hazards model. In particular, it is unclear how gradient-based optimization error propagates to population risk under partial likelihood,…
While analysing time-to-event data, it is possible that a certain fraction of subjects will never experience the event of interest and they are said to be cured. When this feature of survival models is taken into account, the models are…