The classical Cox proportional hazards model is a benchmark approach to analyze continuous survival times in the presence of covariate information. In a number of applications, there is a need to relax one or more of its inherent assumptions, such as linearity of the predictor or the proportional hazards property. Also, one is often interested in jointly estimating the baseline hazard together ...

The accelerated failure time (AFT) model is an important alternative to the Cox proportional hazards model (PHM) in survival analysis. For multivariate failure time data we propose to use frailties to explicitly account for possible correlations (and heterogeneity) among failure times. An EM-like algorithm analogous to that in the frailty model for the Cox model is adapted. Through simulation i...

MOTIVATION Univariate Cox regression (COX) is often used to select genes possibly linked to survival. With non-proportional hazards (NPH), COX could lead to under- or over-estimation of effects. The effect size measure c=P(T(1)<T(0)), i.e. the probability that a person randomly chosen from group G(1) dies earlier than a person from G(0), is independent of the proportional hazards (PH) assumptio...

Proportional hazards regression model assumes that the covariates affect the hazard function through a link function and an index which is a linear function of the covariates. Traditional approaches, such as the Cox proportional hazards model, focus on estimating the unknown index by assuming a known link function between the log-hazard function and covariates. A linear link function is often e...

BACKGROUND There are numerous unanswered questions in the application of artificial neural network models for analysis of survival data. In most studies, independent variables have been studied as qualitative dichotomous variables, and results of using discrete and continuous quantitative, ordinal, or multinomial categorical predictive variables in these models are not well understood in compar...

We propose a new sparse estimation method for Cox (1972) proportional hazards models by optimizing an approximated information criterion. The main idea involves approximation of the ℓ0 norm with a continuous or smooth unit dent function. The proposed method bridges the best subset selection and regularization by borrowing strength from both. It mimics the best subset selection using a penalized...

The Cox proportional hazards model is frequently used in medical statistics. The standard methods for fitting this model rely on the assumption of independent censoring. Although this is sometimes plausible, we often wish to explore how robust our inferences are as this untestable assumption is relaxed. We describe how this can be carried out in a way that makes the assumptions accessible to al...

BACKGROUND Medical practitioners use survival models to explore and understand the relationships between patients' covariates (e.g. clinical and genetic features) and the effectiveness of various treatment options. Standard survival models like the linear Cox proportional hazards model require extensive feature engineering or prior medical knowledge to model treatment interaction at an individu...