Cox's proportional hazards model is often t to grouped survival data, i.e. occurrence/exposure data over given time intervals and covariate strata. We derive a Sheppard correction for the bias in the grouped data analogue of Cox's maximum partial likelihood estimator. This is done via a large sample theory in which the covariate strata and time intervals shrink as the sample size increases.

Recently, a new optimizer, called the Aquila Optimizer (AO), was developed to solve different optimization problems. Although AO has significant performance in various problems, like other algorithms, suffers from certain limitations its search mechanism, such as local optima stagnation and convergence speed. This is general problem that faces almost all which can be solved by enhancing process...

A survival analysis on a data set of 295 early breast cancer patients is performed in this study. A new proportional hazards model, hypertabastic model was applied in the survival analysis. We assume a proportional hazards model, and select two sets of risk factors for death and metastasis for breast cancer patients respectively by using standard variable selection methods. To evaluate the perf...

Objectives The Cox proportional hazards (PH) model is commonly used in randomised clinical trials (RCTs) to assess a treatment effect after adjusting for known prognostic factors. However, the Cox model requires that a covariate effect is constant over time. Violation of this assumption invalidates the simple Cox model. Various PH checks exist, some in the form of statistical tests and some emp...

There are several statistical methods for time-to-event analysis, among which is the Cox proportional hazards model that is most commonly used. However, when the absolute change in risk, instead of the risk ratio, is of primary interest or when the proportional hazard assumption for the Cox proportional hazards model is violated, an additive hazard regression model may be more appropriate. In t...

We fit a Cox proportional hazards (PH) model to interval-censored survival data by first subdividing each individual's failure interval into nonoverlapping sub-intervals. Using the set of all endpoints in set, those that fall are then used as cut points for Each sub-interval has an accompanying weight calculated from parametric Weibull based on current parameter estimates. A weighted PH is with...