Simultaneous monitoring for regression coefficients and baseline hazard profile in Cox modeling of time-to-event data

Summary The Cox model is the most popular tool for analyzing time-to-event data. The nonparametric baseline hazard function can be as important as the regression coefficients in practice, especially when prediction is needed. In the context of stochastic process control, we propose a simultaneous monitoring method that combines a multivariate control chart for the regression coefficients and a profile control chart for the cumulative baseline hazard function that allows for data blocks of possibly different censoring rates and sample sizes. The method can detect changes in either the parametric or the nonparametric part of the Cox model. In simulation studies, the proposed method maintains its size and has substantial power in detecting changes in either part of the Cox model. An application in lymphoma survival analysis in which patients were enrolled by 2-month intervals in the Surveillance, Epidemiology, and End Results program identifies data blocks with structural model changes.

Proportional hazard model for cutting tool recovery in machining

The proportional hazard model is a statistical method capable of including information on environmental and operating conditions. In machining, in the reliability field of a cutting tool, the interest of using proportional hazard model is highlighted. On one hand, the environmental and operating conditions are described and taken into account as explanatory variables. Three covariates are considered, namely, the vibration signal, the hardness material, and the lubrication/cooling. On the other hand, a new baseline hazard function is designed according to phenomena of tiny tool breakage followed by a self-sharpening process. This latter phenomenon, which can be considered as a rare event, prompted us to study extreme value theory to propose an adequate baseline hazard function. The newly obtained baseline hazard function will be named generalized extreme value proportional hazard model. This function is obtained thanks to the Gumbel function and has the property to be non-monotonic, an increasing then decreasing function. An alternative option as a baseline hazard function, based on the flexible Weibull distributions, is also proposed. Results produced in this article show the impact of all these variables on the surface roughness of the machined parts. According to reliability studies, the premature replacement of the cutting tool implying financial losses can be delayed. This may be of particular significance and benefit, in terms of sustainable development, in the case of mass production, by limiting the frequency of tool replacement.

Bayesian Survival Approach to Analyzing the Risk of Recurrent Rail Defects

This paper develops a Bayesian framework to explore the impact of different factors and to predict the risk of recurrence of rail defects, based upon datasets collected from a US Class I railroad between 2011 and 2016. To this end, this study constructs a parametric Weibull baseline hazard function and a proportional hazard (PH) model under a Gaussian frailty approach. The analysis is performed using Markov chain Monte Carlo simulation methods and the fit of the model is checked using a Cox–Snell residual plot. The results of the model show that the recurrence of a defect is correlated with different factors such as the type of rail defect, the location of the defect, train speed limit, the number of geometry defects in the last three years, and the weight of the rail. First, unlike the ordinary PH model in which the occurrence times of rail defects at the same location are assumed to be independent, a PH model under frailty induces the correlation between times to the recurrence of rail defects for the same segment, which is essential in the case of recurrent events. Second, considering Gaussian frailties is useful for exploring the influence of unobserved covariates in the model. Third, integrating a Bayesian framework for the parameters of the Weibull baseline hazard function as well as other parameters provides greater flexibility to the model. Fourth, the findings are useful for responsive maintenance planning, capital planning, and even preventive maintenance planning.

Simulating Duration Data for the Cox Model

The Cox proportional hazards model is a popular method for duration analysis that is frequently the subject of simulation studies. However, no standard method exists for simulating durations directly from its data generating process because it does not assume a distributional form for the baseline hazard function. Instead, simulation studies typically rely on parametric survival distributions, which contradicts the primary motivation for employing the Cox model. We propose a method that generates a baseline hazard function at random by fitting a cubic spline to randomly drawn points. Durations drawn from this function match the Cox model’s inherent flexibility and improve the simulation’s generalizability. The method can be extended to include time-varying covariates and non-proportional hazards.