Proportional hazards modeling of time-dependent covariates using linear regression: a case study [mine power cable reliability]

In the proportional hazards model, the effect of a covariate is assumed to be time-invariant. In this paper a graphical method based on a linear regression model (LRM) is used to test whether this assumption is realistic. The variation in the effect of a covariate is plotted against time. The slope of this plot indicates the nature of the influence of a covariate over time. A covariate is time-dependent if a drastic change in the slope of the plot is found and the time-point, at which this drastic change occurs provides guideline in redefining a time-dependent covariate into two or more time-independent covariates. This method is applied to failure data of cables used for supplying power to electric mine loaders. The results obtained by applying only the proportional hazards model were misleading as the graphical method based on the LRM showed that one covariate was highly time-dependent. This graphical method should be used to supplement the proportional hazards model, not as a separate method. This avoids misinterpretation of the influence of a time-dependent covariate in the proportional hazards model. The proportional hazards model should be used to identify the most important covariates, while the LRM should be used as an explanatory tool to check the consistency of the influence of the covariates. The LRM involves matrix computations which can be quite time consuming for large data-sets. Also, tests for the statistically significant effect of a covariate are not yet well established in the model