Semi-parametric proportional intensity models robustness for right-censored recurrent failure data

This paper reports the robustness of the four proportional intensity (PI) models: Prentice–Williams–Peterson-gap time (PWP-GT), PWP-total time (PWP-TT), Andersen–Gill (AG), and Wei–Lin–Weissfeld (WLW), for right-censored recurrent failure event data. The results are beneficial to practitioners in anticipating the more favorable engineering application domains and selecting appropriate PI models. The PWP-GT and AG prove to be models of choice over ranges of sample sizes, shape parameters, and censoring severity. At the smaller sample size (U=60), where there are 30 per class for a two-level covariate, the PWP-GT proves to perform well for moderate right-censoring (P_c≤0.8), where 80% of the units have some censoring, and moderately decreasing, constant, and moderately increasing rates of occurrence of failures (power-law NHPP shape parameter in the range of 0.8≤δ≤1.8). For the large sample size (U=180), the PWP-GT performs well for severe right-censoring (0.8<P_c≤1.0), where 100% of the units have some censoring, and moderately decreasing, constant, and moderately increasing rates of occurrence of failures (power-law NHPP shape parameter in the range of 0.8≤δ≤2.0). The AG model proves to outperform the PWP-TT and WLW for stationary processes (HPP) across a wide range of right-censorship (0.0≤P_c≤1.0) and for sample sizes of 60 or more.