Eternal Weibull Regression analysis for Evaluation of the Effects of Different Covariates on Retinal Redetachment following Retinal Detachment Surgery

To evaluate the effect of age, sex, type of surgery, extent of retinal detachment (RD), vitreous incarceration in wound, and myopic degeneration on the rate of retinal redetachment following RD surgery using eternal Weibull regression analysis. We performed a survival analysis on a multi-center randomized controlled trial conducted on patients with pseudophakic or aphakic RD to compare the anatomic outcome of scleral buckling vs primary vitrectomy alone. Patients were examined one week and then 1, 2, 4 and 6 months after the operations. We applied modification to the survival, density and hazard function and considered the two-parameter Weibull distribution for survival times. Herein we evaluated the appropriateness of the modified model vs unmodified model with and without the effects of covariates. The mean survival time for the unmodified model was 2920 days confirming the eternal nature of the survivor function whereas the mean survival time for the modified model was 43.06 days. In the absence of covariates, the eternal proportion in the modified model was estimated to be 0.73. Taking the effects of covariates into account, the modified model revealed that the risk of redetachment is 76% higher among males than females and is almost 4 times greater in eyes with myopic degeneration, while this risk was 2.6 times for males and 2.7 times for those with myopia in the unmodified model. Moreover, vitreous incarceration in the wound played a significant role in the unmodified model whereas it had been set aside in the modified model. Comparing the two final models showed the superiority of modified model: -2 log Ĺm - (-2 log Ĺ Um) = 46.274 (P<0.001). This study strongly suggests the benefit of using the modified over the unmodified model of eternal Weibull regression analysis in situations such as the present study in which some cases will have the event of interest whereas others will never have the event, given enough time.