We are trying to find if there is an association between postoperative pulmonary complications (PPCs) and overall survival in a cohort of 417 patients. In Kaplan-Meier there is a significant difference in overall survival between patients with and without PPCs. After testing the proportional hazards assumption in cox regression (both through visual analysis and through log minus log plot) we found that our data failed to meet the assumptions. The way I interpret this, it means that the hazard of dying due to a postoperative pulmonary complication varies over time? I'm trying to figure out how to perform a survival analysis now that I can't use the standard cox regression.

From what I understand I could use time dependent coefficients (the same as variables in this example?) but I don't really understand what is meant by that or how I would do it in SPSS. Does it mean I turn my PPCs variable into a time dependent variable and then run the cox regression analysis the way I would if my data would have met the assumptions or how do I do it?

I would be really thankful for guidance or corrections if I have misunderstood something! I'm a PhD student and I don't have much experience in statistics so explain it to me like I'm 5 (a smart 5-year-old!)