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Hope you are all doing great and staying safe during this pandemic. Here is my question about defining covariates for Cox regression. There are structures where I would like to model their reliability using the Cox regression. The data for the structures is the time (number of years) the structures stayed in a given condition rating (CR) (condition rating 5, 6, 7, ...). Each CR definition and damage severity is different. For example, a structure stayed 10 years in CR 8 then dropped to CR 7, and then to CR 6, and so on. In each of the years for a given CR, salt is used as a deicing agent and the amount of salt in each year is different. How should I define the covariate "Salt_Usage" for each structure CRs? Do I average the salt used during the years the structure is in a given CR? Do I lose any information when I use the average "Salt_Usage"? Is there any better alternative for defining the "Salt_Usage" covariate?

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As the salt exposure varies from year to year, it is best to represent it in some way as a time-dependent covariate. This vignette shows how to accomplish that in R, by using one row of data for each structure and period of time, with start and stop times and status indicated for each row. You should consider, based on your understanding of the subject matter, whether you should only consider the prior year's salt exposure, or model the salt exposure in some cumulative measure starting from the beginning of time for the structure.

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