Opposite sign for a parameter estimate in cox regression (freeze and thaw effect on reinforced concrete bridge deck surfaces)

Question

I would like to model the freeze and thaw effect on reinforced concrete bridge deck surfaces using Cox Regression. But the parameter estimate is negative which is the opposite of the reality. When the freeze and thaw cycles increase the concrete deck should degrade faster, but it has a negative sign in Cox regression. Other covariates I consider are snow days, salt used (tons/lane miles), span length, and structure length. These data are collected every year and it is not constant as well. There are some less than 20% missing values as well. A portion of the bridges is spanning on water and most with under highway. I calculated the VIF for these covariates under consideration and snow and freeze and thaw has VIF>30.

But even when the freeze and thaw are in the model on its own, the parameter estimate is negative. Could anyone point out if there is anything from the statistical point of view? Can I ignore this covariate and provide a reason that its estimate is with a negative sign which does not make sense from an engineering point of view. I have a minor in statistics but want to have your opinions.

Answer 1

Without knowing exactly how you coded your survival analysis I can't say for sure, but one possible reason for more freeze/thaw cycles appearing to be related to longer bridge survival is survivorship bias. I particularly recommend that you read the description of how Abraham Wald (of Wald Test fame) used survivorship bias to identify the parts of aircraft that needed increased protection during World War II.

A structure that hasn't failed yet will have undergone more freeze/thaw cycles than a structure that failed early in its life. Unless the analysis is set up properly, you thus might well find the counter-intuitive result that you report. More freeze/thaw cycles could well seem to predict a longer-lived structure.

To analyze this situation properly you need to perform survival analysis with time-dependent covariate values. In setting that up, you will need to be careful that the values represent those in place just before a structure is at risk of an event. Things like salt use, freeze/thaw cycles, etc should probably be coded as their accumulated values since the structure went into service. Your understanding of the subject matter might, however, indicate some other handling of those values. You might also need to consider including interactions among your predictors in your model.

Even with proper handling of time-dependent covariates, you might still find the same counter-intuitive result with respect to freeze/thaw cycles. If failure is driven in large part by something other than the number of freeze/thaw cycles, then it might be difficult to avoid survivorship bias with the number of cycles as a single predictor. If that's included as a predictor in a multiple regression, then a negative regression coefficient (HR < 1) might mean that the other covariates associated with freeze/thaw cycles have been credited with too strong an association with shorter survival in the model, and the negative coefficient for freeze/thaw cycles is effectively correcting for that.