I am new to survival analysis and currently very confused regarding a model selection process (forward stepwise) in cox proportional hazard model.
What happens is basically the following step by step:
- I identified n number of statistically significant independent variables, and none of them were correlated with each other.
- I wanted to put one last variable, which has the largest effect on AIC reduction out of all the variables.
- However, this variable is also very insignificant (p-value of parameter is about 0.88).
- I checked the correlation of this variable with other independent variables in the model and could not find anything.
- Plotted against all to see if I observe any type of nonlinear dependence, still no pattern.
- Tried to look at vif as suggested on the internet but all seem to be smaller than 2.
From here on I am not sure how to proceed. While my statistically highly significant variables are reducing my AIC by something between 4 and 10, this particular statistically insignificant variable (which was a variable I thought should be in the model definitely before building the model, and the parameter relationship is as expected intuitively) does reduce AIC by 250-300 (by far the most among all others), yet it does not come out significant.
Please guide me on what to do in this type of analysis. What statistical approaches should I take?
Not necessarily looking for a direct answer, so I'd appreciate if there is any article you can direct me as well.