I am running Cox regressions on a data set and I have encountered a situation where two of the variables are non-significant in univariate analysis but become significant in the following multivariate analysis.
To exemplify the situation, I am investigating variables A, B and C, which are all continuous variables. For A and B, higher values are expected to increase the hazard ratio. For C, lower values are expected to increase the hazard ratio.
In univariate analysis, regressions are performed individually for A, B and C with none of them being significant. However, in the following multivariate analysis, when A, B and C are all included in the model together, A and C suddenly becomes significant?
I am not quite sure on how to interpret this and I would be very interested in learning the reasons how this can happen—both generally and in the above example?
I have tried to look it up and the explanations range from suppression to the data being sampled poorly, so any input on how to approach this would be very welcome.
