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While methodologists have provided us ample notice of both the problem of non-proportional hazards and the means of correcting them, less attention has been paid to the post-estimation interpretation. The suggested inclusion of time interactions in our models is more than a statistical fix: these corrections alter the substantive meaning and interpretation of results. Framing the issue as a specific case of multiplicative-interaction modeling, I provide detailed discussion of the problem of non-proportional hazards and present several appropriate means of interpreting both the substantive impact and the significance of variables whose effects may change over time.