Methods

Licht, Amanda A. (2011) “Change Comes with Time: Substantive Interpretation of Nonproportional Hazards”. Political Analysis, 19(2): 227-43.

Abstract: Although methodologists have provided us ample notice of both the problem of nonproportional hazards (NPHs) and the means of correcting for them, less attention has been paid to the postestimation 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 NPHs and present several appropriate means of interpreting both the substantive impact and the significance of variables whose effects may change over time.

Replication files for this paper are available at the Political Analysis dataverse, here.

Full text of the paper can be accessed in pdf or html for those with access to the journal.

Note: I would like to acknowledge a typo in Equation 8. Clearly, in order to calculate the first difference, once must difference rather than sum the values of x_i and x_j. Many thanks to Kyle Joyce for catching this silly error. The final form of the equation should read:

Might Time's Log Lie? Assessing use of the natural log as the functional form of time dependence in the NPH Cox model

Abstract: When the Schoenfeld residuals test suggests one should rejects the null, it has become standard procedure to interact offending variables with the natural log of survival time and include these terms in our NPH Cox models. Doing so, we assume, will assuage the bias in our coefficient estimates for variables whose effects change nonproportionally over time. This is likely true if the change in effect over time is roughly smooth and monotonic. But what if the relationship is more complicated? In this paper, I will identify situations in which we might expect non-monotonic and non-smooth changes in variable effect over time and perform Monte Carlo alayses to evaluate the appropriateness of using the log of time when it is not the true functional time.

Current status: In October of 2011, I ran initial simulations to assess the effect of threshold NPH effects, where the effect of a variable alters at a certain point in survival time. Thus far the results are interesting, but I have put them on hold while I work on putting more of my sanctions and foreign aid papers under review. The simulations log from my first investigations can be found below. Any comments or suggestions are extremely welcome!