st: Testing non-proportionality in a discrete-time survival model in which the main effect of time is treated as continuous.

 From "Kevin Daley" To Subject st: Testing non-proportionality in a discrete-time survival model in which the main effect of time is treated as continuous. Date Fri, 16 Nov 2007 13:32:31 -0500

```Hello, I have a question which, I must warn any reader, is not strictly to do with Stata, and is largely statistical.  That being said, I would really appreciate the input of any users familiar with the estimation of discrete-time event-history/duration models.

I'm running a discrete-time survival analysis of time-to-drop-out on a sample of adult students.  While many people following the same methodological approach (I'm running a logit model on a data-set arranged in person-terms at risk of drop-out) will model the "main effect" of time using a series of dummy variables, I have opted to use a more parsimonious specification, treating time as a continuous variable, and modeling the hazard through a fourth order set of polynomial terms.  This lets me cut down the number of parameters by 13 and successfully addresses the problem of very low risk sets and/or low hazard probabilities in the later terms-so I would very much like to keep this specification if possible.  The problem that I have run into is this: one of my predictors (wages) has a strong effect, but when hazard profiles categorized by wages are compared, it becomes clear that this effect is only truly pronounced in the first two terms.  After the second term wages tend no!
t to predict much of a difference in the vertical elevation of these hazard profiles. In other words, my model needs to adjust for the non-proportionality of the effect of wages on the hazard of drop-out.  Most of the material written on this model, however, only deals with such adjustment when time has been specified using the abovementioned dummies (one creates interactions between the predictor and the time dummies).  I have come up with a solution that seems to work quite well, but I'm not sure if it is statistically legitimate.  Because the magnitude of the wage effect in the first term and that in the second term are quite close and the tiny amount of vertical differentiation after the first two terms remains fairly constant over time, I simply created a dummy variable dividing the sample into observations from term 1 or term 2 and observations in any other term.  I then multiplied this dummy by my continuous wage variable and entered this interaction (yet not the tim!
e dummy) into the model already including the polynomial specification

of time and the wage variable.   All variables are highly significant.  Am I breaking some basic rule of statistics, however, by using an interactive term derived from a different specification of the variable (time) than the main effect included in the model?

Some researchers adjust for non-proportionality using an interaction based on a continuous specification of time (or the log of time) when its main effect was categorized, so it seems that the reverse would be just as reasonable (an interaction derived from a categorized effect of time while the main effect was modeled as a continuous variable). Again, however, I may be quite wrong and would appreciate being corrected in as great detail as possible as well asreceiving any suggestions for how I might better adjust for non-proportionality in this case.  Thank you very much (if you managed to finish this monster email that is).

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