Plotting predicted probabilities and 95CIs following discrete time proportional hazards modelling

[jameskb101]

Dear all

I am looking for some advice about the best way to graphically plot a non-linear continuous predictor in a discrete time proportional hazards model. I have found Stephen Jenkins' pages on DTPH very useful, but have got to a position where I require some guidance from the community.

I am modelling the time to an outcome on the age scale (years) and wish to see if two variables (moving house in a given year, binary) and total distance moved (continuous variable) predict the outcome, having controlled for a set of covariates.

I find that a model with a cubic term for moves gives best fit to the data as follows:

cloglog outcome discrete_age i.moved_house c.distance c.distance#c.distance c.distance#c.distance#c.distance, eform

I assume I have set up the model correctly an specified the cubic term properly.

I have tried to use the margins command to estimate the marginal hazard but understand that this is not advisable in a proportional hazards scenario since the underlying hazards are not known. If I do so, however, I run the following

margins, at (distance=(min(range)max))
marginsplot, noci

which produces the figure here.



While this gives me some visual clue as to the relationship, I am concerned it is wrong to do this, but do not know what to do instead. When 95%CIs are added to the plot, I am sure these are wrong, as I get the following:



I presume they should get broader over greater distances because a histogram shows the vast majority of participants have very small cumulative distances, with very few over 2000km. The dataset size is 1.4m participants

I would be grateful for any advice on a correct way to visually plot this non-linear relationship between distance and outcome, with correct 95% CIs, following discrete time proportional hazards modelling.

Thanks

James

[Nick Cox]

As a geographer I findsuch a distance function fairly implausible unless as a side-effect of something else in your dataset. Exponentials or inverse powers usually work better than polynomials.

[jameskb101]

Dear Nick
Thanks for the suggestion, I will run some alternative parameterisations of the distance function. That said, should I be doing something other than margins/marginsplot to inspect the data?
Many thanks for your time
James