Interpreting values on the Y-axis in hazard functions (Survival Analysis)

[Chris Boulis]

Hi All.

The Y-axis on a survivor function is straightforward to interpret as it is denoted by 1 and represents all of the subjects in the study. However, the values on the Y-axis of a hazard function is not straightforward. I've searched for an interpretation of what these values represent to no avail, so I am hoping someone here can kindly shed some light.

I've added two hazard functions (the first is non-parametric using -sts graph- with the option -kernal(epan2)-, the second is semi-parametric using -stcurve-. The risk to failure is represented by relationship failure (break-up) of married and de facto couples. What do the Y-axis values mean with respect to the hazard rates? In case it is of help, I've included the Cox model output where mrcurr=1 (married) =2 (de facto). Also, what does the hazard ration of 3.60 mean?

[Maarten Buis]

The hazard is the expected number of events per unit of time. So in Graph 1 you see that the non-married couples in the first years experience more than 1 breakup per year (assuming they become immediatly at risk after breaking up).

That is not a problem. That does not mean that everybody breaks up and noone can ever reach a long term relationship. This could happen when you include in your data all relationships including the very short duration ones. If you have lots of relationships in your data that lasts just a couple of weeks, then you will get this kind hazards. This is not necessarily a problem. However, I see you also use Cox regression, and it is unlikely that variables will have the same effect on these very short relationships and long term relationships, i.e. you should carefully check the proportional hazard assumption.

[Chris Boulis]

Hi Maarten Buis. Thank you for explaining how to interpret the Y-axis. That's great! The minimum relationship is a year given the survey is taken annually (panel data based on an annual survey similar to the G-SOEP). So based on the first graph, could we observe that the hazard faced by de facto couples is about three-times that faced by married couples and to that end, the Cox regression results are consistent?

you should carefully check the proportional hazard assumption

Do you mean the 'shape' of the hazard function relating to marital status faced by each individual is unlikely the same? To test this, I applied the -linktest- as recommended in "An Introduction to Survival Analysis Using Stata". I'm not sure how to interpret the output of this test.



This text then proposes to test the proportional hazard assumption by interacting analysis time with the covariates and test that these interacted variables are not different to zero. To this end, I perform the following. Your insights on how to interpret the output is appreciated.


Do these tests suggest the proportional hazards assumption is violated and if so, does that mean I should use parametric and/or non-parametric analysis methods? Thank you in advance.

[Chris Boulis]

Hi Maarten Buis. Following your post in #2, I am still trying to determine whether it is appropriate for me to use semi-parametric methods, such as the Cox regression model or whether I should use parametric methods. The hazard ratios I've obtained using the Cox model appears consistent with results from the Kaplan-Meier hazard estimate. To this end, I would really appreciate some feedback on my post in #3. Specifically, did I carry out the correct tests to check the proportional hazard assumption, and if so how should I interpret the output of the tests? Your help/guidance is appreciated. Chris