Survival anlysis with interval censorship

[Viet Nguyen UoB]

Hi experts,

I am working on survival analysis with interval censorship. In our dataset, an object are required to attend a regular checkup and if it fails to showup at a particular checkup, we know that it dies. However we don't know exactly when it dies but rather an interval between the last attended checkup and the recent unattended checkup.

I am aware of stinreg that is specifically designed to handle this kind of dataset but we need to make some distributional assumption.

I am just wonder whether it is possible to use any semi-parametric or non-parametric for the case?

What happen if I use stcox and specify the death at the recent unattended checkup? How stcox deals with interval censorship?

Thanks for your help!

[Clyde Schechter]

To my knowledge there are no Stata commands for non- or semi-parametric survival analysis with interval censoring. If somebody else knows of one, I'd be eager to see this as well.

What happen if I use stcox and specify the death at the recent unattended checkup?

This would be wrong. -stcox- assumes left censoring. The interpretation of left censoring in your data would be to say that the patient becomes censored as of the date of the last check-up they attended, the last moment they are known to be alive.

[John Sgr]

Dear Clyde,

Would interval censoring be a problem in case of multiple failures data? For example my data is:

 +----------------------------------------+
|id time0 time failure size_tumor failure_risk |
|---------------------------------------------|
 9. | 0      12     1       1          1       |
 9. | 14     14     1       1          2       |
 9. | 16     18     0       1          3       |
+------------------------+

Can't I use stcox still?

Best regards,
John

[Clyde Schechter]

Multiple failures does not imply interval censoring. Censoring refers to not knowing the exact time at which a failure occurs. That can happen with single failures or multiple failures. Or you can have exact failure times with either single or multiple failures. Really, they are completely independent concepts.

If your failures are interval censored, whether they occur singly or multiply, then you cannot use -stcox-. If they are exact or right-censored, then -stcox- is applicable, whether they are single or multiple failures.

[Paul Dickman]

Many of your questions are answered in https://onlinelibrary.wiley.com/doi/...Na_QVh51H0l9lu

In case the link doesn't work, it's "Tutorials in Biostatistics: Methods for interval‐censored data", Stat Med, by Jane Lindsey and Louise Ryan.

It's neither recent or Stata-specific but relevant. I hope it serves as a basis for more recent and Stata-specific results.

[John Sgr]

Dear Clyde and Paul,

Thank you for your reply. It would be good to see Stata packages which are handling interval censoring in semi-parametric models as well.

[Stephen Jenkins]

John: it would help you were more precise in what you mean by "semi-parametric". Whatever, please note that a discrete time cloglog model fitted to interval-censored data estimates the slope coeffcients of an underlying continous time proportional hazards model. Using binary indicator variables for each duration interval, you get a "semi-parametric" model, in the sense that the discrete time baseline hazard function is allowed to vary from interval to interval and no assumption is made about the shape of the continuous time hazard. This result is found in many places; I borrowed it in my Survival Analysis course materials available here

[John Sgr]

Dear Professor Jenkins,

Thank you for your answer. I've been following your excellent guideline. I have a panel data with monthly observations of individuals' depression status (multiple failures - ordered event). My research question is how individual characteristics affect the duration of depression stage. I think most appropriate Cox model for my RQ is the conditional risk set model of Prentice et al. (1981). Let me explain my questions in detail with my data:

I have multiple failures has missing observations:

 +----------------------------------------+
|id time0 time failure gender failure_risk |
|---------------------------------------------|
9. | 0       12     1      1     1    |
9. | 14      14     1      1     2    |
9. | 16      18     0      1     3    |
+------------------------+

So I don't observe individual 9 all the time and as it is recurrent event I could not get the status of individual in terms of failure (it's not like mortality). My questions:

1) I think censoring mechanism could be related to failure event, i.e. if individual is severely depressed she won't attend the survey. Is there any package which account for informative censoring?
2) Can I leave data structure as it is shown in here? Or do I need to drop observation like second row where I observed individual only in one survey?
3) Is it true to define exit and enter as following: exit(time .) enter(time0) or exit is the only last occurrence not exit before the missing observations?
4) What time0=0 means actually? I replace the first observation with time0=0 while in the original data it's the first check-up so time0=1. Does it matters in the Cox model?

Best regards,
John