Type of censoring in discrete time survival

Question

*I have a prospective longitudinal study. In this study, the patients come to the hospital every three months for check-ups. T0 ( one week before surgery), T3 (Three months after surgery), T6 (6 months after surgery), T9,T12,,,,,,,T24(24 months after surgery). So there are 9 time points.

We are interested in a predictive Cox regression including a binary time dependent covariate and a continuous independent variable. Cases who dropped out before event, completed follow up (T24) event-free, or showed specific level of the time dependent covariate at the end of the study are censor.

*It seems that in the counting process method, there are only right censors. And in order to use the discrete time survival, the following conditions must be satisfied (please correct me if I am not right)

1. the same time interval for all patients
2. A limited number of time points
3. Interval censors*

1. I am not sure about the type of censoring in my study. Can we use the discrete time survival method if there are both right censors and interval censors in the study?

2. If the study allows patients to rejoin the trial after missing one interval point (all obs are missing for one time period), I was wondering how we should evaluate them. Can we still use discrete time survival analysis when there is missing info. For example, the patient did not show up for his T6 appointment (six months after surgery), but he returned to study at T9.

Further information about the study

The event variable is progressing disease (YES-NO), and the main covariate (time dependent variable-variable of interest) is mental abilities(Yes-No). We are investigating if changing the state of mental abilities can predict rising disease.

Answer 1

Yes, you can consider a discrete-time model here. Interval censoring means that you know an event happened within some time interval, but you don’t know exactly when. That’s how you treat event times in discrete-time models.

Right censoring is when you only have a lower limit to an event time, because of dropout or the administrative end of follow up. Individuals with right-censored times are removed from analysis after you no longer have information about their event times. In a discrete-time model you need to think about the interval at which you cease including an individual with a right-censored time in the analysis. Those who complete the full study follow up without an event should be included in all time intervals. Those who drop out part-way should be removed after the last interval during which you know that you had information.

In response to edited question and comments

Don't forget the importance of having a clear definition of the time = 0 reference time for the survival analysis. Statements of time values or time intervals are then all with respect to that reference time. If the reference time is the date of surgery, and the times intervals between visits are the same for all individuals, then the time intervals relative to the reference are the same for purposes of discrete-time survival analysis even if the calendar dates differ.

If you have individuals who miss some follow-up visits and then come back with an event, you have wider spreads of interval censoring for those individuals. You might be better off using models that can handle arbitrary interval censoring, like those provided by the icenReg package, instead of discrete-time analysis.

Now that you've provided more information about your study, it's clear that it requires a lot of care in thinking about and setting up the data beyond these issues of interval censoring of event times. One big question is the time interval in which you should first include a change in cognitive status that was identified at a follow-up visit. You don't know when, during the interval since the prior visit, that change in status occurred. So do you mark cognitive function during the time interval prior to identifying the change in status as YES or NO?

Also, I question the binary treatment of cognitive function as a predictor. There are graded measures of cognitive function, like the Montreal scale; an arbitrary cutoff of a graded score is not typically a wise choice. Furthermore, a graded score would be more amenable to the type of joint modeling of covariates and events that might handle this situation better.

I'm glad to have been able to provide help up to this point to clarify the principles involved, but you should get some experienced local statistical advice before you proceed with designing and performing this study. The issues are too complicated and specific to the field of study to provide detailed help on a site like this.