# Censoring for a compount event

I have a data set consisting of patients undergoing a treatment. The data set contains treatment start date, treatment end date, and date of death (if the patient has died). I also have a set of laboratory test results. The laboratory results are used to determine "disease progression" which may be assumed to have occurred at a specific point in time. The laboratory results are the only source of this information.

The study protocol defines a compound event defined to be the time from the start of treatment until "disease progression" or death, censoring at the end of study.

The analysis is to be done using a Kaplan-Meier approach.

None of the patients have been lost to follow-up however I have been told two things regarding the lab results:

1. they are not recorded for some patients and
2. the laboratory results where available are only until the end of treatment

Ignoring this will affect the analysis and probably bias the estimates.

I am interested in estimating the time to the compound event. There are no covariates involved. The issue for me is the uncertainty about the date of the compound event, caused by the laboratory data to be used for determining the "disease progression" date.

My question is how should I procede in the analysis in terms of censoring under the assumption that there is no relationship between the recording of laboratory results and the patient/treatment.

Specifically should I

a) censor those patients with lab results at the end of their treatment (when I know that the lab results are no longer available).

b) for patients with no lab results - how should I handle them - does censoring at the start of treatment make sense and should I do it? If not, what approach could I take?

I would be grateful for any pointers.

• Are the laboratory results the only measure of "disease progression"? Is there some systematic reason why there aren't lab results for some patients (e.g., tests only done on the sickest patients)? Is time = 0 the start or the end of treatment? Is your goal just to report the experience with this cohort of patients, or are you looking at relationships between covariates and survival? Please provide this information by editing the question, as comments are easy to overlook and can be lost. The more information you provide about your study, the better the answers you are likely to get.
– EdM
Jul 23 at 14:27
• Thanks @EdM, I've made some minor edits: time = 0 is the start of study (now specified), no covariates involved I just want estimates of the time to this event, no relationship between the recording of lab results and patients / treament - the assumption is that there is no systematic reason
– Ray
Jul 23 at 14:49

The problem here is in the definition of "disease progression," based on laboratory values that are not only missing from some individuals but also are unavailable after the end of treatment.

In principle, data that are missing can be dealt with by multiple imputation, even outcome data. That was my first reaction.

But there's an additional problem here. If the length of treatment differs among patients and the lab data to determine "disease progression" are only available during treatment, then there is a risk of survivorship bias when your event is the compound "disease progression or death."

If progression can only be detected during treatment, then those with shorter treatment durations will be less likely to be followed up to progression. Thus their "survival times" will tend to be the longer time until death, instead. Those with longer treatment durations will face the reverse situation, tending to favor the shorter time to progression as the "survival time."

I don't know of a way around the inherent bias with that compound event.

This is different from the "disease progression" situation typical of cancer studies. In those studies "disease progression" does present lots of problems. Time to disease progression depends on how much cancer remained after therapy and how quickly it regrows to a clinically detectable level. In turn, the time to clinically detectable regrowth can depend on the part of the body in which the recurrence grew, how frequently evaluations were done, methods used for screening recurrences, etc.

But in most cancer studies there is always the possibility of finding a recurrence at some time between the end of therapy and death. There is no inherent bias with a compound event "disease progression or death," just a potentially large amount of variance. That's quite unlike the situation in this question.

So I don't think that handling of censoring will solve the analysis problem here. With the limitation in time for detecting progression, you need to evaluate progression separately. There is still a danger that censoring of progression events at the end of treatment will be informative, related to clinical considerations that determine the duration of treatment. But at least you won't have the inherent survivorship bias with a compound event that takes either recurrence or death as the event.

Then assess time to death separately. If you have data available, you could evaluate death from this disease for a result that might be of more clinical interest.

• Thanks @EdM. There are certainly somethings to be considered here and this has helped to clarify them for me. Fortunately, we can assess time to death separately, which is a more important measure for this study.
– Ray
Jul 27 at 10:06