# Methods to evaluate time-depedent variables observed intermittently in survival analysis

Hi, I wanted to ask what are the best solutions to evaluate the prognostic effect of time-dependent covariates observed intermittently. In this particular case, I need to assess the prognostic effect on the survival of a certain exposure. Patients are seen every two months (2, 4, 6, 8, 10 months). At some point in that intervals, the covariable ‘exposure’ goes from 0 to 1, but the specific date is not known. Using the midpoint of the interval I suppose can involve a bias. What approaches have been proposed? Is there an R package that does this easily?
Thanks.

I forgot to tell that the event is NOT interval censored…

maybe the clock starts once they are exposed? it depends on the context

What we want to know is whether the worst toxicity to an antineoplastic therapy is associated with prognosis (OS). The problem is that researchers see patients at two-monthly intervals, and do not record the exact time at which toxicity occurs. The clock starts counting with cycle 1, the date of death or last follow-up is well collected, and the problem is that exposure (in this case, toxicity) is a time-dependent variable that occurs within an interval.

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i have stumbled upon that kind of thing before eg “We model efficacy as a time-to-event endpoint and toxicity as a binary endpoint, sharing common random effects in order to induce dependence between the bivariate outcomes.” But i agree that the difficulty might be that time is known to occur within a 2 month window. There must be something out there on that particular problem, it sounds familiar, but i don’t know off the top of my head…

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Yes, it is still sadly common for some to analyze toxicity as a fixed factor, and come to the conclusion that “in the end, toxicity is good”. I remember a discussion I had at a congress with a doctor who reported that severe thrombopenia was a good prognostic factor, without taking into account that in order to have severe thrombopenia, a requirement was to be alive long enough. Toxicity is normally evaluated at intervals, every 2-3 weeks. I think researchers tend to record toxicity dates within the cycle, or ascribe it to the next cycle that is delayed, in the case of a short interval. The problem here is that the intervals are large (every 2 months), although the median survival is about 24 months. I do not know if a solution is to abscribe here also the date to that of the successive cycle with the premise that if they attended the consultation, there was indeed no event.

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I’ve assembled a public Zotero library on precisely this matter, as part of my work on dose individualization of cancer drugs.

Is the dose of therapy fixed, or variable? It sounds as if these doctors would be too busy to titrate dosing to toxicity. What a shame.

As far as the broader methodological question:

you may wish to consider partially observed Markov processes as a suitable formalism.

Thank you very much David.
Doses had two possible levels. I think titration is not an issue here since adverse events were usually reversible.
I will try to look at that pomp package of R although it seems quite complex. Once again, it is very interesting to see how very common situations generate a great mathematical complexity. As for the references in Zotero, it would be interesting to do a methodological review on this subject. Often, immortal time bias is not contemplated.

As I point out in this tweet, reversibility of AEs in fact underscores the possibility and value of dose titration.

This seems to amalgamate Simon’s (1997) accelerated titration design with CRM. Given that “thrombocytopenia and other AEs were monitorable, manageable and reversible,” this agent looks ripe for #DoseIndividualization. pic.twitter.com/qZ1vkoJ8Sk

— David C. Norris, MD (@davidcnorrismd) November 30, 2018

Well, the prognostic impact of toxicity can be seen from two points of view. On the one hand, toxicity can have a negative effect on survival. For example, neutropenia prevents patients from receiving effective doses of chemotherapy. This has a negative impact on the progression of cancer. However, on the other hand, there are other toxicities that could be indirect markers that the drug is reaching its targets, and that its kinetics are correct. This type of toxicity could be associated with a good prognosis, unlike the previous one. An example would be hypothyroidism by sunitinib, hyperglycemia with mTOR inhibitors, rash associated with antiEGFR, etc. If the dose is titrated to reduce toxicity, the effect is likely to be reduced as well, so it is a trade-off. In any case, the problem is that toxicity analysis remains common as if it were a basal fixed variable, when in fact it is often cumulative or late.

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