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I'm investigating the survival of patients with a certain disease, and whether or not they progress to a more severe form of this disease based on several covariates (see EDIT). Currently, I'm attempting to run two standard survival analyses -- Kaplan-Meier and CoxPH.

My dataset consists of ~80,000 patients, each of whom has a measurement for at least 2 time points (clinic visits). The dataset is restricted to only those patients who do not have the severe form of the disease at their first visit. I've run the model, and something jumped out at me -- 60%+ of the patients in the dataset have only 2 measurements.

My question: is this problematic? The survival time of these patients appears to be entirely dependent on when they come for their second appointment, and would seem to reflect that rather than their true disease progression. Should I use a time-invariant model like logistic regression instead of CoxPH/KM?

Thanks!

EDIT: I'm trying to estimate the time from treatment initiation to onset of severe disease. In particular, I want to test whether patients with an intermediate level of the disease when they initiate treatment progress to the severe form more quickly than those with a low level of the disease at initiation.

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  • $\begingroup$ It's good that you caught that association between survival and having a second appointment: sounds like an example of survivorship bias. For some survival studies, just knowing patient characteristics at the start and knowing the time of last follow up or of the event is enough. So please edit the question to say more about just what survival time you are trying to measure: age at death, time from diagnosis to death, or something else? What hypothesis are you testing? That will help get an answer that works in your situation. $\endgroup$
    – EdM
    Jul 21, 2021 at 20:09
  • $\begingroup$ Thank you for the response! I'm trying to estimate the time from treatment initiation to onset of severe disease. I'm honestly not totally sure if survival analysis makes sense in this context (although it is common in the literature), since unlike death the severe form of the disease is not inevitable -- censored patients may not ever get there. In particular, I want to test whether patients with an intermediate level of the disease at t0 progress to the severe form more quickly than those with a low level of the disease at t0. I'll edit the question to include this information as well! $\endgroup$
    – k13
    Jul 22, 2021 at 14:23
  • $\begingroup$ Great question. Is the follow-up scheduled at clinically meaningful intervals, or do you expect that a patient could feasibly wait a long time after progression before their follow-up? The small number of visits could imply one of two things, either that the visits are far apart in time and therefore give poor resolution for timing events (many events but uncertain event times), or that the second visit closely followed the first and that the study just had an insufficient follow-up period (few events and many censored patients). The implications will be somewhat different. $\endgroup$ Jul 22, 2021 at 14:46

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This sounds like the onset of severe disease really happens at a different time than the measurement, but the measurement detects it. In that case, this seems like a case of interval censoring: you know the onset of severe disease happened between the previous measurement and the one that detects it. A lot of models can deal with interval censored data (including the Cox model, parametric survival methods, machine learning models with a time-to-event loss function etc. - it depends a bit on what you want to do with the results whether one makes more sense than the others and whether there's some plausible assumptions based on the underlying biology). However, the coarser the measurement process is (i.e. the further apart the measurements are), the less you'll learn about the pattern over time.

Things might be more tricky, if the timing of the measurements is determined by how the patients feel/whether they have symptoms/etc., or if there is possibly measurement error/uncertainty around the diagnosis of severe disease onset. In those cases, a bespoke model for the data generating process might be necessary.

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