This question relates to the optimal study design when looking at survival to event based on observational data (i.e. the precise time of event will be unobserved but we can observe status at times not entirely under our control).

Specifically we will look at the development of anti-drug antibodies in patients treated with drug X (~50% of patients are expected to develop them over the first 12 months of treatment). We will only have the opportunity to obtain blood samples from patients a handful of times over 12 months, so if a test at time T comes back positive we don't know the precise time that antibodies developed, only that it happened before time T (and after any previous negative tests).

We want to look at the association of antibody-free "survival" with several measured variables of interest.

My questions are:

  • Is this type of dataset amenable to Cox proportional hazards testing, if the precise event times are not known? Can anyone recommend a good introduction to this approach (e.g. review article)?
  • We have a limited budget so the number of antibody tests we can perform in total is fixed. Do we maximise power for this analysis by sending more samples from the same patients (e.g. 3-4 samples each for 200 patients, spread across 12m) or fewer samples from many different patients (e.g. 1-2 samples each for 500 patients)? Are there good rules of thumb?
  • $\begingroup$ If just interested in percent of patients developing the antibody over the first 12 months of treatment and number of test < 1000, I would collect the blood sample at the end of 12 month treatment, get the positive/negative results, fit a logistic regression model. $\endgroup$
    – user158565
    Commented Nov 4, 2018 at 16:44
  • $\begingroup$ Thanks @a_statistician, but unfortunately patients have been seen during routine clinic visits so we don't have complete control over sample timing. Some will have serum available close to 12m but others may only have serum from much earlier visits, even if they are on treatment for the full 12m. Also, some patients stop treatment due to inefficacy, which may or may not be related to antibody development. Hence for both of these reasons I assumed that the survival approach would be more appropriate than logistic regression in this case? Would you agree? $\endgroup$
    – Nick
    Commented Nov 4, 2018 at 23:19
  • $\begingroup$ My comments was from study design aspect. It seems you have difficult on both frequent tests and getting the blood sample at the 12 months. Then I have no idea how to perform this study. $\endgroup$
    – user158565
    Commented Nov 5, 2018 at 2:56
  • $\begingroup$ Yes, that's true - hence why I think of this as an "observational" proportional hazards study, although not entirely sure this terminology is correct! $\endgroup$
    – Nick
    Commented Nov 5, 2018 at 7:50

1 Answer 1


Yes, this type of data is amenable to using a Cox model with the exact handling off ties (i.e. you assume that the event happened prior to the assessment time, but you do not know what order all tied event times happened in, so you consider all possible permutations). Alternatively, this is a case off interval censoring.

What sampling scheme makes sense depends on what you want to do. To describe the time pattern, you clearly need multiple assessments per patient, to just see whether it happens, you don't.

  • $\begingroup$ Thanks @Bjorn. Does the exact handling of ties only depend on the order, and not specific times? Since we will have several hundred participants with only one or a handful of observations each, it would seem to me that even calculating all possible permutations of the order could be computationally prohibitive (due to factorial growth, although I may be misunderstanding) - would any approximate method be valid? $\endgroup$
    – Nick
    Commented Nov 8, 2018 at 17:06
  • 1
    $\begingroup$ It depends on the order (just like Cox regression does in general). A few hundred or thousands participants might well be fine with a good efficient implantation like the one in SAS PROC PHREG with TIES=EXACT. Whether approximations perform well depends on the specific situation, you tend to hardly see a difference when there's just a few ties. $\endgroup$
    – Björn
    Commented Nov 8, 2018 at 17:42

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