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I am trying to motivate a secondary analysis of a trial that had event related data. The primary study treated the data as an interrupted time series (ITS). I would like to justify using survival analysis for my secondary analysis.

The ITS approach created unnecessary interval censoring (given that exact dates for the event were available, but were aggregated at each ITS observation point). So far I have identified the following consequences (with associated questions):

i. Intra-individual correlation due to recurrent events is lost between ITS intervals, this underestimates the variance of the main effect size for the whole group.

QUESTION 1: Would better accounting of recurrent events also improve inference in a subgroup analysis independent of improved confidence intervals?

ii. An ecological type of bias could be introduced, because the event data is treated as an aggregate rate at the ITS observation point.

iii. Temporal bias (or increased ambiguity) could be introduced, related to the lost “temporal resolution” (is there a better way of describing that?).

QUESTION 2: In this case is an ecological bias and temporal bias referring essentially to the same thing (i.e., omitted data from the unreported observations 'lost' in the aggregation)?

QUESTION 3: Closely related to question two; if the ecological and temporal bias are separate, do they reduce efficiency (i.e., fewer observations) and/or alter accuracy independently?

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