I am conducting a retrospective cohort study to determine the association between receiving medicine X with death during the first 100 days of therapy for patients with leukemia, from 2010-2020. Starting in 2015, all patients began receiving medicine X on Day 10 (t=10) of therapy to prevent infection, whereas nobody received it before. So, I have two cohorts to compare: those receiving medicine X, and those who didn’t.

Assuming era-dependent confounders are controlled for (e.g., quality of supportive care in each era, etc.), I’d like to determine the effect of medicine X on survival using a Cox PH model, but I am faced with the problem that many patients (10% of total cohort, 20% of events) die before day 10 and therefore die before they can receive medicine X (the exposure). As expected, this survivorship bias contributes to a large association between survival to 100 days and medicine X.

What strategy do you recommend to approach the issue of survivorship bias here, allowing for basic limitations to retrospective, non-randomized studies? Given that patients aren’t at risk of the event (death given medication X status) until they actually receive medication X, my first instinct is to simply left-truncate the data and describe the effect of medicine X as the hazard of death given survival to Day 10 (when they receive medicine X), assuming that confounders between those receiving medication X and those surviving are controlled for. Are there any other approaches I should consider? I considered a time-varying exposure, but I think it is inappropriate here given the specifics of medication X and the specific disease here, as the effect of medication X is expected to be quite different in days 1-10 than it would be in days >10, and I’m not interested in that question right now.



1 Answer 1


The easiest thing to defend is to model survival as a function of X starting from day 10. If no one ever received X prior to day 10, then any model of survival as a function of X that involves event times prior to day 10 violates causality: you can't look forward to a later predictor value to explain earlier survival, as you note. Left truncation at day 10, which evaluates subsequent survival conditional upon surviving 10 days, is an appropriate approach.

If you do include X as a time-varying covariate and model from day 0, then the intervals containing X will be interpreted as left-truncated prior to the administration of X in any event. One might argue that including time points before day 10 will help evaluate how well your model is handling "era-dependent confounders," but you would need to consult with colleagues to see if that actually makes sense in your situation and if it would be defensible in publication. If you choose that route, be very clear that no coefficient involving X provides information on X prior to the left-truncation time.

Even then, there are potentially big problems. As I understand the scenario, the use of X seems completely tied to the calendar date of treatment. It's not clear how well you can disentangle X from other "era-dependent confounders," and you might end up just having to compare pre- and post-2015 survival while noting that use of X might have played an important role. Perhaps a smoothed, continuous model of calendar date as a predictor will show an appropriate jump at 2015 when X came into use, which could strengthen your case.

  • $\begingroup$ Thanks, yes, agree with all the above. This is really an exploratory analysis given the dataset. We'll be evaluating the real question of the efficacy of medication X in the setting of a prospective study. Thanks $\endgroup$
    – Casey
    Apr 4, 2023 at 12:31

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