Treatment effect on survival in observational data with treatment times after diagnosis

Dear experts,

I need to analyze the treatment effect on survival using CoxPH models from observational data (registry data). Patients are diagnosed having a disease (at t0), and some of these patients are at some time later treated with drug X (every patient is treated at a different time after diagnosis, some very early, others years later). Simply comparing treated to untreated patients leads to an “immortal time bias”, because the treated patients must obviously have survived until the time they received the treatment. I read that a landmark analysis is a way to eliminate or correct for this kind of bias, but I can only find examples where the landmarking is about a co-variable and not the variable of interest (here: treatment). An example is here.

Is it possible to use the landmark analysis in this context?

What patients are labelled as “treated” then (among those that survived the landmark time)? All patients been treated only before the landmark time, or all patients that have been treated any time?

As a related but a bit different approach I thought to select patients that have been treated within a short period of time after t0 and compare only those to the patients that have not been treated at all. This ignores data from all patients that are treated somewhat later after diagnosis. This may limit the power, but if the registry is large enough and the treatment effect is statistically significant - is there any strong argument against it (e.g. because this introduces another kind of bias)?

Thank you for any help!


You also have confounding issues in this kind of data (unless the treatments were assigned randomly at each time point). Depending on what determines treatment assignment (e.g. physician’s assessment of prognosis, of disease severity, of likelihood that treatment will work - all based on some patient characteristics or tests? -, health insurance status, …), how strongly those things are associated with the survival time, whether you have measured all of these things frequently over time (or at least the important ones frequently enough) and how much data (treated/untreated with event you have), this might be a realistic question to address or a hopeless one.

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Thank you, Bjoern. Yes, I am aware of these additional difficulties, and some of them is in fact a hopeless question to address, as you state. There is no record on what basis the treatement is (has been) given. The only handle we have is an insufficiently frequently recorded series of the WHO functional class (FC), but there is no obsevable association between a change in the FC and the treatment. But despite all these problems my main question remains. The immortal time bias is surely extreme and very relevant, and efficiently reducing this kind of bias will help interpreting the possible treatment effect. This will then, for the reasons you mention, still not be perfect, but given the data we have it’s the best one can do (I think - unless some of you have better ideas). The results are not ment to eventually prove or demonstrate a treatment effect but to be suggestive or “hypothesis generating”, delivering arguments for initiating RCTs or at least to highlight the relevance of a better data recording in future registries.

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I think generally it’s difficult to compare to a no-treatment control is these kinds of studies for the reason you mentioned but also because people who aren’t being treated are different in ways that are probably relevant. Is it possible to compare alternative active therapies within a new-user design? Alternatively, could you imagine a clinical trial where each patient is potentially eligible at multiple timepoints and then count time to event for each of these forward (so you have multiple time zeroes for each patient) and then pray at the alter of robust errors? Something like

coxph(Surv(time, event) ~ trt + strata(index))

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I am tempted to suggest, as you note in your original post here, and in the context of this being an observational study, where hopefully by convenience, you have a lot of data, that you consider only including patients where treatment started within some clinically reasonable time point after diagnosis for the treatment group, or never started at all for your effective control group.

It is common, for example, in prospective studies that patients need to start treatment within some reasonable, protocol defined, time frame after study entry, to minimize the risks of safety events, or even study endpoints, occurring prior to actually starting treatment, because those events get tracked as soon as the patient is considered to be enrolled. In the prospective setting, beginning treatment after that time period would typically be a major protocol violation, where those patients would be excluded in a per protocol analysis, if one is done. Even though you are doing this retrospectively, I do think that the basic concepts can still apply here.

If relevant treatments in the treated group started on the order of years after diagnosis for some patients, as you note, it suggests the patients in the untreated group are still effectively “at risk” of treatment starting at some future date beyond the end of their current follow up period. Unless, of course, you can clearly define the clinical framework in which decisions to begin the treatment of interest were being made.

Part of the consideration that comes to mind in these ongoing observational settings, is that there can be temporal dynamics with patient characteristics, treatment options/strategies, changes to the indications for the same treatment based upon new clinical experience, as well as trends in the prevalence of the outcomes of interest, that can add additional confounding to your analysis. Those dynamics, if present, might reasonably constrain the time window that you use for T0, to have a more consistent group of patients for subsequent comparison during the follow up period.

If this is, as with most observational studies, a hypothesis generating analysis, then you want to be able to observe reasonable, if imperfect, signals in the data that would give cause for a more formalized prospective, powered, future RCT to be conducted. That signal does not have to be a statistically significant finding, given all of the caveats to the results that would be applied, but should provide sufficient evidence to relevant decision makers to commit the time, resources and budget to a new study.