What is immortal time bias?

Immortal time bias arises when a study defines exposure by something that takes time to occur — receiving a treatment, completing a course, achieving a response — and credits the time before that event to the exposed group. Patients cannot die before becoming exposed, so the exposed group contains a stretch of guaranteed survival and appears to live longer regardless of any real effect.

Immortal time bias is measurable, directional and reproducible, which makes it unusual among biases. Samy Suissa’s reanalysis of inhaled corticosteroids after a chronic obstructive pulmonary disease hospitalisation moved the adjusted rate ratio from 0.69 (95% CI 0.55–0.86) to 1.00 (95% CI 0.79–1.26) by changing one thing: how person-time before the first prescription was allocated (American Journal of Respiratory and Critical Care Medicine 2003;168:49–53). No covariate was added and no patient was removed.

Where the term comes from

Immortal time was named in pharmacoepidemiology by Suissa, who defines it as “a span of cohort follow-up during which, because of exposure definition, the outcome under study could not occur” (American Journal of Epidemiology 2008;167:492–499). The word “immortal” is literal rather than rhetorical: within that span the hazard of the outcome is set to zero by the classification rule, not by the treatment.

The structure was identified in the 1970s in cohort studies of the survival benefit of heart transplantation. Mitchell Gail’s reassessment in Annals of Internal Medicine (1972;76:815–817) is the canonical early statement: patients who received a transplant had to survive on the waiting list long enough for a donor heart to become available, so comparing transplanted with non-transplanted patients from the date of acceptance onto the programme credits the waiting period to the transplanted group.

Suissa and Dell’Aniello later placed immortal time inside a family of six time-related biases — protopathic, latency time, immortal time, time-window, depletion of susceptibles, and immeasurable time — illustrated in a Quebec cohort of 124,030 patients with COPD aged 50 or over treated between 2000 and 2015 (Pharmacoepidemiology and Drug Safety 2020;29:1101–1110). Knowing which of the six a reviewer means matters, because the remedies differ and only immortal time is fixed by reallocating person-time.

Oncology and surgical literature frequently name the identical mechanism differently: guarantee-time bias, for a status — tumour response, clear resection margins, discharge alive from the index admission — that a patient must be alive long enough to earn rather than be assigned at baseline. The person-time arithmetic is the same problem under the pharmacoepidemiology name and the oncology name; only the field’s vocabulary differs.

How it happens

Immortal time bias happens when the time origin of follow-up and the moment exposure is determined are two different dates, and the gap between them is credited to the exposed group.

A cohort is defined at diagnosis. Patients who eventually received a drug are compared with those who did not. But a patient who died in week two never had the chance to receive it, so they are classified as unexposed. The exposed group is, by construction, made of people who survived long enough to be treated.

The bias is not subtle in size. It has produced apparent survival benefits for treatments later shown to have none. Suissa and Dell’Aniello concluded from their six-bias illustration that many observational studies reporting unrealistic effectiveness for older drugs in new indications were affected by avoidable time-related biases, and that the apparent effectiveness often disappears once the design and analysis are corrected.

The arithmetic is worth doing once. A rate is events divided by person-time. Immortal time adds person-time to the exposed denominator that carries, by definition, zero events in the numerator, so the exposed rate falls and the hazard ratio moves below 1, toward apparent protection. Suissa’s 2008 paper shows the bias in the rate ratio increases proportionately to the duration of the immortal span, and is more pronounced when the outcome hazard decreases over time — the Weibull case — than under a constant exponential hazard. The practical reading is that the bias is largest exactly where the early period is most dangerous, which is most post-discharge, post-diagnosis and post-surgery cohorts.

Immortal time bias is not confined to observational cohorts. A per-protocol analysis of a randomised trial — one that classifies patients by the treatment they actually completed rather than the arm they were assigned to — imports the identical error, because a patient who dies before finishing the protocol can never be counted among per-protocol completers. Intention-to-treat analysis is immune for exactly this reason: assignment at randomisation, not receipt of treatment, sets exposure, so no one’s follow-up is reclassified after the fact.

Common questions about immortal time bias

Is immortal time bias the same thing as survivorship bias?

No. Survivorship bias is a broad selection problem — conclusions drawn only from units that survived some filter, with no reference to follow-up time. Immortal time bias is a specific person-time allocation error inside a survival analysis: a stretch of follow-up in which the outcome could not occur is credited to the exposed group by the exposure definition itself.

Why is it called “immortal” time instead of just biased follow-up?

Because within that span the outcome is not merely rare, it is impossible by construction: the classification rule sets the hazard to zero, not the treatment. Suissa’s original 2008 definition calls it “a span of cohort follow-up during which, because of exposure definition, the outcome under study could not occur” — impossibility, not improbability, is the whole point of the name.

My reviewer said my study has immortal time bias — what are they actually objecting to?

A reviewer flagging this means your exposed group’s follow-up clock started before exposure was determined, so some of its person-time carries guaranteed survival. They are objecting to the design, not the covariates: no amount of statistical adjustment fixes it, because the problem is which patients could appear in which group before you ever ran a model.

The three cohort designs that create it

Immortal time enters through three cohort definitions, and Suissa’s 2008 taxonomy names them: time-based, event-based and exposure-based. Recognising which one a manuscript uses tells you where the immortal span begins and ends.

Time-based. Cohort entry is a fixed calendar or clinical date — hospital discharge, diagnosis, index prescription — and exposure is defined by any dispensing within a subsequent window, such as 90 days. Every exposed patient must survive that window; every day of it is immortal.

Event-based. Cohort entry is the first prescription of any drug in a class, and exposure is defined by a later switch, escalation or addition. The time from first prescription to the defining event is immortal for the exposed group.

Exposure-based. Follow-up begins at the first prescription of the study drug for the exposed and at cohort entry for the unexposed, so the two arms have different time origins. This design does not merely misclassify immortal time; it excludes it, which biases the estimate in the same direction by a different route.

Suissa distinguishes misclassified immortal time — time given to the exposed group — from excluded immortal time, which is dropped from the analysis altogether. Both inflate the apparent benefit, and a manuscript can contain one without the other. A comment may name only the first, so an author who fixes the misclassification and keeps the mismatched time origins has not fixed the study.

Worked example: inhaled corticosteroids after a COPD admission

Inhaled corticosteroids after a COPD hospitalisation is the clearest published demonstration of immortal time bias, because Suissa re-analysed one identical dataset two ways and got two different answers from it. The cohort was 979 residents aged 55 or over first hospitalised for COPD between 1990 and 1997, followed for one year from discharge until first COPD readmission or death; 389 had an event. Exposure was any inhaled corticosteroid dispensing within 90 days after discharge (American Journal of Respiratory and Critical Care Medicine 2003;168:49–53).

The time-fixed adjusted rate ratio was 0.69 (95% CI 0.55–0.86) — a 31% apparent reduction. The time-dependent rate ratio, on the same patients and the same covariates, was 1.00 (95% CI 0.79–1.26).

The diagnostic detail is the dose-response of the bias itself. Lengthening the exposure-definition window drove the time-fixed rate ratio from 0.98 at 15 days to 0.51 at 365 days, while the time-dependent estimate stayed between 1.06 and 0.94 across the same windows. An effect estimate that tracks the length of an administrative window rather than the drug is not an effect estimate.

The 2020 Quebec follow-up separates immortal time from its neighbours. For inhaled corticosteroids and lung cancer incidence, the hazard ratio was 0.32 (95% CI 0.30–0.34) with latency and immortal time misclassified, 0.50 (95% CI 0.48–0.53) after correcting immortal time alone, and 0.96 (95% CI 0.91–1.02) after also correcting latency time. Correcting immortal time closed less than half the gap to the null; latency time accounted for more of the apparent protection.

Worked example: responders versus non-responders

Comparing responders with non-responders is immortal time bias in oncology’s native vocabulary, and the primary source is old. Anderson, Cain and Gelber wrote in Journal of Clinical Oncology (1983;1:710–719) that “the usual method of comparing responders and nonresponders is biased in favor of responders, and these results are frequently misinterpreted as providing evidence that response prolongs survival, or that the treatment under study is effective.”

A patient must survive to the first scheduled response assessment — weeks into therapy, wherever the protocol places the first restaging scan — before they can be called a responder. Everyone who dies before that scan is a non-responder by arithmetic. Anderson and colleagues’ conclusion is stronger than most authors realise: a comparison of survival by response category “may be useful descriptively, but such a comparison should not be used for inference concerning treatment effectiveness.”

The same structure produced a famous non-medical result. Redelmeier and Singh reported in Annals of Internal Medicine (2001;134:955–962) that Academy Award winners lived 3.9 years longer than matched, less recognised performers (79.7 versus 75.8 years, P = 0.003), a 28% relative reduction in death rate (95% CI 10% to 42%), across 1,649 performers and 772 deaths. Sylvestre, Huszti and Hanley reanalysed the same data with methods that avoided crediting an actor’s pre-award years to the post-award period, and the advantage fell to roughly one year and was no longer statistically significant (Annals of Internal Medicine 2006;145:361–363). Winning an award, like receiving a second-line therapy, is something you must be alive to do.

Questions about responder-versus-non-responder comparisons

Why is comparing responders to non-responders considered bad statistics?

Because a patient must survive to the first scheduled response assessment before they can be labelled a responder, so everyone who dies earlier is scored as a non-responder by arithmetic, not by biology. Anderson, Cain and Gelber called this comparison useful only descriptively in 1983, never for inference about whether treatment prolongs survival.

Is it ever okay to report survival broken down by response status?

Only descriptively, and only if labelled as such. Anderson, Cain and Gelber’s own conclusion allows a responders-versus-non-responders table as a description of what happened in the trial, but rules it out as evidence that response caused longer survival — the same numbers support one claim and not the other.

How to detect it in your own work

Immortal time bias is found by reading the exposure definition against the time origin, not by any statistical test — no diagnostic, goodness-of-fit statistic or proportional-hazards check detects it.

Ask one question: could a patient have been classified as exposed on day one? If exposure requires an event that occurs later, and follow-up starts before that event, you have immortal time.

The tells are: exposure defined as “ever received”, follow-up beginning at diagnosis while exposure is determined at treatment, and comparisons of responders with non-responders, where response cannot be assessed until a patient survives to be assessed.

Four further checks find it in a manuscript you are reviewing or drafting.

Compare the two time origins. Write down, in one sentence each, the date follow-up starts for an exposed patient and for an unexposed patient. If those sentences differ, the design is exposure-based and the origins need aligning.

Look for zero early events in the exposed arm. A Kaplan-Meier curve in which the treated arm is flat for the first weeks while the untreated arm drops steeply is the visual signature, and it is often mistaken for a rapid treatment effect. The flat segment is usually the immortal span.

Reconcile person-time, not just headcount. STROBE item 13 and the flow diagram give patient numbers, and item 14 asks only for summarised follow-up time; immortal time is a denominator problem, so ask for person-years by exposure group and for the median delay from time origin to exposure. A median delay of 90 days across a one-year follow-up means roughly a quarter of exposed follow-up is immortal.

Vary the exposure window on purpose. Re-run the analysis with a 30-day, 90-day and 180-day exposure-definition window. A stable estimate is reassuring; a monotone drift, as in Suissa’s 0.98-to-0.51 sequence, is close to diagnostic.

Questions about spotting immortal time bias

How do I know if my cohort study has immortal time bias?

Ask whether a patient could have been classified as exposed on day one of follow-up. If exposure requires an event — a prescription, a response, a completed course — that necessarily happens later, and follow-up starts before that event, the design has immortal time. Comparing the two groups’ time origins in one sentence each usually reveals it immediately.

Does a flat start on the Kaplan-Meier curve always mean immortal time bias?

Not always, but a treated arm that stays flat for the first weeks while the untreated arm drops steeply is the classic visual signature, and it is routinely misread as an early treatment effect. Check whether that flat segment coincides with the exposure-ascertainment window before crediting it to the drug rather than to the study design.

Can propensity score matching fix immortal time bias?

No. Propensity scores balance measured covariates between groups that are already correctly defined over time; they do nothing about person-time that was misallocated before matching ever happens. A propensity-matched analysis that still classifies exposure as fixed at baseline carries the same immortal time bias into the matched sample unchanged.

The remedies

Immortal time bias has three standard remedies, and all three work by making exposure status and the start of follow-up agree rather than by adjusting for anything.

Time-varying exposure — patients contribute unexposed person-time until the moment of exposure, then exposed person-time afterwards. The standard fix.

Landmark analysis — choose a fixed time after the origin, classify exposure as of that landmark, exclude anyone who did not survive to it, and start follow-up there.

Target trial emulation — specify the trial you would have run and align eligibility, treatment assignment and follow-up start to a single time zero.

Each remedy carries a trade-off, and naming that trade-off is what separates a competent methods paragraph from a citation.

Time-varying exposure is implemented as a time-dependent covariate in a Cox model, and it answers a subtly different question from a trial: it estimates the effect of being currently exposed, which is not the effect of a treatment strategy initiated at baseline. When exposure status is affected by earlier outcomes or by time-varying confounders on the causal pathway, a conventional time-dependent Cox model is biased and marginal structural models with inverse probability of treatment weighting are the standard replacement.

Landmark analysis, formalised by Anderson, Cain and Gelber in 1983, is transparent and easy to explain, but it discards everyone who died before the landmark and everyone exposed after it, and the estimate depends on where the landmark is placed. Pre-specify the landmark, justify it clinically, and report the result at two or three landmarks as a sensitivity analysis.

Target trial emulation, set out by Hernán and Robins in American Journal of Epidemiology (2016;183:758–764), fixes the problem at the design stage rather than the model stage by forcing eligibility, treatment assignment and the start of follow-up to coincide. Its practical implementation for a delayed treatment is the clone-censor-weight approach: each patient is cloned into every strategy arm, each clone is censored when its observed data stop being compatible with that strategy, and inverse probability of censoring weights undo the censoring that the design created. Maringe and colleagues’ tutorial on surgery in patients aged 70 to 89 with early-stage lung cancer shows what the correction is worth — a naive Kaplan-Meier comparison gave a 22 percentage-point one-year survival difference, cloning without weights gave 17 points, and the weighted emulation gave 11 points (International Journal of Epidemiology 2020;49:1719–1729).

The clone-censor-weight method is not free of assumptions. It requires positivity: at every event time, patients who are, in fact, still eligible for either strategy must exist in the data. Positivity fails when treatment is systematically given only very late in a patient’s course — there is then no clone still following the early-treatment strategy left to weight, and the censoring weights become unstable or undefined rather than merely imprecise.

Frequently asked questions about fixing immortal time bias

Reviewer 2 says my exposed group has immortal time — how do I respond without rerunning the whole study?

Re-analyse the existing data with a time-dependent Cox model, moving each patient from unexposed to exposed person-time at the date they were actually treated — the same dataset, no new patients required. Report the original and time-varying estimates side by side; a large gap between them is itself evidence the reviewer’s concern was correct.

Does adjusting for more covariates fix immortal time bias?

No — this is the single most common wrong fix. Immortal time bias is an error in when follow-up starts relative to when exposure is known, not an error in who was compared; adding covariates leaves the misallocated person-time exactly where it was. The repair is time-varying exposure, a landmark, or target trial emulation, never regression adjustment.

What do I do if a landmark analysis would exclude most of my events?

Report the number of deaths before your chosen landmark alongside the landmark estimate, so a reader can see what was excluded, and present the time-varying Cox analysis as the primary result rather than the landmark. A landmark that discards most events belongs in a sensitivity table, not as the headline number.

When the obvious remedy is unavailable

Immortal time bias sometimes cannot be removed, and the honest response is to bound it rather than to state that results should be interpreted with caution.

When exposure dates are missing. Claims databases and registries often record that a drug was dispensed within an interval but not on which day. Use the interval endpoints as a two-sided sensitivity analysis: assign exposure at the earliest possible date and at the latest, and report both estimates. If they bracket the null, the data cannot answer the question, and saying so is a result. Registry structure imposes several such limits at once — see registry and database limitations.

When a landmark would empty the cohort. In diseases where much of the mortality falls in the first weeks, a landmark late enough to capture exposure removes most events. Report the number of deaths before the landmark alongside the landmark estimate, so a reader can see what was excluded, and give the time-varying analysis as the primary result.

When the exposure is a completed course. “Completed six cycles” and “achieved a sustained virological response” cannot be assigned at baseline at all. Redefine exposure as an initiation strategy — “initiated the regimen with the intent of six cycles” — which is the observational analogue of intention-to-treat, and treat per-protocol completion as a secondary, explicitly weighted analysis.

When the paper is already published. Immortal time bias is directional: it inflates apparent benefit. A meta-analyst can therefore treat susceptible studies as an upper bound, stratify the pooled estimate by whether exposure was handled as time-varying, and report the two subgroups separately rather than pooling across them.

What immortal time bias is not

Immortal time bias is a person-time allocation error, and three biases that travel with it are not.

Not confounding by indication. Confounding arises from a common cause of exposure and outcome — sicker patients being selected for or against treatment. It can, in principle, be adjusted for with covariates, propensity scores or weighting. Immortal time survives every one of those, because the error is in how time was assigned, not in who was compared. A manuscript that answers an immortal time comment by adding covariates has misread the comment.

Not lead-time bias. Lead-time bias comes from moving the diagnosis date earlier through screening, so survival is measured from a different starting point in the screened group. Immortal time comes from moving the exposure date later than the start of follow-up. Both distort survival time, from opposite ends.

Not selection bias, though it is a close relative. Selection bias arises from conditioning on a common effect of exposure and outcome when choosing whom to analyse. Immortal time bias is frequently created by an eligibility criterion that requires surviving long enough to receive treatment, which is a selection gate as well as a time-allocation error — the two coexist in the same design more often than either is named alone.

Not the healthy adherer effect. Patients who fill prescriptions differ from those who do not in ways unrelated to the drug. That is a confounding structure with its own remedies, and correcting immortal time does not touch it.

What a reviewer will say

A reviewer raises immortal time bias by naming the specific design failure rather than the term itself, and there are three failures to name: that exposure is time-dependent and was analysed as fixed, that responders were compared with non-responders, or that follow-up begins before exposure is determined.

Each has a different repair, which is why the specific name matters more than the general one. A time-dependent exposure analysed as fixed needs the person-time reallocated. A responder comparison needs a landmark or a formal response-duration model. Mismatched time origins need the design rebuilt around a single time zero, because no amount of reallocation inside a misaligned cohort will align it.

The comments arrive in a small number of recognisable phrasings, and they decide papers. “Follow-up begins at diagnosis while exposure is ascertained over the following 12 months; please treat exposure as time-varying.” “Patients had to survive to receive the treatment, so the reported survival advantage is partly guaranteed by design.” “The comparison of responders with non-responders is not evidence of a treatment effect; a landmark analysis is required.” “The exposed and unexposed groups do not share a time origin.” “Please report the median time from cohort entry to first exposure and the corresponding immortal person-time.” “The magnitude of the estimate changes with the exposure ascertainment window, which suggests the association is a function of the window rather than the drug.”

Yadav and Lewis’s JAMA Guide to Statistics and Methods piece (2021;325:686–687) is the short clinical-audience statement of the problem, and Suissa’s 2008 paper the methodological one; a comment will often point to one or the other. Naming the specific design failure in your response — time-based, event-based or exposure-based — is far more persuasive than a general assurance that the analysis was appropriate.

How to report it

Report the handling of immortal time in the methods, not in the limitations, and give four things in order: the time origin, the exposure definition with its ascertainment window, the analytic method, and the amount of immortal person-time.

State the time origin in one sentence and confirm it is identical for both groups. State the exposure definition with the window used and whether the window was pre-specified. Name the method — time-varying Cox model, landmark analysis with the landmark and its justification, or target trial emulation with the cloning and weighting scheme. Report person-years by exposure group and the median delay from origin to exposure, so a reader can compute what fraction of exposed follow-up was immortal.

Where censoring may itself depend on exposure, treat that as a competing risks and censoring question rather than an administrative footnote, and if the treated and untreated curves meet or invert, read my survival curves cross before reporting a single hazard ratio. If immortal time could not be removed, state its direction — toward apparent benefit — and give the bounded estimate, which makes a stronger limitations section than an acknowledgement. Keep the causal wording proportionate to the design, which is the substance of causal language discipline.

Related

Lead-time bias · Selection bias · My survival curves cross · Hazard ratio · Epidemiology review

PerfectPaper compares the stated time origin, the exposure ascertainment window and the survival model in a manuscript, and reports where a patient could not have been classified as exposed on the first day of follow-up.

Checked by competing risks and time-related bias, which reports exposures defined after the time origin and names the remedy.

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