Immortal Time Bias Handling

Immortal time is a span of follow-up during which, by the study's own definition, the outcome cannot occur. It arises when group assignment depends on a future event (typically the first prescription fill) but follow-up is started earlier (at diagnosis, hospitalization, surgery, or cohort entry). Every patient classified as "exposed" had to survive event-free from the earlier time-zero until their qualifying fill; that survival is guaranteed by construction, not earned by the drug.

When this period is attributed to the exposed group as event-free person-time — or, equivalently, when patients who die before filling are pushed into the unexposed group — the exposed rate is mechanically deflated and the hazard ratio is biased toward benefit. The bias is large and predictable: in the canonical Lévesque example, statins appeared to halve diabetes progression (HR ~0.69) purely from time misclassification, collapsing to the null (HR ~0.99) once exposure was modeled as time-varying.

Core conceptual distinction

Immortal time bias is fundamentally about when person-time is counted and to which arm, not about who is in the cohort — it is a temporal-classification error, distinct from confounding. Two remedies operate on different levers and must not be conflated. (1) Design prevention aligns three clocks at a single time zero — eligibility is met, the treatment strategy is assigned, and follow-up starts — so no unexposed-but-immortal interval can exist (the new-user / target-trial solution).

(2) Analytic correction keeps the misaligned data but stops crediting immortal time to the exposed arm: time-dependent (time-varying) exposure modeling lets a patient contribute unexposed person-time until the fill date and exposed person-time thereafter; landmark analysis classifies exposure as of a fixed landmark and discards earlier follow-up; clone-censor-weight assigns immortal time to every compatible strategy and censors-with-weighting when behavior diverges.

The estimand differs across these: design prevention and clone-censor-weight target an initiation/sustained-strategy contrast (ITT-like or per-protocol), time-dependent Cox targets the instantaneous effect of current exposure status, and landmark targets the effect among those who survived to the landmark — interpretations that are not interchangeable and must be pre-specified.

Pros, cons, and trade-offs

• Design prevention (new-user + target-trial time-zero) vs analytic correction. Prevention is transparent, requires no modeling assumption about the exposure-time relationship, and removes the bias at the root; it is the regulator-preferred default. Cost: it can shrink the cohort to true initiators with an observable washout and cannot rescue an already-extracted dataset whose time zero was set at diagnosis. Prefer prevention whenever you control cohort construction and the question is about treatment initiation.
• vs `standard-cox-time-dependent` (time-varying exposure). Time-varying Cox is the standard analytic fix and is exactly right when exposure genuinely starts mid-follow-up (e.g., a procedure or device implanted during an index hospitalization). Cost: it answers an as-treated, current-status question and is vulnerable to time-varying confounding affected by prior exposure (where g-methods, not Cox, are required). Prefer it when exposure timing is intrinsically post-baseline and a current-status estimand is the goal.
• vs `landmark-analysis`. Landmarking is simple, communicates well, and sidesteps the modeling of exposure timing. Cost: it discards events before the landmark, is sensitive to landmark choice, and conditions on survival to the landmark (a selected population). Prefer it for a quick, robustness-oriented sensitivity analysis or when exposure is reliably ascertained only after a fixed interval.
• vs `clone-censor-weight-per-protocol`. Cloning correctly handles "treatment within a grace period" rules that create eligibility-time ambiguity and emulates sustained strategies. Cost: it is the most complex to specify, defend, and weight. Prefer it when the protocol genuinely requires a grace period or a dynamic per-protocol estimand that simpler fixes distort.

When NOT to use — and when it is actively misleading or dangerous

Do not bolt an analytic correction onto a fundamentally answerable design question — if the real question is the effect of initiating a drug, the clean fix is a new-user design, and forcing a time-varying model onto a time-fixed ever/never definition can mask the problem while leaving residual misclassification.

It is actively dangerous to

1. treat a time-varying exposure Cox model as a remedy for confounding — it fixes only the temporal error, and an as-treated current-status estimand can re-introduce healthy-adherer bias and confounding by indication;
2. apply standard time-varying Cox when exposure influences later confounders that themselves affect both subsequent treatment and the outcome — this treatment-confounder feedback requires marginal structural models / g-methods, and naive adjustment is biased in either direction;
3. choose a landmark after inspecting the data, which invites a landmark that flatters the hypothesis; or
4. "correct" immortal time while ignoring competing risks, so that a deflated event count is misread as benefit when it is differential mortality.

A correction that changes the estimand without acknowledging the change is worse than the original bias, because it looks rigorous.

Data-source operational depth

• Claims (FFS): The classic substrate for immortal time. Group-defining events are pharmacy fills (NDC + `fill_date` + `days_supply`) or procedure codes; the trap is starting follow-up at a `dx`-coded index (diagnosis, MI, cancer) and assigning the arm by a subsequent fill. Failure mode: any patient who dies before the qualifying fill is structurally absent from the exposed arm. Workaround: set time zero at the qualifying fill (new-user) or, if exposure is intrinsically post-baseline, build a time-varying exposure indicator that flips on at `fill_date` and lets the patient accrue unexposed person-time before it.
• Medicare Advantage (MA) vs FFS: MA enrollees lack complete fee-for-service claims, so a "no prior fill" washout can be missingness rather than a true drug-free period, and exposure start dates can be unobserved — manufacturing apparent immortal time from invisible early fills. Workaround: restrict to enrollees with observable Parts A/B/D (or commercial medical+pharmacy) and exclude MA-only person-time before time-zero assignment.
• EHR: Better clinical timestamps for "start of risk" (order/administration dates, problem-list onset), but dispensing is often incomplete; a patient who fills outside the system looks unexposed during truly exposed time. Visit-driven capture also makes loss to follow-up informative. Workaround: link to pharmacy claims to confirm initiation and define observation windows explicitly.
• Registry / linked: Registries capture the triggering event and adjudicated outcomes well but often miss full drug exposure; transplant and oncology registries are textbook immortal-time settings (time on the waitlist before transplant is immortal for the transplanted group). In elderly claims, differential competing risk of death by exposure status compounds the bias — a deflated exposed event count partly reflects survival selection. Workaround: link to a death index, model the transplant/exposure as time-varying from its actual date, and report cause-specific and subdistribution effects so competing mortality is not silently absorbed.

Worked claims example

Question: do oral anticoagulants reduce stroke after a new atrial-fibrillation diagnosis? A naive analysis sets time zero at the first AF `dx` claim and labels anyone with a subsequent DOAC fill (NDC list) as "anticoagulated." Patients who stroke or die in the weeks between diagnosis and their first fill cannot be in the DOAC arm — that pre-fill interval is immortal, and the DOAC arm gains guaranteed event-free person-time, biasing the HR below 1.

Correct design fix: require 365 days of continuous A/B/D enrollment with no prior oral anticoagulant fill, set time zero at the first qualifying DOAC fill (new-user), and pair with an active comparator (e.g., warfarin initiators) so both arms share a time zero at initiation.

Correct analytic fix when the initiation cohort is not feasible: keep time zero at the AF diagnosis but model anticoagulation as a time-varying covariate — each person contributes UNEXPOSED person-time from `index_date` (AF dx) until `fill_date`, then EXPOSED person-time from `fill_date` to the earliest of stroke, death, disenrollment, or end of data.

Concretely, split each person's follow-up at `fill_date` into two records: record 1 spans [`index_date`, `fill_date`) with `exposed=0`, record 2 spans [`fill_date`, `exit_date`) with `exposed=1`; the event flag attaches only to the interval containing the stroke. Fit Cox on this (start, stop, event, exposed) structure. In data like this the naive HR ~0.6 typically moves toward ~1.0 once the immortal interval is returned to unexposed person-time — the same diagnostic signature Lévesque demonstrated for statins.

Interpreting the output

In the DOAC cohort modeled on Lévesque et al., fixed-exposure analysis assigns the 30-day pre-treatment window to the "treated" category. The result before correction: naive HR ≈ 0.69 (apparent 31% survival benefit). After re-coding exposure as time-varying and attributing the pre-treatment window to the unexposed risk set: corrected HR ≈ 0.99.

(1) Formal interpretation. The naive HR of 0.69 arises because Patient 1001 and similarly coded patients cannot experience an event during the days between cohort entry and first fill — they must survive to receive treatment. This immortal person-time, when attributed to the treated denominator, deflates the event rate in the treated arm and produces a spurious apparent benefit. The corrected HR of 0.99 redistributes that window to the unexposed risk set via a counting-process (start, stop, status) layout with a time-varying exposure indicator.

The gap between 0.69 and 0.99 — approximately 30 hazard-ratio points — is entirely an artifact of index-date misalignment, not a pharmacological effect.

(2) Practical interpretation. An HR of 0.69 would suggest a clinically meaningful survival advantage; an HR of 0.99 indicates essentially no effect. The difference between a publishable finding and a null result is a 30-day coding decision. Any RWE study that defines treatment by "ever filled a prescription" after cohort entry, or links treatment start to a dispensing date that lags the index date, must demonstrate that its time-zero alignment eliminates immortal person-time before the HR can be interpreted.

Decision diagram

flowchart LR
  T0[Time zero set at DIAGNOSIS<br/>follow-up starts here for all] --> IMM[Immortal interval<br/>diagnosis to first fill<br/>outcome cannot occur:<br/>patient must survive to fill]
  IMM --> FILL[First qualifying fill<br/>arm assigned = EXPOSED]
  FILL --> RISK[Genuine at-risk exposed time]
  IMM -. naively credited to .-> EXP[EXPOSED arm<br/>gains guaranteed<br/>event-free person-time<br/>HR biased below 1]
  FILL -. patients who die<br/>before filling .-> UNEXP[forced into UNEXPOSED arm]

flowchart TD
  Q{Is the question about<br/>treatment INITIATION,<br/>and do you control<br/>cohort construction?} -->|Yes| NU[Design prevention:<br/>new-user cohort, time zero<br/>at first fill, active comparator]
  Q -->|No: exposure is intrinsically<br/>acquired during follow-up| TV{Does exposure affect<br/>later confounders that<br/>also affect treatment + outcome?}
  TV -->|No| COX[Time-varying exposure Cox<br/>split follow-up at fill date]
  TV -->|Yes treatment-confounder feedback| GM[g-methods / MSM<br/>not naive time-varying Cox]
  NU --> SENS[Sensitivity: landmark analysis,<br/>washout length, grace period,<br/>negative-control outcome]
  COX --> SENS
  Q -->|Grace period / dynamic<br/>sustained strategy required| CCW[Clone-censor-weight<br/>per-protocol emulation]
  CCW --> SENS

Worked example

Scenario

A researcher wants to know whether blood-thinners (DOACs) prevent stroke in patients newly diagnosed with atrial fibrillation (AF). She pulls claims data and finds every patient whose first AF diagnosis code appeared in 2024. She labels anyone who later filled a DOAC prescription as 'treated' and everyone else as 'untreated', then compares stroke rates from the AF diagnosis date forward. Patient 1001 was diagnosed on 2024-01-10 and picked up her first DOAC on 2024-02-09 — exactly 30 days later. The naive analysis credits those 30 days to the treated group. But a patient who suffers a fatal stroke on 2024-01-25 — before ever filling a prescription — is forced into the untreated group. The treated group never loses anyone in those first 30 days; the untreated group absorbs all early deaths. The treated group's stroke rate looks artificially low.

Dataset

Claims records for one patient showing the AF diagnosis date (cohort entry) and the first DOAC fill. No stroke occurred during the pre-treatment window; stroke happened on 2024-04-15.

FIG. 1 — DESIGN TIMELINE

Steps

Result

Label

Pre-treatment survival window = 30 days (2024-01-10 to 2024-02-08). Biased treated person-time from cohort entry = 95 days. Correct untreated person-time = 30 days; correct treated person-time = 65 days. Returning those 30 days to the untreated column is the entire correction.

Value

30

Trade-offs

Runnable example

import pandas as pd
from lifelines import CoxTimeVaryingFitter

def build_time_varying(cohort: pd.DataFrame, rx: pd.DataFrame) -> pd.DataFrame:
    # First exposure fill per person; persons absent from rx never become exposed.
    first_fill = (rx.sort_values(["person_id", "fill_date"])
                    .groupby("person_id", as_index=False)["fill_date"].first()
                    .rename(columns={"fill_date": "fill_date"}))
    df = cohort.merge(first_fill, on="person_id", how="left")

    # Days from the early time zero (index_date) to each transition, on a single clock.
    df["t_exit"] = (df["exit_date"] - df["index_date"]).dt.days
    df["t_fill"] = (df["fill_date"] - df["index_date"]).dt.days
    # Exposure starting at/after exit contributes nothing exposed; clamp into [0, t_exit].
    df["t_fill"] = df["t_fill"].clip(lower=0, upper=df["t_exit"])

    rows = []
    for r in df.itertuples(index=False):
        exposed_ever = pd.notna(r.fill_date) and r.t_fill < r.t_exit
        if not exposed_ever:
            # Entire follow-up is unexposed (includes patients who exited before filling).
            rows.append((r.person_id, 0, r.t_exit, 0, r.event))
        else:
            # Unexposed interval [0, t_fill): never carries the event.
            rows.append((r.person_id, 0, r.t_fill, 0, 0))
            # Exposed interval [t_fill, t_exit): carries the event if one occurred.
            rows.append((r.person_id, r.t_fill, r.t_exit, 1, r.event))
    out = pd.DataFrame(rows, columns=["person_id", "start", "stop", "exposed", "event"])
    return out[out["stop"] > out["start"]]

tv = build_time_varying(cohort, rx)
ctv = CoxTimeVaryingFitter()
ctv.fit(tv, id_col="person_id", event_col="event",
        start_col="start", stop_col="stop")
ctv.print_summary()  # HR for time-varying 'exposed' is immune to immortal time bias

library(data.table)
library(survival)

build_and_fit <- function(cohort, rx) {
  setDT(cohort); setDT(rx)
  setorder(rx, person_id, fill_date)
  first_fill <- rx[, .(fill_date = fill_date[1L]), by = person_id]
  d <- merge(cohort, first_fill, by = "person_id", all.x = TRUE)

  # Single clock in days from the early time zero (index_date).
  d[, `:=`(t_exit = as.integer(exit_date - index_date),
           t_fill = as.integer(fill_date - index_date))]
  d[, t_fill := pmin(pmax(t_fill, 0L), t_exit)]   # clamp into [0, t_exit]

  # Base record: full follow-up, event at exit.
  base <- d[, .(person_id, t_exit, event)]
  base[, `:=`(tstart = 0L)]
  tv <- tmerge(base, base, id = person_id,
               death = event(t_exit, event))
  # Add the time-dependent exposure: switches to 1 at the fill date (NA = never exposed).
  tv <- tmerge(tv, d[!is.na(fill_date) & t_fill < t_exit],
               id = person_id, exposed = tdc(t_fill))
  tv$exposed[is.na(tv$exposed)] <- 0L

  coxph(Surv(tstart, tstop, death) ~ exposed, data = tv)
}

fit_tv <- build_and_fit(cohort, rx)
summary(fit_tv)  # exposed HR free of immortal time; contrast with naive ever/never coxph

/* Time-varying exposure: EXPOSED becomes 1 only after the first fill (fill_days). */
/* PHREG evaluates the programming statement at each event time, so immortal      */
/* pre-fill person-time is automatically credited as UNEXPOSED.                   */
proc phreg data=work.surv;
  model fu_days*event(0) = exposed / risklimits ties=efron;
  /* . (missing) fill_days => never exposed => exposed stays 0 for all of follow-up */
  if fill_days ne . and fu_days >= fill_days then exposed = 1;
  else exposed = 0;
run;

/* Naive (biased) comparison: ever-exposed treated as a baseline (time-fixed) covariate. */
/* The HR here is biased toward benefit because pre-fill immortal time is credited to     */
/* the exposed arm; the gap between this HR and the time-varying HR is the immortal-time   */
/* bias (cf. Lévesque 2010: ~0.69 naive vs ~0.99 corrected).                              */
data work.naive;
  set work.surv;
  ever_exposed = (fill_days ne .);
run;

proc phreg data=work.naive;
  model fu_days*event(0) = ever_exposed / risklimits ties=efron;
run;

Citations

1. [1]Suissa S. Immortal time bias in pharmacoepidemiology. American Journal of Epidemiology. 2008;167(4):492-499.
2. [2]Hernán MA, Sauer BC, Hernández-Díaz S, Platt R, Shrier I. Specifying a target trial prevents immortal time bias and other self-inflicted injuries in observational analyses. Journal of Clinical Epidemiology. 2016;79:70-75.
3. [3]Hernán MA, Robins JM. Using big data to emulate a target trial when a randomized trial is not available. American Journal of Epidemiology. 2016;183(8):758-764.

1. [4]Lévesque LE, Hanley JA, Kezouh A, Suissa S. Problem of immortal time bias in cohort studies: example using statins for preventing progression of diabetes. BMJ. 2010;340:b5087.

1. [5]ENCePP Guide on Methodological Standards in Pharmacoepidemiology (Revision 11, 2023). Chapter on biases and study design — immortal time, protopathic, and latency biases and their prevention via time-zero definition and new-user approaches.