Time-Updated Exposures and Cumulative Dose

In plain language

When researchers study how a drug affects the body over time, they need to track not just whether a patient ever took the drug, but exactly when the drug was active and how much had been taken up to each point.

Time-updated exposure construction does this by dividing each patient's follow-up into small intervals and labeling each one with the exposure status at that moment — for example, whether a pill supply was currently on hand (current use) or how many total milligrams had accumulated up to that day (cumulative dose). This approach prevents a well-known counting error called immortal time bias, which occurs when a study incorrectly marks days before a patient even started the drug as if they were already exposed.

Without it, a static ever/never label collapses the entire timeline into one flag and hides the most important information: the timing and amount of what was actually taken.

When to use it

—When a time-dependent survival/pooled-logistic model needs exposure that changes over follow-up, not a baseline adherence summary.

—Always, as the upstream input; the Cox/pooled-logistic fit is the separate modeling step.

—Use a plain time-dependent model when there is no treatment-confounder feedback; escalate to an MSM when there is.

Watch out for

—More complex and less standardized; PDC is the better instrument when adherence itself is the quantity of interest.

—This concept is the data-construction layer only — it does not address confounding or estimation.

—A standard time-dependent Cox is biased when time-varying confounders are affected by prior exposure; only g-methods (IPTW/MSM) recover the causal effect there.

Real treatments are rarely a single fixed dose held over follow-up. Patients fill late, stockpile, titrate, switch route, pause for surgery, combine therapies, and discontinue for toxicity or cost. Time-updated exposure construction turns a stream of pharmacy fills, infusion administrations, or procedure claims into a person-time representation in which the exposure value assigned to each interval reflects what was actually being taken at that point in follow-up. This data step is not preprocessing to be rushed — it is the analysis.

A correct estimand and a sophisticated model cannot rescue an exposure variable that mislabels person-time.

The common exposure scales, all defined as of a time `t` strictly before any outcome it could plausibly cause: current use (an active supply/administration episode covers `t`); recent use (exposure within a risk window, e.g. the prior 30 days, to capture carry-over pharmacology); cumulative duration (total exposed days before `t`); cumulative dose (sum of daily-dose × exposed days, or dispensed quantity, before `t`); dose intensity (cumulative dose per unit of exposed or protocol time); and weighted cumulative exposure (WCE), in which past doses contribute to current hazard through an estimated recency/latency weight function rather than a flat sum.

Core conceptual distinction

The decisive choice is what biologic quantity drives risk, and it dictates both the exposure variable and the estimand. A static `ever_exposed` flag answers "did this person ever take the drug" and, when used as a baseline covariate in a survival model, mislabels the unexposed lead-in as exposed (or forces follow-up to begin before the exposure decision), manufacturing immortal time.

A time-varying current-use indicator answers "is risk elevated while on drug" (acute pharmacology); cumulative dose/duration answers "does risk accrue with total burden" (cumulative toxicity, e.g. anthracycline cardiomyopathy); WCE answers "how does the timing of past doses shape current risk" when a flat cumulative sum is biologically wrong (recent doses matter more, or a latency lag applies).

These are not interchangeable: the estimand — a hazard ratio per active-use interval, per 1000 cumulative mg, or a WCE weight curve — must be pre-specified, and each maps to a different model (time-dependent Cox / pooled logistic on the long format, or, when the time-varying exposure is affected by prior outcomes/confounders, a marginal structural model fit by IPTW).

Pros, cons, and trade-offs

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

Do not reach for time-varying exposure when the estimand is an initiation (intention-to-treat-like) contrast — there, exposure is fixed at time zero by design and adding post-baseline time-varying status re-introduces the very informative-censoring and mediator-adjustment problems the new-user design was built to avoid.

It is actively dangerous to

feed cumulative dose into a model without lagging: using exposure measured up to and including the outcome day lets reverse causation and protopathic effects (the prodrome drives the prescription) masquerade as a dose-response, fabricating a spurious gradient;
update exposure using information that is a consequence of incipient disease, which conditions on a collider;
apply a standard time-dependent Cox when time-varying confounders are affected by prior treatment — this silently produces a biased estimate that looks rigorous.

When dose is changed in response to the outcome process, only g-methods recover the causal effect.

Data-source operational depth

Worked claims example

Question: dose-dependent risk of acute kidney injury (AKI) with an oral nephrotoxin, FFS claims. (1) Eligibility/time zero: first qualifying fill (`index_date`) after 365 days of continuous A/B/D enrollment and a drug-free washout; exclude members with any MA-only span in the lookback.

(2) Build episodes: sort fills by `person_id`, `fill_date`; stitch with carry-over (start of fill `i` = `max(fill_date_i, covered_until_{i-1})`, `stop = start + days_supply`, daily dose from NDC strength × quantity / days_supply); cap stockpiled supply at 30 days; allow a 14-day grace before an episode is closed as discontinued. (3) Long format: split each person's follow-up at every episode boundary, every outcome/censoring date, and at the first day of each calendar month, emitting `(person_id, tstart, tstop, current_use, cum_days, cum_dose_mg)`.

(4) Lag for latency/protopathic protection: compute `cum_dose_mg` and `current_use` as of `tstart` and lagged 30 days — exposure on the AKI day itself is excluded so a prodromal creatinine bump that triggers a refill cannot create false dose-response. (5) Censor: at disenrollment, death, end of data, and — for an as-treated contrast — at the end of the last episode + grace; bridge any inpatient stay by design and flag it.

(6) Model: `coxph(Surv(tstart, tstop, aki) ~ cum_dose_100mg + current_use + baseline_covariates)` (or weighted pooled logistic), with the cumulative-dose coefficient reported per 100 mg; if creatinine both responds to the drug and drives subsequent dosing, escalate to an IPTW marginal structural model rather than adjusting for time-varying creatinine in the Cox model.

Decision diagram

flowchart TD
  Q{What biologic quantity<br/>drives the outcome?} -->|Active pharmacology<br/>while on drug| CU[Current / recent use<br/>time-varying indicator]
  Q -->|Risk accrues with<br/>total burden| CD[Cumulative duration / dose<br/>lagged running sum]
  Q -->|Timing of past doses<br/>matters / latency| WCE[Weighted cumulative exposure<br/>spline weight function]
  CU --> FB{Time-varying confounders<br/>affected by prior exposure?}
  CD --> FB
  WCE --> FB
  FB -->|No| TDC[Time-dependent Cox /<br/>pooled logistic on long format]
  FB -->|Yes| MSM[Marginal structural model<br/>IPTW]

Choosing the exposure metric from the biologic question, then the estimation layer from whether treatment-confounder feedback exists.

timeline
  title One patient, day 90 outcome - the chosen metric changes the exposure value
  Day 0 : Fill 30 days supply, low dose : current_use = 1
  Day 25 : Refill (stockpiling begins) : cum_days rising
  Day 55 : Supply exhausted, no refill : current_use - 0
  Day 80 : High-dose 14-day course starts : current_use = 1 again
  Day 90 : Outcome assessed : current=yes, recent=yes, cum_dose high, WCE weights recent dose heavily

A static ever/never flag collapses all of this to "exposed." Current use, recent use, cumulative dose, and WCE give materially different values at day 90 - and a different estimand.

Worked example

Scenario

A researcher is studying whether long-term methotrexate use raises the risk of liver injury. She is following one patient, Maria (ID 2001), who started methotrexate on January 10, 2024. She has three pharmacy fills over about 100 days. Rather than label Maria as simply ever-exposed, the researcher builds a person-time table that records, for each interval of follow-up, whether Maria had an active supply on hand (current use = 1 or 0) and exactly how many total milligrams she had accumulated up to the start of that interval. This lets the survival model ask: does the liver-injury rate go up as cumulative dose grows?

Dataset

Maria's three pharmacy fills as they appear in a claims pharmacy table. Each row is one dispensed prescription.

person_id	fill_date	drug	days_supply	daily_dose_mg
2001	2024-01-10	methotrexate	30	10
2001	2024-02-15	methotrexate	30	10
2001	2024-03-20	methotrexate	30	10

Horizontal timeline for patient 2001 across 99 days showing three methotrexate fills as green bars, two grey gaps between fills, and a cumulative dose annotation on each interval (0 mg, 300 mg, 300 mg, 600 mg, 600 mg) demonstrating how the running total builds up across fills while current-use toggles on and off. — Each colored bar shows one fill; grey gaps show days without active supply (current_use=0). The cumulative-dose label on each interval shows how much Maria had taken before that interval began — the value a survival model would use as the exposure at that point in time.

Steps

1Fill 1 starts January 10 and covers 30 days, so it runs through February 8 (Jan 10 + 30 days). Maria has an active supply during this whole stretch. Episode dose = 30 days x 10 mg/day = 300 mg.

2Fill 2 arrives February 15. Her previous supply ended February 8, so there is a 6-day gap (Feb 9 through Feb 14). The 14-day grace period rule keeps this gap inside the same treatment episode rather than counting it as a restart, but during those 6 days current_use = 0 because no supply was on hand.

3Fill 2 restarts coverage on February 15 and runs through March 15 (30 days). Cumulative dose at the start of this interval is 300 mg (what was taken in Fill 1).

4Fill 3 arrives March 20. Supply from Fill 2 ended March 15, creating a 4-day gap (Mar 16 through Mar 19) where current_use = 0 again.

5Fill 3 restarts coverage March 20 through April 18. Cumulative dose at the start of this interval is 300 mg + 300 mg = 600 mg.

6By the end of Follow-up (April 18), Maria has completed all three fills. Total dose dispensed = 3 fills x 300 mg = 900 mg. A survival model can now ask whether the hazard of liver injury at any interval is higher when cumulative dose is 300 mg vs 600 mg vs 900 mg.

Result

At the start of the third fill interval (March 20), Maria's cumulative dose is 600 mg (Fill 1: 300 mg + Fill 2: 300 mg). Her current_use flag on March 20 is 1 (active supply). During the two gap intervals (Feb 9-14, Mar 16-19) current_use = 0, but cumulative dose continues to hold its running value of 300 mg and 600 mg respectively because dose already taken does not disappear.

Trade-offs

vs. Proportion of Days Covered (PDC)

Pros of this

—Preserves the timeline so the hazard model can use interval-level exposure; represents time-varying risk rather than a single adherence scalar over a fixed denominator.

vs. Cox Regression with Time-Dependent Covariates

Pros of this

—Supplies the gap-handled, lagged, long-format exposure intervals that a valid time-dependent Cox model requires; bad exposure construction cannot be repaired downstream.

vs. Marginal Structural Models and G-Methods

Pros of this

—The same long-format exposure history is the required input to an MSM; simpler to fit a time-dependent Cox when no exposure-affected time-varying confounding exists.

Runnable example

Build time-updated exposure intervals from pharmacy claims. Required input (cleaned, de-duplicated): fills : person_id, fill_date (datetime64), days_supply (int), daily_dose (mg/day, from NDC strength) Returns one row per gap-handled exposure episode with carry-over (stockpiling) and per-episode cumulative dose.

requires: pandas

import pandas as pd

STOCKPILE_CAP_DAYS = 30   # max carry-over of unused supply
GRACE_DAYS = 14           # gap tolerated before an episode is closed as discontinued

def build_exposure_episodes(fills: pd.DataFrame) -> pd.DataFrame:
    fills = fills.sort_values(["person_id", "fill_date"])
    rows = []
    for pid, g in fills.groupby("person_id", sort=False):
        covered_until = None     # running end of stockpiled supply
        cum_dose = 0.0           # mg accrued so far for this person
        for r in g.itertuples():
            if covered_until is None or r.fill_date > covered_until + pd.Timedelta(days=GRACE_DAYS):
                start = r.fill_date                       # new episode
            else:
                carry = min((covered_until - r.fill_date).days, STOCKPILE_CAP_DAYS)
                start = r.fill_date + pd.Timedelta(days=max(carry, 0))   # cap stockpiling
            stop = start + pd.Timedelta(days=int(r.days_supply))
            episode_dose = int(r.days_supply) * float(r.daily_dose)
            rows.append({
                "person_id": pid, "tstart": start, "tstop": stop,
                "daily_dose": r.daily_dose, "current_use": 1,
                "cum_dose_start": cum_dose,                # cum dose BEFORE this episode (lag-ready)
                "cum_dose_end": cum_dose + episode_dose,
            })
            cum_dose += episode_dose
            covered_until = stop
    return pd.DataFrame(rows)

Same exposure-episode construction in data.table, then a join to outcome/censoring intervals producing the (tstart, tstop, event) long format consumed by a time-dependent Cox model. Inputs: fills : person_id, fill_date (Date), days_supply (int), daily_dose (numeric) followup : person_id, fu_start (Date), fu_end...

requires: data.table · survival

library(data.table)
library(survival)
STOCKPILE_CAP <- 30L; GRACE <- 14L

build_episodes <- function(fills) {
  setDT(fills); setorder(fills, person_id, fill_date)
  fills[, {
    covered_until <- as.Date(NA); cum <- 0; out <- list()
    for (i in seq_len(.N)) {
      fd <- fill_date[i]; ds <- days_supply[i]; dd <- daily_dose[i]
      if (is.na(covered_until) || fd > covered_until + GRACE) {
        start <- fd
      } else {
        carry <- min(as.integer(covered_until - fd), STOCKPILE_CAP)
        start <- fd + max(carry, 0L)
      }
      stop <- start + ds
      out[[i]] <- data.table(tstart = start, tstop = stop, daily_dose = dd,
                              current_use = 1L, cum_dose_start = cum)
      cum <- cum + ds * dd; covered_until <- stop
    }
    rbindlist(out)
  }, by = person_id]
}

epi <- build_episodes(fills)
# Restrict episodes to each person's follow-up and attach the event flag at the closing interval.
long <- epi[followup, on = .(person_id), nomatch = 0L][
  tstart < fu_end & tstop > fu_start]
long[, `:=`(tstart = pmax(tstart, fu_start), tstop = pmin(tstop, fu_end))]
long[, event := as.integer(!is.na(event_date) & event_date > tstart & event_date <= tstop)]
coxph(Surv(as.numeric(tstart), as.numeric(tstop), event) ~
        I(cum_dose_start / 100) + current_use, data = long)   # HR per 100 mg cumulative dose

RETAIN/BY-group construction of gap-handled exposure episodes with stockpiling cap, then a PROC SQL split against follow-up to emit the long-format (person_id, tstart, tstop, current_use, cum_dose_start, event) consumed by PROC PHREG with a counting-process (tstart, tstop) specification.

%let cap = 30;   /* stockpiling carry-over cap (days) */
%let grace = 14; /* gap tolerated before episode closes */

proc sort data=work.fills; by person_id fill_date; run;

data episodes;
  set work.fills; by person_id;
  retain covered_until cum_dose;
  if first.person_id then do; covered_until = .; cum_dose = 0; end;

  if covered_until = . or fill_date > covered_until + &grace then
    tstart = fill_date;                                   /* new episode */
  else do;
    carry = min(covered_until - fill_date, &cap);
    tstart = fill_date + max(carry, 0);                   /* cap stockpiling */
  end;
  tstop = tstart + days_supply;
  current_use = 1;
  cum_dose_start = cum_dose;                              /* dose BEFORE this episode (lagged) */
  output;
  cum_dose = cum_dose + days_supply * daily_dose;
  covered_until = tstop;
  format tstart tstop date9.;
run;

/* Clip episodes to follow-up and flag the event in its closing interval. */
proc sql;
  create table long as
  select e.person_id,
         max(e.tstart, f.fu_start) as tstart format=date9.,
         min(e.tstop,  f.fu_end)   as tstop  format=date9.,
         e.current_use, e.cum_dose_start,
         (f.event_date is not null and
          f.event_date >  max(e.tstart, f.fu_start) and
          f.event_date <= min(e.tstop,  f.fu_end)) as event
  from episodes e inner join work.followup f
    on e.person_id = f.person_id
  where e.tstart < f.fu_end and e.tstop > f.fu_start;
quit;

/* Time-dependent Cox via counting-process intervals; HR per 100 mg cumulative dose. */
proc phreg data=long;
  model (tstart, tstop) * event(0) = cum_dose100 current_use;
  cum_dose100 = cum_dose_start / 100;
run;

Citations

FOUNDATIONAL / METHODS

APPLIED EXAMPLES