Aligning Eligibility, Assignment, and Time Zero

Why a Common Time Zero Matters

A target trial needs a definite point at which its participants enter the study, their eligibility is assessed, and the strategies being compared are assigned. This point is time zero. If these events occur at different times, the study may compare people selected from different populations or give one group a different opportunity to experience an outcome. A carefully stated causal question is not enough: its timing must also be implemented consistently in the observational data.

The target-trial protocol and the operational definition of treatment strategies establish what counts as eligible and what strategies are being compared. The timing question is how to make those elements refer to the same moment. A strategy can specify treatment actions after time zero, but group assignment must be defined at time zero rather than retrospectively from what a person later does.

Definition: Time zero, written $t_0$, is the common start of trial participation. Eligibility is assessed at $t_0$, assignment to a strategy is defined at $t_0$, and outcome time is measured from $t_0$. Information used to determine eligibility or assignment must be available by that point, not obtained later.

For a person to enter the target population at $t_0$, the eligibility criteria must hold then. Let $E(t_0)=1$ indicate that a person meets those criteria. Let $A(t_0)$ denote the strategy assigned at that time, and let $L(t_0)$ denote baseline covariates measured before assignment. In an observational emulation, assignment may not be recorded as a formal decision; the analyst still needs to define its observational analog at the same time and using information available then.

These definitions do not by themselves ensure that the comparison is unconfounded. They do establish a coherent population, a common start, and a temporal order: eligibility and baseline information first, strategy assignment at time zero, and subsequent outcomes afterward.

A Result for a Shared Start

The value of a common origin can be stated with potential outcomes. Let $Y^a(\tau)$ indicate whether the outcome would have occurred by $\tau$ units after $t_0$ if an eligible person were assigned strategy $a$. The target risk under that strategy is $P(Y^a(\tau)=1\mid E(t_0)=1)$. In a randomized target trial, this risk is identified by the observed risk in the corresponding assignment group.

Theorem: Suppose eligibility $E(t_0)$ is determined before random assignment; every eligible person is assigned one of the well-defined strategies at $t_0$; assignment is independent of the potential outcomes among eligible people; the observed outcome is consistent with the assigned strategy; and outcomes through $\tau$ are ascertained for all assigned participants. If each strategy has positive assignment probability among eligible participants, then $$ P(Y=1\mid A=a,E(t_0)=1)=P(Y^a(\tau)=1\mid E(t_0)=1). $$

Proof. By consistency, for participants with $A=a$, the observed outcome through $\tau$ equals $Y^a(\tau)$. Therefore,

P(Y=1\mid A=a,E(t_0)=1) =P(Y^a(\tau)=1\mid A=a,E(t_0)=1).

Random assignment makes $Y^a(\tau)$ independent of $A$ among participants with $E(t_0)=1$, so conditioning on $A=a$ does not change the distribution of $Y^a(\tau)$. Thus,

P(Y^a(\tau)=1\mid A=a,E(t_0)=1) =P(Y^a(\tau)=1\mid E(t_0)=1).

Combining the equalities proves the result. Positive assignment probability ensures the observed conditional risk is defined for each strategy. $\square$

The result depends on both comparability and alignment. In observational data, the randomization condition generally does not hold automatically; measured-confounding assumptions and appropriate analysis are needed. But statistical adjustment cannot repair a definition that assigns people to groups using events that happen after the stated time zero. The emulation must first specify a coherent time origin.

Worked Example: Eligibility and Assignment at a Clinic Visit

A study compares two strategies for adults with newly diagnosed hypertension: initiate medication at the qualifying visit, or receive no medication at that visit. At the visit, 120 patients meet the age, diagnosis, and prior-treatment criteria. Sixty are assigned to each strategy. The visit is $t_0$, and blood pressure and other covariates are recorded before the treatment decision.

Eligibility. All 120 people meet the criteria at the qualifying visit, so the target population is the 120 eligible patients at $t_0$. A patient who would meet the criteria six months later is not automatically part of this entry cohort.

Assignment. The strategy is defined at the visit. The 60 assigned to medication and the 60 assigned to no medication belong to their respective groups from $t_0$; their group labels do not depend on later adherence or treatment changes.

Outcome clock. If the outcome is defined over $\tau$ time units after entry, the risk comparison starts at the same visit for both groups. This makes the denominator and start of outcome time refer to the same eligible cohort. Whether treatment is actually taken as assigned is a separate question from how assignment is defined.

How Delayed Classification Distorts a Comparison

A common misalignment occurs when the study’s apparent time zero is the date of eligibility, but group membership is decided from future treatment. The people later classified as treated must remain available to initiate treatment. Those classified as untreated can include people who had an outcome before that later classification date. The groups therefore do not have the same temporal basis, even if the analyst starts counting outcomes from the earlier date.

Worked Example: Grouping by Future Initiation

Suppose 100 people are eligible on day 0. In a setting where treatment has no effect on the outcome, 10 experience the outcome on days 0–9. The other 90 remain outcome-free through day 10, and none of them experience the outcome through day 30. On day 10, 45 of those 90 initiate treatment and 45 do not. Assume the decision to initiate is random among these 90, and that treatment has no effect through day 30.

If the analyst classifies people according to whether they initiate on day 10 but counts outcomes from day 0, the “initiated” group contains 45 people and has $0/45=0$ outcomes by day 30. The “did not initiate” group contains 45 people who survived outcome-free to day 10 plus the 10 people with an earlier outcome. Its risk is $10/55$, or approximately $0.182$.

The apparent risk difference, initiated minus did not initiate, is therefore $$ 0-\frac{10}{55}\approx -0.182. $$ This contrast is not a treatment effect: treatment has no effect in the example. The discrepancy arises because a future event, initiation on day 10, defines membership in one group, while events are counted from day 0. The group definition has used information from after the stated start.

A valid comparison must instead define the strategies and group assignment at a common time zero, or choose a different time zero and explicitly define the population eligible then. Merely adjusting for measured baseline covariates does not make future-defined group membership a baseline assignment.

A second form of misalignment is to assess eligibility at one date and assign strategies only among people still eligible at a later date. This can be a coherent study if the later date is explicitly the new time zero. It does not, however, target the original group at the earlier date: people who had an outcome or otherwise ceased to qualify before the later date are no longer in the later eligible population.

Worked Example: Moving Entry to a Later Date

On January 1, 100 people meet a study’s eligibility criteria. By March 1, 12 have experienced the outcome and 8 no longer meet an eligibility criterion for another reason. The remaining 80 are assessed and assigned to one of two strategies on March 1.

If March 1 is the defined time zero, the eligible target population at entry consists of 80 people. The 12 earlier outcomes and 8 people who no longer qualify are not members of that March 1 population. The study can estimate a contrast for those eligible on March 1, subject to the other assumptions needed for causal interpretation.

If the intended target population is instead the 100 eligible people on January 1, assigning strategies only to the 80 who remain eligible on March 1 does not implement that target trial. The 20 people who do not reach March 1 cannot simply be ignored while retaining the January 1 target population. The two start dates define different populations and different causal questions.

Practical Checks and Alternatives

Before analysis, write down the time-zero definition and check that every design element refers to it. Useful diagnostics include reviewing a sample of records, comparing eligibility and assignment dates, and checking that baseline covariates were measured no later than assignment. Also inspect whether any group label depends on a future prescription, survival to a later visit, or future information about eligibility. Such patterns signal a timing problem, though they do not by themselves quantify its consequences.

Choose the entry event.
State the observable event that marks $t_0$, such as a qualifying clinical visit, and apply it consistently.

Assess eligibility then.
Specify the target population using criteria satisfied at $t_0$, not criteria learned or satisfied later.

Define strategy assignment at entry.
Use information available by $t_0$ to determine the strategy group; do not classify participants by future treatment receipt.

Start outcome time at the same origin.
Define outcomes relative to $t_0$ for every strategy so the comparison concerns the same entry point.

The main alternative to a shared earlier entry is to choose a later landmark date and make that date the time zero for everyone in the analysis. Eligibility must then be reassessed at that date, and the interpretation is limited to people eligible then. This can be appropriate when the scientific question concerns that later population; it does not recover the effect for people eligible earlier but absent at the landmark.

Design choice	Population and assignment	Interpretation
Common time zero at eligibility	Eligibility and strategy assignment are defined together at entry	Compares strategies for the population eligible at that entry point
Future-treatment classification	Group membership depends on treatment received after the stated entry date	Can create noncomparable groups and a misleading outcome contrast
Later landmark time zero	Eligibility and assignment are defined at the later date	Targets those eligible at the landmark, not necessarily the earlier cohort

Alignment is necessary, but not sufficient. It does not remove confounding in observational treatment assignment, correct inaccurate eligibility or treatment records, or solve missing outcome data. Nor does a common time zero dictate the outcome definition or the length of follow-up; those require explicit specification. The essential safeguard is that the population, group assignment, and outcome clock all refer to the same start.

Common Pitfalls

Using future treatment to label baseline groups. “Treated” means treatment was received at some later point, so the label uses information unavailable at the claimed time zero. Define the strategy group at entry instead.
Calling a later survivor cohort the original eligible cohort. People who do not remain eligible until the later date are absent. A later start changes the target population unless the analysis explicitly accounts for that change.
Measuring baseline covariates after assignment. A value recorded after strategy assignment may reflect post-assignment events. Establish a baseline measurement time before using it as a baseline characteristic.
Assuming alignment guarantees causality. A common time zero fixes a design inconsistency; observational confounding and other identification assumptions still matter.

Check Your Understanding

Answer each question, then compare your reasoning with the solutions below.

A study assesses eligibility on April 1 but classifies participants by whether they start treatment by May 1. What is misaligned?
In the randomized-trial result above, why is positive assignment probability needed?
In the 100-person example, calculate the risk in the group that did not initiate and the apparent risk difference.
If a study moves time zero from January 1 to March 1, what happens to its target population?
Name two checks that can help detect timing misalignment in an observational emulation.

Solutions. (1) Eligibility and outcome time begin April 1, but group membership depends on future treatment by May 1; assignment is not defined at the stated entry. (2) Each strategy must be represented among eligible participants so its conditional observed risk can be estimated. (3) The noninitiator risk is $10/55\approx0.182$; the initiator risk is $0/45=0$, so the apparent difference is $0-10/55\approx-0.182$. (4) The population becomes those eligible on March 1; people who had an outcome or ceased to qualify beforehand are not in that entry population. (5) Check that eligibility and assignment dates coincide, review whether group labels use future treatment, and verify that baseline covariates were measured no later than assignment.