Why Repeated Eligibility Needs an Explicit Rule
Some trial questions concern a single decision point: for example, whether to initiate a treatment at a person’s first qualifying visit. Other questions arise repeatedly. A person may meet the same criteria at several visits or at regularly scheduled assessments, and each occasion could be treated as the start of a new trial. The protocol must say whether the person can enter more than once.
This is not just a data-management detail. A rule that uses only the first eligible occasion and a rule that includes every eligible occasion can represent different populations and assign different influence to people who qualify often. Each entry also needs its own baseline assessment and time zero. Without explicit rules, it may be unclear which eligibility assessment, treatment decision, or follow-up period a row represents.
Let \(i\) index people and \(k\) index a person’s eligible occasions. Write \(t_{ik}\) for the time zero of entry \(k\) for person \(i\). The corresponding analysis record is indexed by \((i,k)\), not by \(i\) alone. Eligibility, baseline covariates, treatment status, and follow-up are defined relative to \(t_{ik}\). The same person’s covariates or treatment status may differ at another entry.
Specify the Entry Rule
A protocol should state which eligible occasions count, how occasions are identified, and whether an earlier entry or treatment changes eligibility for a later one. These rules must be set in substantive terms, not inferred after looking at which choices produce a preferred result.
- First eligible entry: include each person only at their first occasion meeting the criteria during the observation period.
- All eligible entries: include every occasion that meets the criteria, subject to any stated spacing, prior-treatment, or other re-entry conditions.
- Sampled eligible entry: include one occasion selected according to a stated rule, such as a random selection among eligible occasions. The selection procedure and the population it represents must be clear.
An all-entry rule needs a precise definition of a new occasion. For example, eligibility might be checked at each monthly visit, at annual assessments, or only after a person has been untreated for a specified period. If closely spaced visits can qualify, the protocol should say whether each is a separate entry or whether a washout or minimum interval is required. It should also state whether prior trial participation, prior receipt of treatment, or a previous outcome changes eligibility.
Repeated eligibility is not the same as assigning a person to treatment repeatedly within one trial. Each entry is a separate trial baseline with its own eligibility assessment and time zero. The strategies being compared still need to be defined at that entry, using the protocol’s treatment definitions. If follow-up is \(h\) days, for example, the outcome for entry \((i,k)\) is assessed over the \(h\)-day period beginning at \(t_{ik}\), according to the outcome rules of the protocol.
Worked Example: Defining Annual Trial Entries
Hypothetical setting. A protocol asks about starting a preventive medication at an annual review among adults who have not used it recently and meet specified clinical criteria. The review dates are 1 January 2022, 1 January 2023, and 1 January 2024. Suppose one person meets all criteria at the first and third reviews but not at the second.
Under an all-eligible-entry rule, this person contributes two records: \((i,1)\) with \(t_{i1}=\) 1 January 2022, and \((i,2)\) with \(t_{i2}=\) 1 January 2024. The 2023 review contributes no record because the person is ineligible then. If each trial has a 180-day follow-up horizon, the two outcome windows begin on their respective time-zero dates and end 180 days later, subject to the protocol’s endpoint and follow-up rules.
Under a first-eligible-entry rule, the person contributes only the 2022 record. The 2024 occasion is not a new entry, even though eligibility returns. Neither rule is inherently correct for every question: the first asks about the first qualifying decision, while the all-entry rule represents qualifying decisions at multiple reviews. The protocol must choose the rule that matches its target question.
What Population Do Repeated Entries Represent?
Including multiple entries changes the unit represented in an analysis. With all eligible entries, the natural collection of records is the set of eligible person-trial occasions. If every record receives equal weight, a person with four eligible entries contributes four times as many records as a person with one. This may be appropriate when the question concerns the average effect across eligible decisions, but it is not automatically an average effect across people.
The distinction can be shown directly. Let \(M=\sum_i m_i\) be the total number of included entries, where \(m_i\) is the number contributed by person \(i\). If \(Y_{ik}\) is a numeric outcome for entry \((i,k)\), the equally entry-weighted mean is
Thus, the pooled entry mean weights each person’s within-person entry mean by \(m_i/M\). A person-weighted average of those means would instead use weights \(1/n\) for \(n\) contributing people. The expression establishes the weighting difference; it does not by itself establish that either average is a causal effect. A causal interpretation also requires the protocol’s treatment strategies, outcome, and causal identification assumptions to be appropriate.
Worked Example: Unequal Numbers of Entries
Hypothetical data. Four people contribute six eligible entries in total. Their binary outcomes over the specified trial horizon are:
| Person | Number of entries | Outcomes across entries | Person’s entry mean |
|---|---|---|---|
| A | 3 | 0, 1, 1 | 2/3 |
| B | 1 | 0 | 0 |
| C | 1 | 0 | 0 |
| D | 1 | 1 | 1 |
The equally entry-weighted mean is
The equally person-weighted average of the four people’s entry means is
The two values differ because person A contributes three entries to the entry-weighted calculation but only one person-level mean to the person-weighted calculation. Here the outcome is a binary event indicator, so the means are proportions: 0.500 events per entry and approximately 0.4167 as the average of the four person-specific entry proportions. The figures illustrate weighting, not a treatment effect. If trial windows overlap, the same observed event could also appear in more than one entry’s outcome; the estimand must say whether that repeated representation is intended.
Dependence, Overlap, and Protocol Checks
Entries from one person are generally not independent observations. They share a person’s characteristics, and their follow-up periods may overlap. Consequently, treating every entry as if it came from a different person can give an inappropriate account of uncertainty. The protocol should identify the person as the repeated unit and the entry as the trial-level record; the analysis plan should then use an uncertainty method compatible with this structure. The exact method depends on the planned estimator and is not determined by the entry rule alone.
Before emulation, check that the data can support the proposed rule. In particular, verify that eligibility can be assessed at every candidate occasion, that each included entry has an identifiable time zero, and that required baseline variables and outcomes can be linked to that entry. Check how often people re-enter, how close together entries occur, and how often follow-up windows overlap. These checks can reveal that an intended rule cannot be implemented as written.
State when eligibility is assessed and what qualifies as a distinct occasion.
Specify first entry, all eligible entries, or a defined sampling rule, including restrictions on re-entry.
For every included person-trial entry, record eligibility and baseline information at its own time zero.
Say whether the target averages over eligible entries, over people, or over another explicitly defined population.
Document multiple entries per person, possible overlapping follow-up, and the analysis plan for within-person dependence.
Worked Example: Choosing Between First Entry and All Entries
Hypothetical setting. A clinic wants to emulate a trial of two treatment strategies among patients who meet the same clinical eligibility criteria at quarterly assessments. In one year, a patient is eligible at the March, June, and December assessments. The protocol defines a distinct occasion as a quarterly assessment and allows re-entry only when the patient again meets every criterion at a later assessment.
If the question is the effect of strategies at a patient’s first qualifying decision during the year, the first-entry rule produces one record, with time zero at the March assessment. June and December do not create additional records for that patient in this emulation.
If the question concerns eligible decisions at all qualifying assessments, the all-entry rule produces three records, with separate time zeros at the March, June, and December assessments. Eligibility and baseline variables must be assessed anew for each record. The June and December records are not copies of March: the patient’s clinical state and treatment status may have changed.
The protocol must also settle whether prior treatment or a prior trial outcome affects re-entry. If the intended question concerns only treatment initiation among people who remain treatment-naive, later entries must satisfy that rule; if the protocol permits previously treated people to return, the strategies and eligibility criteria must make that population explicit. The data are sufficient only if the assessment dates and all required criteria can be reconstructed at each of the three potential time zeros.
Alternatives and Limitations
The main alternatives answer different questions. A first-entry design is straightforward to interpret when the target question is about an initial qualifying decision, but it discards later eligible decisions. An all-entry design uses more eligible occasions and can represent repeated treatment decisions, but it gives more influence to people who qualify more often unless the target weighting says otherwise. A sampled-entry design limits the number of records per person, but its selection procedure must be specified and its target population interpreted accordingly.
No entry rule repairs incomplete measurement of eligibility, treatment, or outcomes. Nor does repeated entry alone ensure that treatment groups are comparable. A well-defined emulation still needs a clear assignment mechanism and appropriate causal identification assumptions for its intended contrast. Re-entry may also narrow the population if only people who remain observable or satisfy additional later criteria can contribute; describe that population rather than treating repeated records as interchangeable with a sample of distinct people.
A useful diagnostic is to compare the number of unique people with the number of included entries, and to summarize the distribution of \(m_i\). If most people contribute one entry but a few contribute many, an equal-entry analysis may be substantially influenced by the latter. Also compare entry dates and follow-up windows. If windows overlap, clarify whether each entry’s outcome is defined independently by its own baseline and horizon, and whether repeated observation of the same event matches the target question.
Common Mistakes
- Counting records as people. Wrong reasoning: “There are 600 rows, so there are 600 participants.” Correction: rows may be person-trial entries; report both the number of entries and the number of unique people.
- Using one baseline for every entry. Wrong reasoning: “The person’s first recorded covariates apply to later trials too.” Correction: define eligibility and baseline information at each entry’s own time zero.
- Assuming all-entry inclusion is neutral. Wrong reasoning: “More rows only improve precision.” Correction: repeated inclusion also changes representation and weighting, and within-person records may be dependent.
- Leaving re-entry implicit. Wrong reasoning: “Anyone eligible again can obviously enter again.” Correction: state whether re-entry is allowed and how prior treatment, outcomes, or prior participation affect it.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A person meets eligibility criteria at two annual assessments. Under an all-eligible-entry rule, how many records are created, and what must be specified for each?
- Three people contribute 2, 1, and 1 entries. What fraction of the equally entry-weighted records comes from the first person?
- Why might an equally entry-weighted average differ from an equally person-weighted average?
- What information should a protocol provide to make “re-entry is allowed” operational?
- What is one reason that six entries from one person and five entries from five different people should not automatically be treated as eleven independent participants?
Solutions. (1) Two records, each with its own eligibility assessment, time zero, baseline information, treatment-strategy definition, and follow-up outcome window. (2) There are \(2+1+1=4\) entries, so the first person contributes \(2/4=0.500\), or 50%, of the equally weighted records. (3) Entry weighting gives more total weight to people with more entries; person weighting first summarizes each person’s entries and then weights people as specified. (4) It should define candidate occasions, the criteria for a distinct occasion, and how prior eligibility, participation, treatment, or outcomes affect later eligibility. (5) Entries from one person share characteristics and may have overlapping follow-up, so observations can be dependent; the protocol and analysis should retain the person-level repeated structure.