Why Enrollment and Interim Data Availability Differ
At a selection look, the number enrolled in an arm is not necessarily the number whose intermediate-outcome data can be used. Participants may have entered at different calendar times, so they have had different amounts of follow-up by the time the data are reviewed. A participant enrolled recently may still be waiting for a scheduled assessment; another may have completed the assessment, but the record may not yet be available in the analysis dataset.
The calculation therefore starts with a calendar-time question: by the data cutoff for this look, which required measurements have actually been observed and made usable? This is a bookkeeping question about accrual, follow-up, and data flow. Its answer is not, by itself, an assessment of treatment benefit or a claim that the observed data are adequate for every analysis.
The cutoff can precede the meeting date because data need time to be entered, checked, and frozen. If a database is frozen five days before the review, for example, a measurement obtained after that freeze does not belong to the data being reviewed, even if it is available by the meeting. Conversely, enrollment before the look does not guarantee any intermediate measurement is yet available.
Availability is often specific to a measurement, not an all-or-none property of a participant. A participant may have data at an early visit but not at a later visit. If a selection statistic uses only a particular landmark measurement, the relevant count is the number with that landmark available. If it uses repeated measurements, the analysis may use the available visits according to its prespecified method; counting people with at least one visit does not tell us how many observations exist at each visit.
From Enrollment Time to Available Measurements
Suppose the protocol requires a measurement at elapsed time \(d\) after enrollment. In the simplest administrative calculation, a participant can have reached that assessment by the cutoff only if \(E_i+d \leq t_D\). That timing condition is necessary but not always sufficient: the assessment must also have occurred within the allowed visit window, been recorded, and been received in time for the data freeze.
For measurement \(j\) on participant \(i\), write \(V_{ij}\) for the actual measurement time and \(R_{ij}\) for the time its record became usable. Let \(W_{ij}\) indicate whether the measurement satisfies the protocol’s timing and validity rules. A direct availability indicator is:
Here \(I(\cdot)\) equals 1 when its condition is true and 0 otherwise. The number with that measurement available in arm \(a\) is the sum of \(A_{ij}\) over participants assigned to arm \(a\). This record-based count is preferable to a count inferred from enrollment dates when actual visits, withdrawals, or data receipt are known.
When only planned dates are available, the calculation is an estimate based on assumptions. If every participant is expected to attend at elapsed time \(d\), and the measurement is assumed usable immediately, the planned count is the number with \(E_i+d \leq t_D\). A data-processing delay of \(\delta\) days can be allowed for by using an effective cutoff \(t_D=t_L-\delta\). These simplifications should be stated; they do not establish that a measurement was actually collected.
Worked Example: A Fixed Follow-Up Requirement
Suppose a hypothetical trial reviews data on calendar day 180. The database cutoff is day 175, allowing five days for data processing. Six participants enrolled on days 0, 30, 70, 100, 130, and 160. The selection statistic requires a 60-day intermediate assessment. Assume for this calculation that each assessment is completed on schedule and entered by the cutoff if its scheduled date is on or before day 175.
For each participant, calculate follow-up at the cutoff as \(F_i=175-E_i\). A 60-day assessment is scheduled by the cutoff if \(E_i+60\leq175\), equivalently if \(F_i\geq60\).
| Enrollment day \(E_i\) | Follow-up by cutoff \(175-E_i\) (days) | Assessment day \(E_i+60\) | Available under stated assumptions? |
|---|---|---|---|
| 0 | 175 | 60 | Yes |
| 30 | 145 | 90 | Yes |
| 70 | 105 | 130 | Yes |
| 100 | 75 | 160 | Yes |
| 130 | 45 | 190 | No |
| 160 | 15 | 220 | No |
Thus, four of the six enrolled participants are expected to have the required measurement by the cutoff: \(4/6=0.667\), or 66.7%. The other two are enrolled but have not yet reached the scheduled 60-day assessment. The conclusion depends on the stated assumptions; actual visit records and receipt dates would be needed to confirm availability.
Visit Windows, Missing Visits, and Data Receipt
A planned assessment is not always scheduled for exactly one day. If a day-60 visit is allowed within a window of 53 to 67 days after enrollment, the timing rule is \(E_i+53 \leq V_{ij} \leq E_i+67\). For a record to be available at the look, the actual visit must fall in that window and its usable date must be no later than \(t_D\). Being far enough from enrollment to have reached the nominal visit does not prove that the visit occurred.
Withdrawals and missed visits also matter. A participant who withdraws before the required measurement may not contribute that measurement, even if enough calendar time has passed. A missed visit may leave no value for the target assessment. A participant may nevertheless have earlier measurements that can contribute to an analysis of repeated data, if that analysis allows them. The protocol and analysis plan determine which observations count; the calendar alone cannot decide that.
Worked Example: Applying a Visit Window and Data Cutoff
Consider a hypothetical day-230 look with a day-220 data cutoff. The intermediate assessment is scheduled at 60 days after enrollment, with a visit window from 53 through 67 days. The table gives each participant’s enrollment day, actual visit day when observed, and date the record became usable. Assume the listed visits meet all other protocol requirements.
| Participant | Enrollment day | Allowed visit window | Actual visit day | Record usable day | Available by day 220? |
|---|---|---|---|---|---|
| A | 0 | 53–67 | 61 | 62 | Yes |
| B | 25 | 78–92 | 90 | 94 | Yes |
| C | 80 | 133–147 | 142 | 143 | Yes |
| D | 130 | 183–197 | 196 | 225 | No |
| E | 160 | 213–227 | 217 | 218 | Yes |
| F | 200 | 253–267 | — | — | No |
Participants A, B, C, and E each had a visit within their individual window, and each record was usable by day 220. Participant D’s visit met the timing rule, but its record arrived on day 225, after the cutoff, so it is not part of the frozen data. Participant F had not reached the visit window by the cutoff. The available count is therefore four of six, not five of six: D’s observed visit cannot be treated as available at a cutoff that precedes receipt of its record.
Expected Availability Under Staggered Accrual
Sometimes participant-level enrollment dates are not yet known, or a design calculation is needed before enrollment begins. Then the expected available count can be calculated from an accrual model. Suppose participants enter at a constant rate \(\lambda\) per unit time from time 0 to \(T\), and each requires a fixed \(d\) units of follow-up. If the usable-data cutoff is \(T\), only participants entering by \(T-d\) are expected to have reached the assessment. For \(T>d\), the expected available count is:
This result follows because constant-rate accrual produces an expected \(\lambda\) entries per time unit, and the interval from 0 through \(T-d\) has length \(T-d\). More generally, if the accrual rate changes over time and is \(\lambda(u)\) at time \(u\), the expected number with a fixed \(d\)-unit assessment by \(T\) is:
If the look occurs at \(t_L\) but data are frozen \(\delta\) time units earlier, substitute \(T=t_L-\delta\). Under a fixed follow-up requirement, the expected count is then based on the accrual accumulated by \(t_L-\delta-d\), not by the meeting date. For several arms, apply the calculation to each arm’s accrual rate or allocation-specific accrual process; the overall total alone may conceal important differences between arm-specific counts.
Worked Example: Expected Count With Uniform Accrual
Suppose a hypothetical trial accrues 60 participants uniformly over 20 weeks, equivalent to a constant rate of \(\lambda=60/20=3\) participants per week. The selection look is at week 20, but the data cutoff is week 19 because of a one-week processing delay. The required intermediate assessment is six weeks after enrollment.
A participant must enter by week \(19-6=13\) to be expected to have reached the assessment by the cutoff. Under uniform accrual, the expected number enrolled by week 13 is:
Equivalently, the 60 entries are spread uniformly across 20 weeks, and the first 13 weeks account for \(60(13/20)=39\) expected entries. The trial expects 39 participants to have reached the six-week assessment by the week-19 cutoff. This is an expectation, not a guarantee that exactly 39 records will be usable: actual accrual can vary, and missed visits or late data can reduce the observed count.
Justification, Diagnostics, and Alternatives
The fixed-follow-up rule can be justified directly from the timeline. A participant enrolling at \(E_i\) reaches a required assessment \(d\) time units later, at \(E_i+d\). That assessment is scheduled by the cutoff exactly when:
Thus, the eligible enrollment interval ends \(d\) time units before the cutoff. With constant accrual, multiplying the length of this interval by the rate gives the expected count. This derivation assumes a fixed follow-up requirement, a specified cutoff, and the stated accrual model. It does not account automatically for nonattendance, withdrawal, record delays beyond the planned lag, or variation in the required follow-up.
Several checks help detect a faulty availability calculation:
- Check the time scale. Enrollment dates, follow-up durations, data cutoffs, and receipt dates must use the same units and calendar convention.
- Check the cutoff. Use the data freeze, not the date of the selection meeting, when records are not processed instantaneously.
- Check each assessment rule. Apply the specified visit window and distinguish a scheduled date from an observed visit.
- Check for impossible counts. A count of available records cannot exceed the number enrolled by the cutoff. With a common fixed assessment time, it also cannot exceed the number enrolled by \(t_D-d\).
- Check arm-specific totals and records. Unexpected differences may reflect different accrual patterns, missing visits, or data delays rather than different treatment effects.
A common alternative is to report the number enrolled at the look. That is a useful accrual summary, but it answers a different question and can overstate the number with the required measurement. Another alternative is to use an expected count derived from accrual rates; it is useful for planning, but it is not a substitute for a data extract showing actual measurements and receipt dates. For repeated measures, reporting counts at each scheduled visit is often more informative than one overall count of participants with any data.
These calculations have limits. A correct count does not establish that missing data are ignorable, that the participants with observed measurements represent those without them, or that a selection statistic has acceptable operating characteristics. Nor does a date calculation determine how partial follow-up should enter a particular analysis. Those questions depend on the outcome definition, the planned statistical method, and the assumptions underlying it. Availability should be reported transparently rather than treated as evidence of outcome quality or treatment efficacy.
Check Your Understanding
Work each problem using the stated cutoff and assumptions. Solutions follow the questions.
- A look is at day 120, with a day-116 data cutoff. A measurement is required 40 days after enrollment. Which participants, enrolled on days 50, 70, and 80, have reached the scheduled measurement by the cutoff, assuming on-time measurement and receipt?
- A participant enrolls on day 30. A visit is required 28 days after enrollment with a window of 25–32 days. The visit occurs on day 62 and the record is usable on day 65. Is it available at a day-64 data cutoff? Explain.
- A study accrues at 4 participants per week for 15 weeks. The cutoff is week 15, and an assessment requires five weeks of follow-up. Under constant accrual and immediate data receipt, what is the expected number that has reached the assessment?
- At a look, 50 participants have enrolled, but only 31 have records for the required landmark measurement in the frozen dataset. Which number is the available-data count, and why is it not necessarily the count enrolled early enough according to planned dates?
Solutions. (1) The latest qualifying enrollment time is \(116-40=76\). The participants enrolled on days 50 and 70 qualify, while the participant enrolled on day 80 does not; the count is 2. (2) The allowed window is days \(30+25=55\) through \(30+32=62\). The day-62 visit is within the window, but its record is not usable by the day-64 cutoff because it becomes usable on day 65. It is not available at this look. (3) Participants must enroll by week \(15-5=10\). The expected count is \(4\times10=40\) participants. (4) The available-data count is 31, because those are the required records actually present in the frozen dataset. The count enrolled early enough by planned dates may differ because of missed or out-of-window visits, withdrawal, or records not received by the cutoff.