Must recruitment and observation stop together?

No. Follow-up can continue after recruitment closes.

Does an unfinished spell have no useful information?

No. Its elapsed time provides a lower bound on duration.

Is an entrant sample interchangeable with a snapshot?

No. Their selection mechanisms and resulting duration distributions can differ.

AI Glossary / Statistics and probability / Advanced

Flow sampling

Definition

Flow sampling, in duration analysis, selects units through transitions occurring during a defined time interval. A common design recruits units as they enter a state, then follows how long they remain there. For example, a study can sample newly opened service requests and observe time to closure. This differs from stock sampling, which selects requests still open at a particular date. Some literature also discusses samples of leavers; the transition and observation rules must therefore be stated explicitly. This entry concerns duration-data sampling, rather than network-traffic sampling or generative flow models.

What it means

The sampling rule determines which spells can appear in the data. A snapshot of ongoing spells tends to encounter long spells more often than short ones, because long spells occupy more calendar time. An entry-based flow sample instead targets spells beginning during the recruitment interval. These designs can answer different questions even when both report a duration. Neither should be interpreted without its population, eligibility rules and observation window. A sample of completed exits also differs from a prospective sample of entrants with unfinished spells retained.

How it works

Define the state, entry event, exit event and unit of analysis. Select all eligible entrants or a documented probability sample during a recruitment window, then follow them under a stated observation plan. Record elapsed time and an event indicator. If a spell remains unfinished when follow-up ends, its observed time is a lower bound, usually represented as right censoring. Survival-analysis methods can retain that information under appropriate censoring assumptions. The recruitment end and follow-up end need not coincide. If individuals contribute multiple spells, dependence and selection across spells require attention. Models and likelihoods must reflect the actual sampling scheme rather than assuming a stock sample is an ordinary entry cohort.

Three practical examples

Service research: sample new support requests during a specified month and follow time to resolution.
Labor research: recruit people beginning unemployment spells and study subsequent transitions under a defined follow-up protocol.
Customer operations: follow newly initiated onboarding episodes, distinguishing completion, withdrawal and episodes still in progress.

Think of it this way

Think of asking about visit lengths by recording people as they enter a museum. That differs from walking through the museum at noon and interviewing whoever is still there. Long visits have more opportunity to appear in the noon snapshot.

Worked example

Consider three hypothetical spells entering on calendar days zero, one and two. Their eventual durations are two, seven and three days, but follow-up ends on calendar day six. The recorded elapsed times are therefore two, five and three days, with event indicators one, zero and one: the second spell is unfinished. A calculation using only completed spells gives (2 + 3)/2 = 2.5 days, while the eventual mean in this constructed example is (2 + 7 + 3)/3 = four days. The analyst does not know the second spell's final duration at the cutoff. Using the recorded data, the Kaplan-Meier survival estimate after elapsed day three is (1 - 1/3)(1 - 1/2) = one-third; the censoring at elapsed day five creates no additional event drop. Estimating the entire unrestricted mean from this follow-up alone is not supported. The example shows how discarding unfinished spells changes the analysis.

Illustrative case study

Fictional case: Alder Service Research enrolls every newly opened eligible request over two weeks and follows each through a specified later date. Analysts preserve unresolved requests with censoring indicators and distinguish customer withdrawal from successful resolution. A separate dashboard reports the age of requests open today. The team explains that this snapshot and the entry cohort describe different populations and cannot be compared as though they were interchangeable averages. This invented case demonstrates design interpretation without claiming a real reduction in resolution time.

Common misconceptions and mistakes

Do not assume a flow sample contains only completed durations. Do not replace a censored duration by its observation time and treat it as a known exit. Selecting current residents of a state is stock sampling, even if their past entry dates are recorded. The length-bias argument depends on the observation and population process; changing entry rates can complicate simple stationary explanations. An exit-based sample requires its own interpretation. Administrative censoring may be easier to explain than loss to follow-up, but independence assumptions still require consideration, especially when outcomes change across calendar time.

Business use

Organizations can use entry cohorts to understand how new cases progress and to compare well-defined operational periods. Preserve dates, event definitions and follow-up policies, and distinguish calendar time from elapsed duration. Report unresolved cases rather than silently removing them. If different exit types have different meanings, consider competing-risk methods instead of combining them automatically. Align the sampled unit with the decision: an episode-based study can give frequent repeat users more representation than a person-based study. Clear sampling documentation prevents misleading comparisons between active-case dashboards and completed-case reports.

Check your understanding

A team samples all cases open on Monday and analyzes their ages. Is that an entry-based flow sample?

Answer: No. It is a stock sample of cases present at a point in time, with a different selection mechanism from sampling new arrivals.

Related terms

Stock sampling
Survival analysis
Kaplan-Meier estimator
duration analysis
right censoring
length-biased sampling
entry cohort
hazard function
competing risks

Learn next

Learn the difference between censoring and truncation, then study how recruitment rules enter survival-analysis assumptions. Compare entrant cohorts with prevalent-case samples before interpreting duration summaries or fitting hazard models.

Survival analysis

Sources

Chesher and Lancaster, Stock and flow sampling, primary article abstract: https://www.sciencedirect.com/science/article/pii/016517658190094X INSEE, Economie et Statistique / Economics and Statistics 493, discussion of flow and stock sampling: https://www.insee.fr/en/statistiques/fichier/2890096/ES493_EN_web.pdf Primary duration-model discussion: https://www.sciencedirect.com/science/article/abs/pii/S0377221701001084

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