Can entry time be zero?

Yes, when observation begins at the chosen origin.

Does late calendar recruitment always imply delayed entry on every scale?

No. A study measuring time since enrollment may start everyone at zero, while an age-based analysis may have different entry ages.

Is an upload timestamp necessarily entry time?

No. It may only reflect data processing rather than observation or eligibility.

AI Glossary / Statistics and probability / Intermediate

Entry time

Definition

Entry time is the point at which a person or other unit begins contributing observations or risk time to a study. In time-to-event analysis, it must be distinguished from the time origin used to measure event times. If observation starts after that origin, the unit has delayed entry and should contribute to risk sets only after becoming observable and eligible under the study design.

What it means

A machine may begin operating in January but enter a monitoring study in April. Its operating age at entry is three months, even though its observed follow-up begins in April. An analysis using operating age should retain that distinction.
Entry time is therefore not necessarily zero, the date the project began, or the date the data were uploaded. It describes entry into the relevant observation or risk process. The right definition depends on the scientific or business question and the chosen time scale.

How it works

Specify the event, eligibility rules, time origin, and time scale before constructing records. Convert entry and exit to the same scale.
For each unit, record when it enters observation, when observation ends, and whether the event occurs at the endpoint. In a common counting-process convention, an interval is written (entry, exit], open on the left and closed on the right. The unit belongs to a risk set at event time t when entry < t <= exit. Exact handling of ties and endpoints should follow the analysis method consistently.
Delayed entry often corresponds to left truncation: units are observed only if they remain eligible and event-free long enough to enter. Units experiencing the event before possible entry are absent from that observed sample. This differs from left censoring, where an included unit is known to have experienced an event before a recorded limit but its exact event time is unknown.
Appropriate methods build risk sets using entry as well as exit. Merely subtracting entry from exit changes the analysis to time since entry; it may answer a different question from time since installation or attained age. Crediting unobserved pre-entry time can also distort comparisons and create misleading event-free exposure.
Standard delayed-entry methods require appropriate assumptions about the entry mechanism and event process, possibly conditional on measured covariates. Informative enrollment, changing eligibility, or incomplete histories may need additional methods. Correct timestamps alone cannot remove selection bias caused by the way units enter.

Three practical examples

A reliability study recruits machines already in service and records their operating age when monitoring begins.
A customer-retention analysis includes existing accounts but distinguishes account creation from entry into the observable data window.
A longitudinal study uses age as its time scale and adds participants to risk sets only at their age when follow-up starts.

Think of it this way

Think of joining a race observation point after the race has started. You can describe what happens to runners once they become visible, but you should not pretend you watched them from the starting line. The clock measuring race progress and the moment observation begins are different pieces of information.

Worked example

Consider an original machine study using months since installation. Machine A enters at month zero and fails at month four. B enters at month three and fails at month seven. C enters at month five and is censored at month eight. D enters at month zero and is censored at month six.
At the failure time four, A, B, and D satisfy entry < 4 <= exit. C has not entered, so the risk set contains three machines. The event fraction is one-third.
At time seven, A has failed and D has left observation. B and C are at risk, giving an event fraction of one-half. Under the ordinary delayed-entry product-limit calculation, the two survival factors multiply to (1 - 1/3)(1 - 1/2) = 1/3.
The observed follow-up contributions are four, four, three, and six months, totaling seventeen machine-months. This small example illustrates risk-set bookkeeping, not a precise population reliability estimate. Its survival interpretation relies on the sampling, truncation, and censoring assumptions, and C must not be counted in the month-four denominator.

Illustrative case study

Fictional case: Maple Equipment begins collecting sensor records from machines installed in different years. A draft analysis sets every machine's age to zero at the first data upload and reports the result as lifetime reliability from installation.
The analyst separates installation dates, monitoring-entry dates, and exit events. The team decides whether it wants reliability by operating age or remaining service after enrollment, then builds records for that question. It also investigates why some machines joined monitoring late. Correct entry handling makes the estimand clearer without claiming to reconstruct failures absent from the source data.

Common misconceptions and mistakes

Mistake: treating entry time and time origin as interchangeable. They coincide only in some designs.
Mistake: counting a late entrant as observed before entry. That changes risk sets and exposure.
Mistake: calling delayed entry left censoring. Truncation concerns which units become observable; censoring concerns incomplete event-time information for observed units.
Mistake: resetting all clocks without acknowledging the changed question.
Mistake: assuming an entry-aware model automatically fixes informative enrollment or missing historical records.

Business use

Businesses need clear entry times when analyzing equipment failures, customer churn, subscriptions, or other events in records that begin partway through a unit's history. Data specifications should preserve both the origin and the first eligible observation time. Analysts should explain whether estimates describe time since origin or time since entry and identify the population represented. This prevents apparently comparable lifetime metrics from actually measuring different periods.

Check your understanding

Why is machine C excluded from the risk set at month four?

Answer: It does not enter observation until month five.

What changes if all machines are analyzed using exit minus entry?

Answer: The time scale becomes elapsed observed follow-up, which need not answer the original operating-age question.

Related terms

Time origin
Risk set
Survival analysis
delayed entry
left truncation
left censoring
person-time
right censoring
and selection bias

Learn next

draw individual observation timelines, construct risk sets at event times, and compare survival questions measured from origin with those conditioned on enrollment.

Sources

Sources: Harrell, Glossary of Statistical Terms, entry time: https://hbiostat.org/glossary/ . Therneau, survival package Surv documentation: https://www.stat.ethz.ch/R-manual/R-devel/library/survival/html/Surv.html . Therneau, A package for survival analysis in R: https://stat.ethz.ch/R-manual/R-devel/library/survival/doc/survival.pdf . The machine records and risk-set calculations are original.

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