Must every unit have the same calendar start date?

No; they can share a starting rule but begin on different dates.

Can the origin be changed?

Yes, but changing it may change the estimand and require rebuilding the analysis.

AI Glossary / Statistics and probability / Intermediate

Time origin

Definition

The time origin is the reference point from which elapsed time is measured in a study or analysis. In survival analysis it defines time zero for the event process of interest, such as installation, enrollment, or treatment assignment. Choosing the origin determines what a duration means and which units are eligible to contribute to each risk set.

What it means

A duration needs a starting point. Time until cancellation can mean time since registration, paid activation, or a later service change. These are different outcomes even when they end at the same cancellation date.
The time origin is also distinct from the date a unit first comes under observation. A device may be installed before monitoring begins, or a customer may enter a study after already using a product. The analysis should represent that difference rather than silently resetting the relevant history.

How it works

Begin with the question the study is intended to answer. For retention from paid activation, activation is a natural candidate origin. For comparing assigned interventions, align eligibility, assignment, and follow-up with the intended design.
Define the origin consistently across units. A common kind of event can occur on different calendar dates, so every unit can have its own origin date while sharing the same elapsed-time interpretation. This differs from studying events against one common calendar date.
Choose the time scale. Time since entry, chronological age, calendar time, and cumulative operating hours can each be appropriate for different processes. Changing the origin and changing the time scale are related but distinct decisions.
Calculate observed event or censoring times relative to the chosen origin. Retain the underlying dates and an explicit event indicator. Validate negative durations and check whether apparent inconsistencies reflect data errors or genuine observation before the analytical origin.
Represent delayed entry when observation starts after time zero. A unit observed only from elapsed time ten should not automatically be counted as under observation at elapsed time five. The analysis conditions on having remained eligible until entry, under appropriate assumptions.
Avoid defining groups using future information and then assigning their earlier event-free time to those groups without a valid design. For example, classifying people as long-term adopters based on later survival can create immortal-time or selection problems.
For changing exposures, record when the exposure changes instead of treating its eventual value as if known at baseline. A time-dependent exposure may require an analysis that updates risk-set membership or covariate values over follow-up.
State whether a reset is part of the question. Recurrent-event analyses may use time since the last event, while other analyses retain time since initial entry. These choices target different aspects of the event process and affect dependence between records.
Document the origin in figures and reports. An axis labeled months without saying since what can make otherwise correct results uninterpretable. Comparisons across cohorts require checking both elapsed duration and possible calendar-period changes.

Three practical examples

Retention analysis: measure time since paid activation rather than mixing registration and activation dates.
Equipment reliability: distinguish time since installation from time since monitoring software was enabled.
AI rollout evaluation: align the start of follow-up with the actual intervention and eligibility definition.

Think of it this way

Think of resetting a stopwatch. The displayed time depends on when the button was pressed. Two stopwatches can show different durations for the same finishing event because they started at different milestones; neither number is interpretable without its starting rule.

Worked example

Consider an original account history. Registration occurs on January 1, 2026, paid activation on January 11, and cancellation on February 1. Using elapsed calendar days, the registration-to-cancellation duration is 31 days. The activation-to-cancellation duration is 21 days.
Both calculations are correct, but they answer different questions. If the analysis concerns retention after paid activation, the 21-day duration is aligned with that origin. Combining it with 31-day durations from another system would mix definitions.
Now suppose a separate device is installed at elapsed day zero, first enters observation at day ten, and fails at day thirty. With installation as origin, its observed risk interval begins at ten and ends at thirty. It contributes twenty days of observed follow-up but has a failure age of thirty days.
Resetting its event age to twenty would instead describe time since observation entry. Whether that is appropriate depends on the question. A delayed-entry analysis using installation age must not count the device in observed risk sets before day ten.

Illustrative case study

Fictional case: Maple Devices compares failure rates across two service teams. One team's records start at installation, while the other's start at the first maintenance visit. The second team appears to have shorter lifetimes, partly because the clock starts later. Analysts reconstruct installation dates and explicitly represent delayed observation. They report the common time origin and explain remaining differences in which devices became observable, instead of treating the original durations as directly comparable.

Common misconceptions and mistakes

Do not confuse time origin with first observation or database entry. Equal recorded durations can represent different histories. Resetting the clock does not eliminate selection among units that survived until observation. Future exposure status should not be applied retrospectively without a valid method. A graph's calendar date axis and its time-since-entry axis answer different questions.

Business use

Use explicit time-origin definitions to make retention, reliability, and intervention analyses auditable. Agree on the starting milestone before combining datasets or comparing teams. Preserve entry and exit dates so analysts can distinguish complete follow-up, delayed entry, and exposure changes rather than relying on one unexplained duration column.

Check your understanding

How long is retention from paid activation in the account example?

Answer: Twenty-one days.

How long is it from registration?

Answer: Thirty-one days.

When does the device join observed risk sets on the installation-age scale?

Answer: At day ten, not day zero.

Related terms

Survival time
Risk set
delayed entry
left truncation
follow-up
immortal time bias
time-dependent covariate
recurrent events

Learn next

Study delayed-entry risk sets and the alignment of eligibility, assignment, and follow-up. Then compare analyses on age, calendar-time, and time-since-entry scales to see how their questions differ.

Sources

Harrell, Glossary of Statistical Terms: https://hbiostat.org/glossary/ Therneau, survival package vignette: https://cran.r-project.org/web/packages/survival/vignettes/survival.pdf The account dates and device observation example are original.

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